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Course Number: FIN 3403, Spring 2008

College/University: University of Florida

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Fundamentals of Financial Management Eleventh Edition Eugene F. Brigham University of Florida Joel F. Houston University of Florida Fundamentals of Financial Management, Eleventh Edition Eugene F. Brigham and Joel F. Houston VP/Editorial Director: Jack W. Calhoun Editor-in-Chief: Alex von Rosenberg Executive Editor: Michael R. Reynolds Senior Developmental Editor: Elizabeth R. Thomson Senior Production Project...

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of Fundamentals Financial Management Eleventh Edition Eugene F. Brigham University of Florida Joel F. Houston University of Florida Fundamentals of Financial Management, Eleventh Edition Eugene F. Brigham and Joel F. Houston VP/Editorial Director: Jack W. Calhoun Editor-in-Chief: Alex von Rosenberg Executive Editor: Michael R. Reynolds Senior Developmental Editor: Elizabeth R. Thomson Senior Production Project Manager: Deanna Quinn Senior Marketing Communications Manager: Jim Overly Senior Media Technology Editor: Vicky True Senior Technology Project Editor: Matthew McKinney Web Site Coordinator: Karen Schaffer Senior Print Buyer: Sandee Milewski Production House: Elm Street Publishing Services, Inc. Compositor: Lachina Publishing Services, Inc. Printer: R. R. Donnelley, Willard, OH Art Director: Bethany Casey Internal Designer: Stratton Design Cover Designer: Stratton Design Cover Illustration: Stratton Design Photography Manager: Deanna Ettinger Photo Researcher: Robin Samper COPYRIGHT 2007 Thomson South-Western, a part of The Thomson Corporation. Thomson, the Star logo, and South-Western are trademarks used herein under license. Printed in the United States of America 1 2 3 4 5 09 08 07 06 Student Edition: ISBN 0-324-31981-9 (book) ISBN 0-324-31980-0 (package) ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means-- graphic, electronic, or mechanical, including photocopying, recording, taping, Web distribution or information storage and retrieval systems, or in any other manner--without the written permission of the publisher. For permission to use material from this text or product, submit a request online at http:/ /www.thomsonrights.com Library of Congress Control Number: 2005908954 For more information about our products, contact us at: Thomson Learning Academic Resource Center 1-800-432-0563 Thomson Higher Education 5191 Natorp Boulevard Mason, OH 45040 USA PREFACE When the first edition of Fundamentals was published 28 years ago, we wanted to provide an introductory text that students would find interesting and understandable. Fundamentals immediately became the leading undergraduate finance text, and it has maintained that position ever since. Our goal with this edition has been to produce a book and ancillary package that will maintain its lead and set a new standard for finance textbooks. Important changes in the financial environment have occurred since the last edition. New technology and increased globalization continue to transform practices and markets. Continued improvements in communications and transportation have made it easier for businesses to operate on a worldwide basis--a company can be headquartered in New York; develop products in India; manufacture them in China; and sell them in the United States, Europe, and the rest of the world. This has led to major changes in the labor market, especially to an increase in outsourcing, which has resulted in generally lower consumer prices, but it has caused job losses for some U.S. workers and gains for others. There have also been dramatic rises and falls in the stock market, and interest rates have plunged to record lows even as energy prices hit historic highs. Corporate scandals have led to the downfall of such giants as Enron, WorldCom, and AT&T, and this has led to important changes in the laws governing corporate management and financial reporting, as well as to equally important changes in managerial compensation. These issues are discussed in this edition of Fundamentals, where we analyze them from financial and ethical perspectives. VALUATION FOCUS The primary goal of financial management is to help managers maximize their firms' values. Therefore, the concept of valuation underlies everything in Fundamentals. In Chapter 1 we discuss the concept of valuation and explain its dependency on future cash flows and risk, and we show why value maximization is good for society in general. We also discuss the importance of ethical conduct and the consequences of unethical behavior, which include ruined businesses, financial losses for investors, and jail terms for guilty managers. We also explain how incentive compensation, along with the threat of takeovers, can be used to motivate managers to act in the interests of both stockholders and society at large. The valuation theme is continued throughout the text. In Chapter 2, we take up the time value of money (TVM), a fundamental concept that underlies all of finance. The basic valuation equation as developed in Chapter 2 requires inputs--a set of cash flows in the numerator and a discount rate in the denominator. Therefore, in Chapters 3 and 4 we review basic accounting, including a discussion of cash flows and ways to analyze financial statements. Of course, values are not established in a vacuum--stock and bond values are determined in the financial markets, so an understanding of those markets and the way they operate is essential to anyone working in finance. Therefore, in Chapter 5, we discuss the major types of financial markets, the returns that investors have historically earned in those markets, and the risks inherent in different securities. We then cover, in Chapter 6, interest rates and the factors that influence them--risk, inflation, liquidity, and the supply of and demand for capital. This leads directly into a discussion of bonds and bond valuation, in iii iv Preface Chapter 7. Next, in Chapter 8, we discuss risk and returns in the stock market, beginning with the risk of a stock held in isolation and then moving on to the risk of stocks held in portfolios. We then explain, in Chapter 9, how common stocks are valued. With this background, in subsequent chapters we explain the financial tools and techniques managers use to help maximize their firms' values. Included are chapters on capital budgeting, the optimal capital structure, dividend policy, working capital, and financial forecasting. The final section of the book consists of four chapters that deal with derivatives, multinational finance, hybrid securities, and mergers. Our organization has four important advantages: Four important advantages of the Eleventh Edition's organization. 1. Covering TVM and valuation early helps students see how expected future cash flows, along with risk-adjusted discount rates, determine the value of the firm. Also, it takes time for students to digest TVM concepts and to learn how to do the required calculations, and providing this time is another benefit of early TVM coverage. 2. Structuring the book around markets and valuation enhances continuity and helps students see how the various topics are related to one another. 3. Most students--even those who do not plan to major in finance--are interested in stock and bond values, rates of return, and the like. Because the ability to learn is a function of individual interest and motivation, and because Fundamentals covers securities and security markets early, our organization is pedagogically sound. 4. Once the basic concepts have been established, it is easier for students to understand both how and why corporations make specific capital budgeting, financing, and working capital decisions. SIGNIFICANT CHANGES IN THE ELEVENTH EDITION A good working knowledge of finance is essential for success in business, regardless of one's specific job, because everything from marketing to human services is related to financial issues. This makes it important for anyone who plans to work in business to learn the fundamentals of finance. However, reading a finance text is different from reading a novel--one must focus on essential concepts and then work related problems to see how things tie together. For example, inflation affects interest rates, which affect stock and bond prices, which affect the feasibility of capital expenditures. To understand these relationships one must learn some basic principles and then work through problems to see how the various factors interact with one another. Students sometimes find finance relatively abstract, and they don't see its relevance to them. This makes it difficult for professors to get students to do the work necessary to see just how interesting and relevant it really is. Based on our own and others' teaching experiences, in this edition we took a number of steps to alleviate this problem: Increased student interest. Students learn a subject best if they find it interesting, so we need to get them excited about finance. To help here, we use examples that illustrate how successful corporations apply financial principles plus examples that show how firms sometimes go astray and fail. We also explain how financial concepts can help one make better personal decisions, ranging from choosing a job, to investing, to deciding whether to lease or buy a car. Preface v Provided clear explanations. Students justifiably become frustrated and lose interest if a subject is not explained clearly. We have always tried to provide a clear, well-written text, but in this edition we used computer technology to help us make significant improvements. First, the entire book was put on electronic files, which enabled us to edit and re-edit to get the writing as clear as possible. Second, we solved all of the numerical examples with Excel, and this helped us tweak the numbers to make the examples more clear and consistent. Third, we shifted sections around to improve the flow both within the chapters and from one chapter to the next. In total, these changes will help students learn more in less time, which will reduce their stress and thus increase their interest and comprehension. Provided timely within-chapter self-tests. Much of finance involves numerical problems, so students must learn a concept, then become familiar with formulas, and then learn how to apply the formulas to solve specific problems. In our earlier editions, we explained and illustrated the concepts within the chapters, then provided a set of end-of-chapter problems that students could use to practice and test their knowledge. Unfortunately, students learned the concepts and understood the examples when they read the text, but by the time they got to the end-of-chapter problems they had forgotten much and had to go back and re-read the text. With this edition, we provide questions and problems (with answers) immediately after each section, which permits students to work with the concepts while things are still fresh on their minds. Again, this facilitates the learning process. Ranked end-of-chapter problems by difficulty. In past editions we arranged the end-of-chapter problems by topic, not by difficulty level. Students would often start working the problems, hit a difficult one relatively quickly, become frustrated, and give up. In this edition we arranged the problems by difficulty, identifying the first set as "Easy" ones that most students should be able to work without too much trouble; then "Intermediate" problems that are a bit harder; and then "Challenging" problems that are longer, more complex, and will perhaps require some help from the instructor. This new setup again reduces students' stress and frustration. Improved the Test Bank. The Test Bank has been improved substantially, and many questions and problems that resemble the easy and intermediate endof-chapter problems have been added. Moreover, as discussed later in this Preface, many of the problems can be algorithmically modified to create an almost infinite number of alternative versions, with different answers, for a given problem. Different instructors have different views on the way students should be tested, but the new Test Bank and related testing material can be used to provide students with a set of relatively straightforward problems that deal with all aspects of financial management to help them study for the exams. They will then see that if they work hard and learn how to solve the various types of problems, they will have a good grasp of finance and, consequently, should do well on exams that consist primarily of straightforward (easy and intermediate) problems. Most instructors also use a few "challenging" exam problems, where students must figure out how to apply finance concepts to deal with new and different situations they haven't seen before. The "challenging" end-of-chapter problems are representative of this type of exam problem, and a number of them are provided in the Test Bank. Coordinated the text, problems, and Test Bank. Students should be rewarded for their efforts, and they become frustrated if they study hard, learn how to answer most of the problems in the text, and then face an exam where the problems are different from what they have been studying. To alleviate this problem, we have consciously coordinated the text examples, within-chapter vi Preface self-tests, end-of-chapter problems, and Test Bank questions and problems. If students read the text carefully and work the self-test problems, they should be able to work most of the easy end-of-chapter problems, which should prepare them for the intermediate problems, which should help with the challenging problems. Thus, students who work hard should do well on exams based on the Test Bank. Improved coverage of the time value of money. As noted earlier, the time value of money is the most important concept in finance, as it underlies stock and bond valuation, capital budgeting, cost of capital, lease analysis, and other key topics. However, students often have trouble grasping the basics of TVM, and this makes it almost impossible to do well in the course. To help alleviate this problem, we have taken the following steps: We moved TVM forward, from Chapter 6 to Chapter 2. This gives students time to digest TVM concepts before they must use them in the bond, stock, and capital budgeting chapters. As noted earlier, we added self-test problems, with solutions, at the end of each section. This helps students check their understanding of each type of problem before moving on. We explain the basic TVM functions using a five-step procedure: We show a time line setup, go through a numerical step-by-step solution, explain a formula that simplifies the step-by-step approach, explain how the formula is programmed into a calculator and how the inputs can be entered to solve the problem very efficiently, and then (as an optional exercise) show how the problem can be worked using Excel. This procedure helps students see exactly what each function does, understand the mathematics of the solution process, and see how calculators (and Excel) can be used to solve TVM problems. This procedure helps avoid the "black box" problem, where students get answers with a calculator but don't really know what's happening and consequently can't work problems that deviate from those whose solutions they have memorized. We also developed revised calculator tutorials for the most popular TI and HP calculators. The tutorial illustrations are identical to our withintext examples, so when a student reads about, say, the future value in the text, he or she can simultaneously learn from the tutorial how to find the FV with a calculator. Students tell us that learning how to use their calculators as they learn TVM concepts is much more efficient than studying the two separately. The TVM chapter introduces concepts covered in the bond, stock, and capital budgeting chapters, and this makes coverage of those chapters more efficient. For example, we illustrate the present values in the TVM chapter with the same cash flows that are later used in the bond, stock, and capital budgeting chapters, so in those later chapters we can refer students back to TVM for a quick refresher on the concept and solution technique. Clarified capital budgeting. This is another key concept, but again one that students have found difficult. In particular, they have trouble understanding the differences between ranking criteria such as the net present value and the internal rate of return methods. In this edition, we begin by discussing the NPV method, tie it back to the TVM chapter, explain why it's the best ranking criterion, and then explain how the other criteria supplement the NPV. This structure reduces confusion students had in the past and gives them a better understanding of capital budgeting. Reorganized the discussion of the financial environment. Chapter 4 in the last edition was too long to be covered in a reasonable length of time. In this edition, we divided the chapter into two segments, one on financial markets and Preface vii institutions and a second one that deals with interest rates and their determinants. The second chapter leads us into bond valuation. Streamlined the discussion of working capital. Current assets make up about half of the average firm's assets, and most students' first job after graduation is likely to deal with some aspect of working capital. However, this topic is often not covered in the introductory finance course, which means that nonfinance majors never cover it at all (and it may also be skipped in advanced finance courses). We concluded that our coverage was so long, detailed, and indeed boring that many instructors simply skipped it. We totally rewrote the working capital material and cover the key points in a logical and succinct manner. Reviewers unanimously agreed that the new chapter was considerably better than the two old ones, and two reviewers even said that they enjoyed reading the chapter! RELATIONSHIP TO OTHER THOMSON/SOUTH-WESTERN BOOKS The growing body of financial knowledge makes it impossible to include everything about financial management that one might desire in one textbook. This led Gene Brigham to coauthor two other texts that deal with materials that go beyond what can be covered in an introductory course. The first of these is a comprehensive book aimed primarily at MBAs, Financial Management: Theory and Practice, Eleventh Edition, coauthored with Michael C. Ehrhardt. The second is an upper-level undergraduate text, Intermediate Financial Management, Ninth Edition, coauthored with Phillip R. Daves. In addition, Brigham and Houston teamed up with Roy Crum to write a text focused on financial management in an international setting, Fundamentals of International Finance, published by Thomson in 2005. Also, some time ago a survey of professors indicated that some preferred a smaller, more streamlined text than Fundamentals. With that in mind, we created Fundamentals of Financial Management: Concise, which is 20 percent shorter than Fundamentals. Most of Concise's chapters are identical to the corresponding ones in Fundamentals, but Fundamentals includes an additional chapter on capital budgeting plus chapters on derivatives, hybrid securities, and mergers. Although Concise has been well received, there are two significant advantages to a more complete book such as Fundamentals: 1. Fundamentals provides professors with more flexibility in designing their courses. 2. Fundamentals is a more complete reference book for students to use after completing the course. This is especially important for nonfinance majors, who will not otherwise have access to materials that are covered in Fundamentals but are omitted from Concise. In this regard, it should be noted that the chapters in Fundamentals are written in a modular, self-contained format that makes it easy for students to read them on their own. INTENDED MARKET Fundamentals is intended for use in an introductory finance course. The key chapters can be covered in one term, but if it is supplemented with cases and perhaps some outside readings, the book can also be used for a two-term course. When it is covered in one term, instructors generally assign only selected chapters, leaving the others for students to examine on their own or use for reference viii Preface purposes in later courses and after graduation. Note also that the chapters are written in a flexible, modular format that helps instructors cover the material in whatever sequence they choose. ThomsonNOW: A NEW WEB-BASED COURSE RESOURCE PLATFORM ThomsonNOW is Thomson Publishing's new Web-based delivery system, and it contains items that were in the past provided on a CD. Since ThomsonNOW is Web based, it can be changed to reflect new developments and can also operate interactively to create an unlimited number of unique test questions. ThomsonNOW includes the following items, with more to be added over time: Test Bank The Test Bank for Fundamentals has been enhanced in several ways. Many new problems and questions have been added, and those new items are now contained in Part I of each Test Bank chapter, with Part II containing questions carried over from the old Test Bank. The problems and questions are categorized by difficulty, and more relatively short items suitable for quizzes and time-limited exams were added. Many of the problems are set up so that alternative versions can be algorithmically generated--one or more of the input parameters such as the interest rate or project cost is randomly changed and thus creates a similar problem but with a different answer. This feature enables an instructor to create unique exams and online quizzes ensure that each student does his or her own work. Practice Problems ThomsonNOW permits an instructor to generate sets of problems that can be used for Graded or ungraded homework Online or in-class quizzes. Practice sets for students to use as a study aid. With the very large number of problems in the new Test Bank and the algorithmic feature, a virtually unlimited number of unique problems can be generated. Conscientious students can then work many problems and learn how to deal with most finance issues, but they can't memorize answers to specific problems because each problem's answer may be unique. Excel Models A set of new and improved models that go through the calculations in most chapters, plus additional models tied to the end-of-chapter integrated cases, are also provided on ThomsonNOW. These models are used to generate some of the text exhibits, including those used in the capital budgeting chapters. While we do not assume that students know Excel, we do set the models up so that those familiar with spreadsheets can get a better feel for how they are used in practice. We also provide, in the end-of-chapter materials for most chapters, an integrated spreadsheet problem with a model accessible from ThomsonNOW that does an Preface ix analysis similar to that in the chapter, including data tables and graphs that give insights into the sensitivity of key outputs to input changes. Thomson ONE--Business School Edition I/B/E/S Consensus Estimates. Includes consensus estimates--averages, means, and medians; analyst-by-analyst earnings coverage; analysts' forecasts based on 15 industry standard measures; current and historic coverage for the selected 500 companies. Current history is five years forward and historic history is from 1976 for U.S. companies and 1987 for international companies; current data are updated daily, and historic are updated monthly. Worldscope. Includes company profiles, financials, and accounting results and market per-share data for the selected 500 companies; annual information and monthly prices going back to 1980, all updated daily. Disclosure SEC Database. Includes company profiles, annual and quarterly company financials, pricing information, and earnings estimates for selected U.S. and Canadian companies: annually from 1987, quarterly data rolling 10 years, and monthly pricing--all updated weekly. DataStream Pricing. Daily international pricing, including share price (open, high, low, close, P/E), index, and exchange rate data. History is rolling 10 years. ILX Systems Delayed Quotes. Includes 20-minute delayed quotes of equities and indices from U.S. and global tickers covering 130 exchanges in 25 developed countries. Comtex Real-Time News. Includes current news releases. SEC Edgar Filings and Global Image Source Filings. Includes regulatory and nonregulatory filings for both corporate and individual entities. Edgar filings are real-time and go back 10 years; image filings are updated daily and go back 7 years. OTHER FEATURES OF THE ELEVENTH EDITION Recent Financial Events The past few years have witnessed great turmoil in the financial markets. We have seen an incredible rise and fall of the stock market and the stunning collapses of Enron, WorldCom, Arthur Andersen, and others. Some of these problems were caused by fraud and questionable accounting practices, which, in turn, stemmed largely from badly designed executive compensation programs. As we discuss in Chapter 1, the focus of many top executives shifted from maximizing their firms' long-run stock prices to maximizing prices on the day the executives' own stock options vested and could be sold. We consider the effects of this shift in focus, and ways to move the focus back to the long run and thus to benefit all parties, not just executives with stock options. We also updated Chapters 6, 7, 8, and 9 to reflect the many changes that have occurred in the stock and bond markets since the last edition. We also restructured these chapters to improve the flow, and we streamlined the coverage of yield curves. Revised Treatment of Financial Statements In the wake of the corporate scandals, we have taken steps to enhance our discussion of financial statements and accounting-related issues. In Chapter 3, we continue our emphasis on cash flow, and we expanded our discussion of the x Preface differences between net income, net cash flow, and free cash flow. We also streamlined the discussion of taxes, focusing on the major tax issues facing investors and corporations but leaving many details for a Web Appendix, which can be found on ThomsonNOW. Reworked Section on Market Efficiency and Behavioral Finance The events surrounding the stock market bubble have led many to reevaluate the efficiency of financial markets, which, in turn, generated new academic research in the area of behavioral finance. While most authorities still believe that market efficiency is a cornerstone of finance, market efficiency does have limitations. Consequently, we discuss the evidence regarding the extent of stock market efficiency, along with the implications of behavioral finance. Web Appendixes To make room for important new materials and to streamline the book, we moved certain interesting but secondary material to appendixes available through ThomsonNOW. References to these appendixes are provided in the relevant text chapters. Streamlined Discussion of the Time Value of Money As noted earlier, we took several steps to increase the readability of this critically important chapter. First, we moved it from Chapter 6 to Chapter 2 to give students more time to digest it before using it in the bond, stock, and capital budgeting chapters. We also added end-of-section self-tests to ensure that students can work with the function that was just discussed before moving on to the next one, and we provide (on ThomsonNOW) tutorials on the most popular calculators to help in this regard. The new setup helps students understand the fundamental issues in TVM and work problems efficiently, but without falling into the "black box trap" of knowing how to work specific problems but not understanding concepts well enough to deal with problems that are structured somewhat differently. Changes in the Working Capital Chapter As noted earlier, we totally rewrote the working capital material, reducing it from two chapters to one to cover the key points in a logical and succinct manner. Reviewers unanimously agreed that the new chapter was considerably better than the two old ones. A quote from one reviewer summarizes their conclusions: I like the abbreviated one-chapter approach. I looked at the old Tenth Edition chapter again, and I like the new one much better--it is more readable than the original two chapters, and I actually enjoyed reading it. The two-chapter approach provided too much extraneous and confusing information. The new and more concise presentation gives introductory students exactly what they need. Also, the new chapter is so much better than the previous two that I could assign it to students to read and learn on their own. I would, however, cover the cash budget in class because that is a bit more complicated, but even cash budgeting is much better presented here. Another reviewer stated that he has been skipping working capital in his class because, as it was presented, it would take too long to cover it, but that he planned to cover the chapter in its new format. We expect others to agree. Preface xi Analyzing Financial Decisions with Spreadsheets We developed spreadsheet models for each chapter in the book except Chapters 1 and 5. Spreadsheet programs are ideally suited for analyzing many financial issues, and a knowledge of spreadsheets is rapidly becoming essential for people in business. Therefore, we indicate how spreadsheets are used to deal with the issues discussed in the text. However, we recognize that students need to understand basic finance concepts before going into computer modeling. Therefore, in the text chapters, we discuss finance concepts, provide examples, and explain how the concepts are used in the decision process. Where the analysis involves arithmetic, we assume that students are using calculators. However, if the problem is one that could be solved more efficiently with a computer, we briefly describe how the computer would be used. These explanations are short, easy to follow, and can be skipped without loss of continuity. Thus, students get an idea of how they could go from calculators to spreadsheets, but they don't need to take that step. However, if an instructor wants to emphasize computers in the course, or if an individual student wants to learn more about spreadsheets on his or her own, the spreadsheet models available from ThomsonNOW make that relatively easy. Also, we provide on ThomsonNOW an Excel tutorial that explains the functions and procedures used in the models. The tutorial has an index that makes it relatively easy to find information about each function and feature, and students can use the models and tutorial to learn Excel on their own. xii Preface CONTENTS Part I Chapter 1 Introduction to Financial Management An Overview of Financial Management Significantly revised and improved. New vignette, "Striking the Right Balance," discusses trade-off of maximizing shareholder value and making decisions that benefit society. Chapter emphasizes value orientation with discussion of relationship among shareholder value, intrinsic values, and stock prices. Enhanced and expanded discussion of business ethics. New boxes: "Is Shareholder Wealth Maximization a World-Wide Goal?"; "Protection for Whistle-Blowers." Improved! Moved from Chapter 6 to Chapter 2 to allow students more time to grasp the concepts. Discussion made clearer, takes less of a "black-box" approach; formulas are given. Added section, "Finding Annuity Payments, Periods, and Interest Rates." New boxes: "Simple versus Compound Interest"; "Hints on Using Financial Calculators." Improved! New Figure 3-1 diagrams a typical balance sheet to aid students with the discussion. Reorganized chapter so cash flow discussion immediately follows income statement and precedes cash flow statement discussions. "Uses and Limitations of Financial Statements" section moved so it precedes discussion on "Modifying Accounting Data for Investor and Managerial Decisions." MVA and EVA discussion shortened; not as computationally oriented. Updated tax discussion. New box: "Massaging the Cash Flow Statement." Updated vignette. Improved financial leverage discussion in "Debt Management Ratios" section. Updated Table 4-3. New box: "Global Perspectives: Global Accounting Standards: Can One Size Fit All?" Created from dividing Tenth Edition Chapter 4 into two separate chapters. New vignette: "A Strong Financial System Is Necessary for a Growing and Prosperous Economy." Reorganized to present overview of capital allocation process before discussing financial markets and institutions. Brought in discussions on "Market for Common Stock," "Stock Markets and Returns," and "Stock Market Efficiency" from old Stock chapter for better integration. Updated Tables 5-1, 5-2, and 5-3. Added discussion of hedge funds. Updated "Measuring the Market" box. New boxes: "Citigroup Built to Compete in a Changing Environment"; "The NYSE and Nasdaq Combine Forces with the Leading Online Trading Systems"; "A Closer Look at Behavioral Finance Theory." New chapter created from dividing Tenth Edition Chapter 4 into two separate chapters. Vignette highlights the discussion presented in chapter, "Low Interest Rates Encourage Investment and Stimulate Consumer Spending." All figures updated to show current economic situation. Rewrote and clarified section, "Using the Yield Curve to Estimate Future Interest Rates." Reorganized so that discussion of "Other Factors That Influence Interest Rate Levels" immediately follows the section on "Using the Yield Curve to Estimate Future Interest Rates." Updated boxes: "An Almost Riskless Treasury Security Bond" and "Global Perspectives: Measuring Country Risk." New box: "The Links between Expected Inflation and Interest Rates: A Closer Look." Improved! Reorganized chapter so that bond valuation and then bond yields are discussed before the section on "Changes in Bond Values over Time." Added Table 7-1 to clarify discussion of changes in bond values. Reduced discussion of bankruptcy and reorganization (which is in Web Appendix) and enhanced discussion of bond markets. Improved! Moved chapter to immediately precede chapter on stocks to help integrate concepts. Moved extensive footnote in prior edition on using historical data to measure risk into text. Updated box, "The Trade-Off between Risk and Return." Revised Figure 8-7 so partial correlation between stocks coincides with recent studies (0.35 vs. 0.67). Added new section, "Some Concluding Thoughts: Implications for Corporate Managers and Investors." Improved! New vignette, "Searching for the Right Stock." Moved market, returns, and efficient markets discussion to new Chapter 5 to allow for almost immediate discussion on stock valuation. Enhanced discussion of corporate valuation model. Improved! Enhanced discussion on the overview of the WACC along with new Figure 10-1, which is meant to improve students' understanding of different types of capital. WACC equation presented early in the chapter, followed by discussion of the individual cost components and their calculations. Added second-level headings in "Cost of New Common Stock" to clarify the discussion. Eliminated duplication of project risk discussion, which has now been moved to Chapter 12--where it fits better. Improved! New vignette, "Competition in the Aircraft Industry," details the chapter's concepts. Reorganized chapter discussion so NPV discussion appears early and is stressed as the best capital budgeting decision rule. Added discussion section, "Decision Criteria Used in Practice." Part II Chapter 2 Chapter 3 Fundamental Concepts in Financial Management Time Value of Money Financial Statements, Cash Flow, and Taxes Analysis of Financial Statements Chapter 4 Chapter 5 Financial Markets and Institutions Part III Chapter 6 Chapter 7 Chapter 8 Chapter 9 Financial Assets Interest Rates Bonds and Their Valuation Risk and Rates of Return Stocks and Their Valuation Part IV Investing in Long-Term Assets: Capital Budgeting Chapter 10 The Cost of Capital Chapter 11 The Basics of Capital Budgeting Preface xiii Chapter 12 Cash Flow Estimation and Risk Analysis Chapter 13 Other Topics in Capital Budgeting Improved! Chapter begins with a fairly extensive capital budgeting illustration as an overview and lead-in to discussing capital budgeting concepts. Chapter then proceeds with other capital budgeting details, allowing professors to get the general idea of capital budgeting analysis across without having to cover the entire chapter (which was the case in the prior edition). Improved! Reorganized to present real options discussion early. Mutually exclusive projects with unequal lives (both replacement chain and EAA approaches) then discussed. Part V Capital Structure and Dividend Policy Updated vignette on Kellogg Co. and Table 14-4. Clarified illustration and chapter discussion of concepts. Improved! New vignette, "Microsoft Shifts Gears and Begins to Unload Part of Its Vast Cash Hoard," illustrates a recent event that ties in with chapter concepts. Improved discussion of dividend theories for recent tax changes. Enhanced discussion of investor preferences for dividends versus capital gains. Eliminated dividend stability section. Updated box, "Global Perspectives: Dividend Yields Around the World." New box: "Stock Repurchases Soar in 2004." Chapter 14 Capital Structure and Leverage Chapter 15 Distributions to Shareholders: Dividends and Share Repurchases Part VI Working Capital and Financial Forecasting Improved! Combined two chapters into one. Presented overview of working capital management by discussing cash conversion cycle and current asset investment and financing policies. Chapter also discusses some of the more important accounts in greater detail, such as cash (including cash budgeting) and marketable securities, accounts receivable, accounts payable, bank loans, and accrued liabilities. Improved! New vignette, "Forecasting Apple's Future." Rather than focusing on the "mechanics" of forecasting, the presentation stresses understanding the concepts involved. The AFN equation is presented earlier in the chapter to help students understand the concepts involved. Enhanced discussion with use of spreadsheets, regression analysis, and individual ratios in forecasting process. Chapter 16 Working Capital Management Chapter 17 Financial Planning and Forecasting Part VII Special Topics in Financial Management Chapter 18 Derivatives and Risk Management Chapter 19 Multinational Financial Management Reconstructed Table 18-1 to use real numbers developed from data available on the Internet. Added Web address to tell students where to obtain call and put option data. Rewrote box, "Expensing Executive Stock Options," to incorporate the new stock option accounting rule. Reworked OPM illustration and Table 18-2 for a much lower, more current risk-free rate. Revised "Forward and Futures Contracts" section to incorporate hedging example with futures all within same section. "Other Types of Derivatives" section excludes forward and futures and includes only swaps, structured notes, and inverse floater. New box: "Credit Instruments Create New Opportunities and Risks." Improved! Reorganized chapter to present discussion of international monetary system, terminology, and current monetary arrangements early. Exchange rates and cross rates are presented next. Enhanced discussion of international money and capital markets. Updated boxes: "Hungry for a Big Mac? Go to China!" and "Stock Market Indices Around the World." Generally clarified sections for students. Generally updated chapter for new mergers/acquisitions. New vignette about Procter & Gamble merger. Updated Table 21-2 for recent larger mergers. Reworked merger illustration for a lower, more current cost of equity number. Updated "Financial Reporting for Mergers" to exclude pooling method for mergers. New boxes: "Tempest in a Teapot"; "The Track Record of Recent Large Mergers." Chapter 20 Hybrid Financing: Preferred Stock, Leasing, Warrants, and Convertibles Chapter 21 Mergers and Acquisitions xiv Preface THE INSTRUCTIONAL PACKAGE: AN INTEGRATED SYSTEM Fundamentals offers an innovative, technologically advanced ancillary package to enhance students' learning and to make it easier for instructors to prepare for and conduct classes. The integrated package includes many outstanding resources, all of which have been revised and updated for the new Eleventh Edition. Essential Course Management Tools for the Instructor Spreadsheet Models for Integrated Cases--The spreadsheet models were designed to illustrate spreadsheet applications to finance concepts using integrated case data. They can be found on the Instructor's Resource Web site on ThomsonNOW at http://now.swlearning.com/brigham. Instructors' Resources CD-ROM--The new instructor resource system includes electronic versions of the Instructor's Manual, a Word and electronic version of the Test Bank, spreadsheet models, solutions to spreadsheet problems, and PowerPoint presentations. It is laid out to maximize accessibility and minimize search time. Fundamentals of Financial Management Online Course--Delivered via the WebTutor platform, this integrated Web-based learning environment accompanies the textbook and ancillary package with the vast resources of the Internet and the convenience of anytime learning. Extremely user friendly, the powerful customization features of the WebTutor framework enable instructors to customize this online course to their own unique teaching styles and their students' individual needs. Course features include content keyed to the Eleventh Edition, self-tests and online exams, Internet activities and links to related resources, a suggested course syllabus, student and instructor materials, free technical support for instructors, and much more. Available for both Blackboard and WebCT platforms. Instructor's Manual--This comprehensive manual contains answers to all text questions and problems plus detailed solutions to the integrated cases. A computerized version in Word is also available on the Instructor's Resource Web site on ThomsonNOW at http://now.swlearning.com/ brigham. This digital version of the Instructor's Manual is available for posting on a secure, instructor's password-protected Web site. PowerPoint Lecture Presentation--Prepared in PowerPoint, this slide show covers all the essential issues presented in each chapter. Graphs, tables, lists, and calculations are developed sequentially, much as one might develop them on a blackboard. The new and improved slides are even more crisp, colorful, and professor-friendly. Instructors can, of course, modify or delete our slides, or add some of their own. The PowerPoint slide can be found in the Instructor's Resource section of ThomsonNOW at http://now .swlearning.com/brigham. Test Bank--The revised and enhanced large Test Bank contains more than 1,500 class-tested questions and problems, is now broken into two parts, and is available both in print and electronic form. Part I has all new or substantially revised questions and problems, and Part II contains holdover items from the previous Test Bank. Many of the problems in Part I can be algorithmically modified in ThomsonNOW, which enables instructors to create an almost unlimited number of unique problems. Information regard- Preface xv ing the topics, degree of difficulty, and the correct answers, along with complete solutions for all numerical problems, is provided with each question. A version of the Test Bank in Word is also available to instructors for downloading. ThomsonNOW--ThomsonNOW has many features that make test preparation, scoring, and grade recording easy. In addition, questions can be altered to make different versions of a given test, and the software makes it easy to add to or edit the existing test items, or to compile a test that covers specific topics. Technology Supplement--The Technology Supplement contains tutorials for four commonly used financial calculators, for Excel, and for PowerPoint presentation software. The calculator tutorials cover everything a student needs to know about the calculator to work the problems in the text. NewsWire: Finance in the News--Adopters of Fundamentals will have access to a password-protected portion of the South-Western Finance Web site, where they will be provided with summaries of recent articles in The Wall Street Journal, BusinessWeek, or other major business publications, along with discussion questions and references to the text. These summaries, written by Emery Trahan and Paul Bolster of Northeastern University, facilitate incorporating late-breaking news into classroom discussions. Superior Student Ancillary Package ThomsonNOW--http://now.swlearning.com/brigham. ThomsonNOW is Thomson Publishing's new Web-based delivery system, and ThomsonNOW contains items that were in the past provided on a CD. Because ThomsonNOW is Web based, it can be changed to reflect new developments and also to operate interactively. ThomsonNOW provides students with the following robust set of additional online learning tools, with more to be added over time: PowerPoint Lecture Presentation--The slide show covers all the essential issues presented in each chapter and follows the end-of-chapter Integrated Case. E-Lectures--Difficult concepts from each chapter are explained and illustrated via streaming video and animated tutorials. These video clips and tutorials can be extremely helpful review and clarification tools if you have trouble understanding an in-class lecture or if you are more of a visual learner who sometimes has difficulty grasping concepts as they are presented in the text. Introductory Video and Ask the Author Video--Introductory video pieces, as illustrated by text coauthor Eugene F. Brigham, set the tone for the study of each chapter. These streaming video clips provide context for the forthcoming reading and exercises. Upon finishing a chapter, they may be used as excellent review tools for summarizing key points and major concepts. In the Ask the Author video, difficult concepts and frequently asked questions from each chapter are explained and illustrated by the textbook coauthor, Joel F. Houston. These video clips can be extremely helpful review and clarification tools if you have trouble understanding an in-class lecture or if you are a visual learner. Online Homework and Additional Quizzing and Testing--In addition to including online access to the end of chapter problem material, ThomsonNOW offers an opportunity to practice for midterms and finals by taking online quizzes that span multiple chapters. xvi Preface The Problem Bank--The Problem Bank: Practice Problems for Financial Management has been revised to fit specifically with this text and contains more than 400 multiple-choice finance problems with solutions, divided into seven major categories such as time value of money, capital budgeting, and risk and return. Solving these problems requires the use of a financial calculator (general calculator keystrokes also are provided) and is intended to supplement the text's end-of-chapter problems, thereby providing additional practice for students in their preparation of homework assignments and for exams. Spreadsheet Models--ThomsonNOW also contains spreadsheet models that illustrate how concepts covered in the text are implemented in the real world, giving students a significant advantage in the job market. The models include thorough explanations and serve both as an Excel tutorial and as a template for solving financial problems for each chapter of the book. Thomson ONE--Business School Edition--Use the Thomson ONE Academic online database to work a chapter's Thomson ONE--Business School Edition problem. Thomson ONE--Business School Edition, a product from Thomson Financial, combines a full range of fundamental financials, earnings estimates, market data, and source documents for hundreds of real-world companies. This is your opportunity to access and apply the industry's most reliable information to answer the discussion questions and work through group projects. Study Guide--This supplement lists the key learning objectives for each chapter, outlines the key sections, provides self-test questions, and provides a set of problems similar to those in the text and the Test Bank, but with fully worked-out solutions. Spreadsheet Books--Thomson/South-Western has published several books on spreadsheets, including Financial Analysis with Microsoft Excel, Third Edition. Effective Use of a Financial Calculator--Written by Pamela Hall, this handbook is designed to help increase students' understanding of both finance and financial calculators, enabling them to work problems more quickly and effectively. ACKNOWLEDGMENTS This textbook reflects the efforts of a great many people, both those who have worked on Fundamentals and our related books over a number of years, as well as those who worked specifically on this Eleventh Edition. First, we would like to thank Dana Aberwald Clark, who worked closely with us at every stage of the revision--her assistance was absolutely invaluable. Second, Christopher Buzzard did an outstanding job helping us develop the Excel models, the Web site, and the PowerPoint presentations. Our colleagues Roy Crum, Andy Naranjo, M. Nimalendran, Jay Ritter, Mike Ryngaert, Craig Tapley, and Carolyn Takeda gave us many useful suggestions regarding the ancillaries and many parts of the book, including the integrated cases. Also, we benefited from the work of Mike Ehrhardt and Phillip Daves of the University of Tennessee, and Roy Crum of the University of Florida, who worked with us on companion books. Next, we would like to thank the following professors, who reviewed this edition in detail and provided many useful comments and suggestions: Deb Bauer, University of Oregon Mary R. Brown, University of Illinois, Chicago Michael J. Highfield, Louisiana Tech University Preface xvii James Keys, Florida International University Shady Kholdy, California State University, Pomona Karyl Leggio, University of Missouri at Kansas City Adam Y. C. Lei, Louisiana State University Rabih Moussawi, The University of TexasDallas John Wald, Rutgers University Mark D. Walker, North Carolina State University Kenneth Williams, Davenport University Michael Yest, Tulane University We would also like to thank the following professors, whose reviews and comments on our earlier books have contributed to this edition: Robert Adams, Mike Adler, Sharif Ahkam, Syed Ahmad, Ed Altman, Bruce Anderson, Ron Anderson, Tom Anderson, John Andrews, Bob Angell, Vince Apilado, Harvey Arbalaez, Kavous Ardalan, Henry Arnold, Bob Aubey, Gil Babcock, Peter Bacon, Kent Baker, Robert Balik, Tom Bankston, Babu Baradwaj, Les Barenbaum, Charles Barngrover, Sam Basu, Greg Bauer, Bill Beedles, Brian Belt, Moshe Ben-Horim, Gary Benesh, Bill Beranek, Tom Berry, Will Bertin, Scott Besley, Dan Best, Roger Bey, Gilbert W. Bickum, Dalton Bigbee, John Bildersee, Laurence E. Blose, Russ Boisjoly, Bob Boldin, Keith Boles, Michael Bond, Geof Booth, Waldo Born, Rick Boulware, Kenneth Boudreaux, Helen Bowers, Oswald Bowlin, Don Boyd, G. Michael Boyd, Pat Boyer, Joe Brandt, Elizabeth Brannigan, Mary Broske, David T. Brown, Christopher Brown, Kate Brown, Larry Brown, Bill Brueggeman, Paul Bursik, Bill Campsey, Bob Carlson, Severin Carlson, David Cary, Steve Celec, Mary Chaffin, Charles Chan, Don Chance, Antony Chang, Susan Chaplinsky, K. C. Chen, Jay Choi, S. K. Choudhary, Lal Chugh, Maclyn Clouse, Bruce Collins, Mitch Conover, Margaret Considine, Phil Cooley, Joe Copeland, David Cordell, Marsha Cornett, M. P. Corrigan, John Cotner, Charles Cox, David Crary, John Crockett, Jr., Brent Dalrymple, Bill Damon, Morris Danielson, Joel Dauten, Steve Dawson, Sankar De, Fred Dellva, Chad Denson, James Desreumaux, Bodie Dickerson, Bernard Dill, Gregg Dimkoff, Les Dlabay, James D'Mello, Mark Dorfman, Tom Downs, Frank Draper, Gene Drzycimski, Dean Dudley, David Durst, Ed Dyl, Fred J. Ebeid, Daniel Ebels, Richard Edelman, Charles Edwards, U. Elike, John Ellis, George Engler, Suzanne Erickson, Dave Ewert, John Ezzell, L. Franklin Fant, Richard J. Fendler, Michael Ferri, Jim Filkins, John Finnerty, Robert Fiore, Susan Fischer, Peggy Fletcher, Steven Flint, Russ Fogler, Jennifer Frazier, Dan French, Michael Garlington, David Garraty, Sharon Garrison, Jim Garven, Adam Gehr, Jr., Jim Gentry, Wafica Ghoul, Armand Gilinsky, Jr., Philip Glasgo, Rudyard Goode, Raymond Gorman, Walt Goulet, Bernie Grablowsky, Theoharry Grammatikos, Owen Gregory, Ed Grossnickle, John Groth, Alan Grunewald, Manak Gupta, Darryl Gurley, Sam Hadaway, Don Hakala, Gerald Hamsmith, William Hardin, John Harris, Paul Hastings, Bob Haugen, Steve Hawke, Stevenson Hawkey, Del Hawley, Eric M. Haye, Robert Hehre, Kath Henebry, David Heskel, George Hettenhouse, Hans Heymann, Kendall Hill, Roger Hill, Tom Hindelang, Linda Hittle, Ralph Hocking, J. Ronald Hoffmeister, Robert Hollinger, Jim Horrigan, John Houston, John Howe, Keith Howe, Steve Isberg, Jim Jackson, Vahan Janjigian, Narayanan Jayaraman, Zhenhn Jin, Kose John, Craig Johnson, Keith Johnson, Ramon Johnson, Ray Jones, Frank Jordan, Manuel Jose, Sally Joyner, Alfred Kahl, Gus Kalogeras, Rajiv Kalra, Ravi Kamath, John Kaminarides, Michael Keenan, Bill Kennedy, Peppi M. Kenny, Carol Kiefer, Joe Kiernan, Richard Kish, Robert Kleiman, Erich Knehans, Don Knight, Ladd Kochman, Dorothy Koehl, Jaroslaw Komarynsky, Duncan Kretovich, Harold Krogh, Charles Kroncke, Don Kummer, Robert A. Kunkel, Reinhold Lamb, Joan Lamm, Larry Lang, David Lange, P. Lange, Howard Lanser, Edward Lawrence, Martin Lawrence, Wayne Lee, Jim LePage, David E. LeTourneau, Jules Levine, John Lewis, Jason Lin, Chuck Linke, Bill Lloyd, Susan Long, Judy Maese, Bob Magee, Ileen Malitz, Bob Malko, Phil Malone, Abbas Mamoozadeh, Terry Maness, Chris Manning, Surendra Mansinghka, Timothy Manuel, Brian Maris, Terry Martell, David Martin, D. J. Masson, John Mathys, Ralph May, John McAlhany, Andy McCollough, Ambrose McCoy, Thomas McCue, Bill McDaniel, John McDowell, Charles McKinney, Robyn McLaughlin, James McNulty, Jeanette MedewitzDiamond, Jamshid Mehran, Larry Merville, Rick Meyer, Jim Millar, Ed Miller, John Miller, John Mitchell, Carol Moerdyk, Bob Moore, Scott Moore, Barry Morris, Gene Morris, Dianne R. Morrison, Chris Muscarella, David Nachman, Tim Nantell, Don Nast, Edward Nelling, Bill Nelson, Bob Nelson, William Nelson, Bob Niendorf, Bruce Niendorf, Ben xviii Preface Nonnally, Jr., Tom O'Brien, William O'Connell, Dennis O'Connor, John O'Donnell, Jim Olsen, Robert Olsen, Dean Olson, Jim Pappas, Stephen Parrish, Helen Pawlowski, Barron Peake, Michael Pescow, Glenn Petry, Jim Pettijohn, Rich Pettit, Dick Pettway, Aaron Phillips, Hugo Phillips, H. R. Pickett, John Pinkerton, Gerald Pogue, Eugene Poindexter, R. Potter, Franklin Potts, R. Powell, Dianna Preece, Chris Prestopino, John Primus, Jerry Prock, Howard Puckett, Herbert Quigley, George Racette, Bob Radcliffe, Allen Rappaport, Bill Rentz, Ken Riener, Charles Rini, John Ritchie, Bill Rives, Pietra Rivoli, Antonio Rodriguez, James Rosenfeld, Stuart Rosenstein, E. N. Roussakis, Dexter Rowell, Marjorie Rubash, Bob Ryan, Jim Sachlis, Abdul Sadik, Travis Sapp, Thomas Scampini, Kevin Scanlon, Frederick Schadeler, Patricia L. Schaeff, David Schalow, Mary Jane Scheuer, David Schirm, Robert Schwebach, Carol Schweser, John Settle, Alan Severn, James Sfiridis, Sol Shalit, Frederic Shipley, Dilip Shome, Ron Shrieves, Neil Sicherman, J. B. Silvers, Clay Singleton, Joe Sinkey, Stacy Sirmans, Jaye Smith, Patricia Smith, Patricia Matisz Smith, Don Sorensen, David Speairs, Ken Stanley, Ed Stendardi, Alan Stephens, Don Stevens, Jerry Stevens, Glen Strasburg, David Suk, Katherine Sullivan, Timothy Sullivan, Philip Swensen, Bruce Swenson, Ernest Swift, Paul Swink, Eugene Swinnerton, Gary Tallman, Dular Talukdar, Dennis Tanner, Russ Taussig, Richard Teweles, Ted Teweles, Madeline Thimmes, Francis D. Thomas, Andrew Thompson, John Thompson, Arlene Thurman, Dogan Tirtirogu, Janet Todd, Holland J. Toles, William Tozer, Emery Trahan, George Trivoli, George Tsetsekos, David Upton, Howard Van Auken, Pretorious Van den Dool, Pieter Vandenberg, Paul Vanderheiden, David Vang, JoAnn Vaughan, Jim Verbrugge, Patrick Vincent, Steve Vinson, Susan Visscher, John Wachowicz, Joe Walker, Mike Walker, Sam Weaver, Marsha Weber, Al Webster, Shelton Weeks, Kuo-Chiang Wei, Bill Welch, Fred Weston, Richard Whiston, Norm Williams, Tony Wingler, Ed Wolfe, Criss Woodruff, Don Woods, Robert Wyatt, Steve Wyatt, Michael Yonan, John Zietlow, Dennis Zocco, and Kent Zumwalt. Special thanks are due to Chris Barry, Texas Christian University, and Shirley Love, Idaho State University, who wrote many of the boxes relating to small-business issues that are on the Web; to Steven Bouchard, Goldey Beacom College, who helped develop the Cyberproblems; to Emery Trahan and Paul Bolster, Northeastern University, who developed and wrote the summaries and questions for NewsWire; to Dilip Shome, Virginia Polytechnic Institute, who helped greatly with the capital structure chapter; to Dave Brown and Mike Ryngaert, University of Florida, who helped us with the bankruptcy and merger material; to Roy Crum, Andy Naranjo, and Subu Venkataraman, who worked with us on the international materials; to Scott Below, East Carolina University, who developed the Web site information and references; to Laurie and Stan Eakins of East Carolina, who developed the materials on Excel for the Technology Supplement; and to Larry Wolken, Texas A&M University, who offered his hard work and advice for the development of the Lecture Presentation Software. Susan Whitman typed the various manuscripts, and she and Allison Smith helped proof them. Finally, the South-Western and Elm Street Publishing Services staffs, especially Sue Nodine, Elizabeth Thomson, Mike Reynolds, Deanna Quinn, Vicky True, John Barans, Matthew McKinney, Karen Schaffer, Tom Grega, and Alex von Rosenberg, helped greatly with all phases of the textbook's development and production. ERRORS IN THE TEXTBOOK At this point, most authors make a statement like this: "We appreciate all the help we received from the people listed above, but any remaining errors are, of course, our own responsibility." And generally there are more than enough remaining errors! Having experienced difficulties with errors ourselves, both as students and instructors, we resolved to avoid this problem in Fundamentals. As a result of our detection procedures, we are convinced that this book is relatively free of significant errors, meaning those that either confuse or distract readers. Preface xix Partly because of our confidence that few such errors remain, but primarily because we want very much to detect any errors that may have slipped by to correct them in subsequent printings, we decided to offer a reward of $10 per error to the first person who reports it to us. For purpose of this reward, errors are defined as misspelled words, nonrounding numerical errors, incorrect statements, and any other error that inhibits comprehension. Typesetting problems such as irregular spacing and differences of opinion regarding grammatical or punctuation conventions do not qualify for this reward. Given the ever-changing nature of the World Wide Web, changes in Web addresses also do not qualify as errors, although we would like to learn about them. Finally, any qualifying error that has follow-through effects is counted as two errors only. Please report any errors to Joel Houston either through e-mail at fundamentals@joelhouston.com or by regular mail at the address below. CONCLUSION Finance is, in a real sense, the cornerstone of the enterprise system--good financial management is vitally important to the economic health of business firms, hence to the nation and the world. Because of its importance, finance should be widely and thoroughly understood, but this is easier said than done. The field is relatively complex, and it is undergoing constant change in response to shifts in economic conditions. All of this makes finance stimulating and exciting, but also challenging and sometimes perplexing. We sincerely hope that this Eleventh Edition of Fundamentals will meet its own challenge by contributing to a better understanding of our financial system. EUGENE F. BRIGHAM JOEL F. HOUSTON 4723 N.W. 53rd Ave., Suite A Gainesville, Florida 32606-4399 December 2005 BRIEF CONTENTS Preface Part 1 Chapter 1 iii 1 2 Introduction to Financial Management An Overview of Financial Management Part 2 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Fundamental Concepts in Financial Management Time Value of Money Financial Statements, Cash Flow, and Taxes Analysis of Financial Statements Financial Markets and Institutions 23 24 64 100 141 Part 3 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Financial Assets Interest Rates Bonds and Their Valuation Risk and Rates of Return Stocks and Their Valuation 173 174 207 244 289 Part 4 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Investing in Long-Term Assets: Capital Budgeting The Cost of Capital The Basics of Capital Budgeting Cash Flow Estimation and Risk Analysis Real Options and Other Topics in Capital Budgeting 327 328 357 387 415 Part 5 Chapter 14 Chapter 15 Capital Structure and Dividend Policy Capital Structure and Leverage Distributions to Shareholders: Dividends and Share Repurchases 435 436 478 xx Brief Contents xxi Part 6 Chapter 16 Chapter 17 Working Capital and Financial Planning Working Capital Management Financial Planning and Forecasting 511 512 552 Part 7 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Special Topics in Financial Management Derivatives and Risk Management Multinational Financial Management Hybrid Financing: Preferred Stock, Leasing, Warrants, and Convertibles Mergers and Acquisitions 577 578 615 648 683 Appendixes Appendix A Appendix B Appendix C Solutions to Self-Test Questions and Problems Answers to Selected End-of-Chapter Problems Selected Equations and Data A-1 A-27 A-30 Index I-1 CONTENTS PREFACE iii Simple versus Compound Interest 27 Part 1 Introduction to Financial Management 1 Chapter 1 An Overview of Financial Management 2 Striking the Right Balance 2 PUTTING THINGS IN PERSPECTIVE 3 3. Financial Calculators 28 4. Spreadsheets 28 Hints on Using Financial Calculators 29 Graphic View of the Compounding Process 30 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 Present Values 31 Graphic View of the Discounting Process 33 Finding the Interest Rate, I 34 Finding the Number of Years, N 35 Annuities 35 Future Value of an Ordinary Annuity 36 Future Value of an Annuity Due 38 Present Value of an Ordinary Annuity 39 Finding Annuity Payments, Periods, and Interest Rates 40 Finding Annuity Payments, PMT 40 Finding the Number of Periods, N 41 Finding the Interest Rate, I 41 1.1 1.2 1.3 1.4 Forms of Business Organization 4 Stock Prices and Shareholder Value 6 Intrinsic Values, Stock Prices, and Compensation Plans 8 Some Important Trends 11 Is Shareholder Wealth Maximization a Worldwide Goal? 12 1.5 Business Ethics 12 What Companies Are Doing 13 Consequences of Unethical Behavior 13 How Should Employees Deal with Unethical Behavior? 14 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 Perpetuities 42 Uneven Cash Flows 44 Future Value of an Uneven Cash Flow Stream 46 Solving for I with Uneven Cash Flows 47 Semiannual and Other Compounding Periods 48 Comparing Interest Rates 50 Fractional Time Periods 52 Amortized Loans 52 Protection for Whistle-Blowers 15 1.6 1.7 Conflicts between Managers and Stockholders 16 The Role of Finance in the Organization 17 TYING IT ALL TOGETHER 18 Part 2 Fundamental Concepts in Financial Management 23 Chapter 2 Time Value of Money 24 Will You Be Able to Retire? 24 PUTTING THINGS IN PERSPECTIVE 24 TYING IT ALL TOGETHER 54 INTEGRATED CASE First National Bank 62 WEB APPENDIX 2A Continuous Compounding and Discounting 2.1 2.2 Time Lines 25 Future Values 26 1. Step-by-Step Approach 27 2. Formula Approach 27 Chapter 3 Financial Statements, Cash Flow, and Taxes 64 Doing Your Homework with Financial Statements 64 PUTTING THINGS IN PERSPECTIVE 65 xxii Contents xxiii 3.1 3.2 3.3 3.4 3.5 3.6 A Brief History of Accounting and Financial Statements 65 Financial Statements and Reports 66 The Balance Sheet 68 The Income Statement 72 Net Cash Flow 75 Statement of Cash Flows 75 Massaging the Cash Flow Statement 78 4.3 Asset Management Ratios 104 Inventory Turnover Ratio 105 Days Sales Outstanding 106 Fixed Assets Turnover Ratio 106 Total Assets Turnover Ratio 107 4.4 Debt Management Ratios 108 Total Debt to Total Assets 110 Times-Interest-Earned Ratio 110 EBITDA Coverage Ratio 111 4.5 Profitability Ratios 112 Profit Margin on Sales 112 Global Perspectives: Global Accounting Standards: Can One Size Fit All? 113 3.7 3.8 Statement of Retained Earnings 78 Uses and Limitations of Financial Statements 79 Financial Analysis on the Internet 80 3.9 Modifying Accounting Data for Investor and Managerial Decisions 81 Operating Assets and Operating Capital 81 Operating Cash Flows 84 Free Cash Flow 84 Return on Total Assets 114 Basic Earning Power (BEP) Ratio 114 Return on Common Equity 115 4.6 Market Value Ratios 115 Price/Earnings Ratio 116 Price/Cash Flow Ratio 116 Market/Book Ratio 116 3.10 3.11 MVA and EVA 86 The Federal Income Tax System 87 Corporate Taxes 87 Personal Taxes 87 Interest Paid 87 Interest Earned 88 Dividends Paid 88 Dividends Received 88 Tax Loss Carry-Back and Carry-Forward 88 Capital Gains 88 Depreciation 89 Small Businesses 89 4.7 4.8 4.9 Trend Analysis 118 Tying the Ratios Together: The Du Pont Equations 118 Comparative Ratios and "Benchmarking" 121 Looking for Warning Signs within the Financial Statements 123 4.10 4.11 4.12 Uses and Limitations of Ratio Analysis 124 Problems with ROE 125 EVA and ROE 126 Looking Beyond the Numbers 128 TYING IT ALL TOGETHER 89 INTEGRATED CASE D'Leon Inc., Part I 95 WEB APPENDIX 3A The Federal Income Tax System TYING IT ALL TOGETHER 129 INTEGRATED CASE D'Leon Inc., Part II 136 Chapter 5 Financial Markets and Institutions 141 Chapter 4 Analysis of Financial Statements 100 Lessons Learned from Enron and WorldCom 100 PUTTING THINGS IN PERSPECTIVE 102 A Strong Financial System Is Necessary for a Growing and Prosperous Economy 141 PUTTING THINGS IN PERSPECTIVE 142 5.1 4.1 4.2 Ratio Analysis 102 Liquidity Ratios 103 Current Ratio 103 Quick, or Acid Test, Ratio 104 An Overview of the Capital Allocation Process 143 Financial Markets 145 Types of Markets 145 Recent Trends 146 5.2 xxiv Contents 5.3 5.4 Financial Institutions 148 The Stock Market 153 Citigroup Built to Compete in a Changing Environment 154 6.4 6.5 The Term Structure of Interest Rates 187 What Determines the Shape of the Yield Curve? 189 The Links between Expected Inflation and Interest Rates: A Closer Look 192 The Physical Location Stock Exchanges 154 The NYSE and Nasdaq Combine Forces with the Leading Online Trading Systems 155 6.6 6.7 Using the Yield Curve to Estimate Future Interest Rates 193 Other Factors that Influence Interest Rate Levels 196 Federal Reserve Policy 196 Federal Budget Deficits or Surpluses 196 International Factors 197 Business Activity 197 Global Perspectives: Measuring Country Risk 198 The Over-the-Counter and the Nasdaq Stock Markets 156 5.5 5.6 The Market for Common Stock 157 Types of Stock Market Transactions 157 Stock Markets and Returns 160 Stock Market Reporting 160 Stock Market Returns 162 5.7 Stock Market Efficiency 163 Levels of Market Efficiency 163 6.8 6.9 Investing Overseas 199 Interest Rates and Business Decisions 199 Measuring the Market 164 Implications of Market Efficiency 166 Is the Stock Market Efficient? 167 A Closer Look at Behavioral Finance Theory 168 TYING IT ALL TOGETHER 201 INTEGRATED CASE Smyth Barry & Company, Part II 206 TYING IT ALL TOGETHER 169 INTEGRATED CASE Smyth Barry & Company, Part I 170 Chapter 7 Bonds and Their Valuation 207 Sizing Up Risk in the Bond Market 207 PUTTING THINGS IN PERSPECTIVE 208 Part 3 Financial Assets 173 Chapter 6 Interest Rates 174 Low Interest Rates Encourage Investment and Stimulate Consumer Spending 174 PUTTING THINGS IN PERSPECTIVE 175 7.1 7.2 Who Issues Bonds? 208 Key Characteristics of Bonds 209 Par Value 210 Coupon Interest Rate 210 Maturity Date 210 Call Provisions 211 Sinking Funds 211 Other Features 212 6.1 6.2 6.3 The Cost of Money 175 Interest Rate Levels 176 The Determinants of Market Interest Rates 180 The Real Risk-Free Rate of Interest, r* 181 The Nominal, or Quoted, Risk-Free Rate of Interest, rRF 182 Inflation Premium (IP) 182 Default Risk Premium (DRP) 183 7.3 7.4 Bond Valuation 213 Bond Yields 216 Yield to Maturity 216 Yield to Call 217 Current Yield 218 7.5 7.6 7.7 Changes in Bond Values Over Time 218 Bonds with Semiannual Coupons 222 Assessing a Bond's Riskiness 223 Interest Rate Risk 223 Reinvestment Rate Risk 225 Comparing Interest Rate and Reinvestment Rate Risk 226 An Almost Riskless Treasury Bond 184 Liquidity Premium (LP) 186 Maturity Risk Premium (MRP) 186 Contents xxv 7.8 Default Risk 227 Various Types of Corporate Bonds 228 Bond Ratings 229 Bankruptcy and Reorganization 233 TYING IT ALL TOGETHER 280 INTEGRATED CASE Merrill Finch Inc. 286 WEB APPENDIX 8A Calculating Beta Coefficients 7.9 Bond Markets 234 TYING IT ALL TOGETHER 236 INTEGRATED CASE Western Money Management Inc. 243 WEB APPENDIX 7A Zero Coupon Bonds WEB APPENDIX 7B Bankruptcy and Reorganization Chapter 9 Stocks and Their Valuation 289 Searching for the Right Stock 289 PUTTING THINGS IN PERSPECTIVE 290 9.1 Legal Rights and Privileges of Common Stockholders 290 Control of the Firm 290 The Preemptive Right 291 Chapter 8 Risk and Rates of Return 244 No Pain No Gain 244 PUTTING THINGS IN PERSPECTIVE 245 9.2 9.3 Types of Common Stock 292 Common Stock Valuation 292 Definitions of Terms Used in Stock Valuation Models 293 Expected Dividends as the Basis for Stock Values 294 8.1 Stand-Alone Risk 246 Probability Distributions 247 Expected Rate of Return 248 Measuring Stand-Alone Risk: The Standard Deviation 250 Using Historical Data to Measure Risk 252 Measuring Stand-Alone Risk: The Coefficient of Variation 254 Risk Aversion and Required Returns 255 9.4 Constant Growth Stocks 296 Illustration of a Constant Growth Stock 296 Dividend and Earnings Growth 297 When Can the Constant Growth Model Be Used? 298 The Trade-Off between Risk and Return 256 9.5 9.6 8.2 Risk in a Portfolio Context 257 ^ Expected Portfolio Returns, r p 258 Portfolio Risk 259 Expected Rate of Return on a Constant Growth Stock 299 Valuing Stocks Expected to Grow at a Nonconstant Rate 300 Evaluating Stocks That Don't Pay Dividends 304 The Benefits of Diversification Are More Important Than Ever 263 Diversifiable Risk versus Market Risk 263 The Concept of Beta 266 Global Perspectives: The Benefits of Diversifying Overseas 270 9.7 Valuing the Entire Corporation 305 The Corporate Valuation Model 306 Other Approaches to Valuing Common Stocks 308 8.3 The Relationship between Risk and Rates of Return 271 Comparing the Total Company and Dividend Growth Models 308 Estimating the Market Risk Premium 272 9.8 9.9 9.10 Stock Market Equilibrium 310 Changes in Equilibrium Stock Prices 311 The Impact of Inflation 275 Changes in Risk Aversion 275 Changes in a Stock's Beta Coefficient 277 Investing in International Stocks 313 Preferred Stock 315 Global Perspectives: Investing in Emerging Markets 316 8.4 8.5 Some Concerns about Beta and the CAPM 277 Some Concluding Thoughts: Implications for Corporate Managers and Investors 278 TYING IT ALL TOGETHER 316 xxvi Contents INTEGRATED CASE Mutual of Chicago Insurance Company 322 Chapter 11 The Basics of Capital Budgeting 357 Competition in the Aircraft Industry 357 PUTTING THINGS IN PERSPECTIVE 358 Part 4 Investing in Long-Term Assets: Capital Budgeting 327 Chapter 10 The Cost of Capital 328 Creating Value at GE 328 PUTTING THINGS IN PERSPECTIVE 329 11.1 11.2 11.3 11.4 11.5 Generating Ideas for Capital Projects 358 Project Classifications 359 The Net Present Value (NPV) Criterion 360 Internal Rate of Return (IRR) 363 Comparison of the NPV and IRR Methods 364 NPV Profiles 364 NPV Rankings Depend on the Cost of Capital 365 Independent Projects 367 Mutually Exclusive Projects 367 10.1 10.2 10.3 10.4 An Overview of the Weighted Average Cost of Capital 329 Basic Definitions 331 Cost of Debt, rd(1 T) 332 Cost of Preferred Stock, rp 333 Funny-Named Preferred-Like Securities 334 11.6 11.7 11.8 11.9 11.10 11.11 11.12 Multiple IRRs 369 Modified Internal Rate of Return (MIRR) 371 Payback Period 373 Conclusions on Capital Budgeting Methods 375 Decision Criteria Used in Practice 376 Using Capital Budgeting Techniques in Other Contexts 377 The Post-Audit 378 10.5 Cost of Retained Earnings, rs 335 The CAPM Approach 336 Dividend-Yield-plus-Growth-Rate, or Discounted Cash Flow (DCF), Approach 336 Bond-Yield-plus-Risk-Premium Approach 339 How Much Does It Cost to Raise External Capital? 340 10.6 Cost of New Common Stock, re 340 Add Flotation Costs to a Project's Cost 341 Increase the Cost of Capital 341 When Must External Equity Be Used? 342 TYING IT ALL TOGETHER 379 INTEGRATED CASE Allied Components Company 385 10.7 10.8 Composite, or Weighted Average, Cost of Capital, WACC 343 Factors That Affect the WACC 344 Factors the Firm Cannot Control 344 Factors the Firm Can Control 344 Global Perspectives: Global Variations in the Cost of Capital 345 Chapter 12 Cash Flow Estimation and Risk Analysis 387 Home Depot Keeps Growing 387 PUTTING THINGS IN PERSPECTIVE 388 10.9 10.10 Adjusting the Cost of Capital for Risk 346 Some Other Problems with Cost of Capital Estimates 348 12.1 12.2 Background on the Project 388 Project Analysis 390 Input Data, Part 1 390 Depreciation Schedule, Part 2 390 Salvage Value Calculations, Part 3 391 Projected Cash Flows, Part 4 392 Appraisal of the Proposed Project, Part 5 393 TYING IT ALL TOGETHER 349 INTEGRATED CASE Coleman Technologies Inc. 355 WEB APPENDIX 10A The Cost of New Common Stock and the WACC 12.3 Other Points on Cash Flow Analysis 394 Cash Flow versus Accounting Income 394 Timing of Cash Flows 395 Incremental Cash Flows 395 Contents xxvii Replacement Projects 395 Sunk Costs 395 Opportunity Costs 396 Externalities 396 TYING IT ALL TOGETHER 426 INTEGRATED CASE 21st Century Educational Products 431 12.4 12.5 Estimating Project Risk 397 Measuring Stand-Alone Risk 398 Sensitivity Analysis 398 Scenario Analysis 400 Monte Carlo Simulation 401 Global Perspectives: Capital Budgeting Practices in the Asian/Pacific Region 402 Part 5 Capital Structure and Dividend Policy 435 Chapter 14 Capital Structure and Leverage 436 Debt: Rocket Booster or Anchor? 436 PUTTING THINGS IN PERSPECTIVE 437 12.6 12.7 Different Capital Structures 403 Incorporating Risk into Capital Budgeting 403 14.1 14.2 The Target Capital Structure 437 Business and Financial Risk 439 Business Risk 439 Operating Leverage 441 Financial Risk 444 TYING IT ALL TOGETHER 404 INTEGRATED CASE Allied Food Products 409 APPENDIX 12A Tax Depreciation 413 WEB APPENDIX 12B Replacement Project Analysis WEB APPENDIX 12C Refunding Operations WEB APPENDIX 12D Using the CAPM to Estimate the Risk-Adjusted Cost of Capital WEB APPENDIX 12E Techniques for Measuring Beta Risk 14.3 Determining the Optimal Capital Structure 450 WACC and Capital Structure Changes 450 The Hamada Equation 452 The Optimal Capital Structure 453 14.4 Capital Structure Theory 456 Yogi Berra on the M&M Proposition 457 The Effect of Taxes 457 The Effect of Potential Bankruptcy 458 Trade-Off Theory 459 Signaling Theory 460 Using Debt Financing to Constrain Managers 461 Chapter 13 Real Options and Other Topics in Capital Budgeting 415 Keeping Your Options Open 415 PUTTING THINGS IN PERSPECTIVE 416 14.5 Checklist for Capital Structure Decisions 462 Global Perspectives: Taking a Look at Global Capital Structures 465 14.6 Variations in Capital Structures 465 TYING IT ALL TOGETHER 466 INTEGRATED CASE Campus Deli Inc. 472 WEB APPENDIX 14A Degree of Leverage 13.1 13.2 13.3 13.4 13.5 13.6 Introduction to Real Options 416 Abandonment/Shutdown Options 417 Investment Timing Options 419 Growth Options 420 Flexibility Options 421 Comparing Mutually Exclusive Projects with Unequal Lives 422 Replacement Chains 422 Equivalent Annual Annuities (EAA) 423 Conclusions about Unequal Lives 424 Chapter 15 Distributions to Shareholders: Dividends and Share Repurchases 478 Microsoft Shifts Gears and Begins to Unload Part of Its Vast Cash Hoard 478 PUTTING THINGS IN PERSPECTIVE 479 13.7 The Optimal Capital Budget 424 xxviii Contents 15.1 Dividends versus Capital Gains: What Do Investors Prefer? 479 Dividend Irrelevance Theory 480 Reasons Some Investors Prefer Dividends 480 Reasons Some Investors May Prefer Capital Gains 481 16.1 16.2 Working Capital Terminology 513 The Cash Conversion Cycle 513 Calculating the Targeted CCC 514 Calculating the Actual CCC 515 Some Firms Operate with Negative Working Capital! 516 15.2 Other Dividend Policy Issues 482 Information Content, or Signaling, Hypothesis 482 Clientele Effect 482 16.3 16.4 Alternative Current Asset Investment Policies 517 Alternative Current Asset Financing Policies 518 Maturity Matching, or "Self-Liquidating," Approach 519 Aggressive Approach 519 Conservative Approach 519 Choosing between the Approaches 521 15.3 Establishing the Dividend Policy in Practice 483 Setting the Target Payout Ratio: The Residual Dividend Model 483 Global Perspectives: Dividend Yields Around the World 488 Earnings, Cash Flows, and Dividends 489 Payment Procedures 490 16.5 16.6 The Cash Budget 521 Cash and Marketable Securities 525 Currency 526 Demand Deposits 526 Marketable Securities 527 15.4 15.5 Dividend Reinvestment Plans 493 Summary of Factors Influencing Dividend Policy 494 Constraints 494 Investment Opportunities 494 Alternative Sources of Capital 495 Effects of Dividend Policy on rs 495 16.7 16.8 Inventories 528 Supply Chain Management 529 Accounts Receivable 530 Credit Policy 530 Setting and Implementing the Credit Policy 531 Monitoring Accounts Receivable 532 15.6 Stock Dividends and Stock Splits 495 Stock Splits 496 Stock Dividends 496 Effect on Stock Prices 497 16.9 16.10 Accounts Payable (Trade Credit) 534 Bank Loans 537 Promissory Note 537 Line of Credit 538 Revolving Credit Agreement 538 Costs of Bank Loans 539 15.7 Stock Repurchases 498 The Effects of Stock Repurchases 498 Stock Repurchases Soar in 2004 499 Advantages of Repurchases 500 Disadvantages of Repurchases 501 Conclusions on Stock Repurchases 501 TYING IT ALL TOGETHER 502 INTEGRATED CASE Southeastern Steel Company 508 WEB APPENDIX 15A An Example: The Residual Dividend Model 16.11 16.12 16.13 Commercial Paper 541 Accruals (Accrued Liabilities) 542 Use of Security in Short-Term Financing 542 TYING IT ALL TOGETHER 543 INTEGRATED CASE Ski Equipment Inc. 548 WEB APPENDIX 16A Inventory Management Part 6 Working Capital and Financial Planning 511 Chapter 16 Working Capital Management 512 Best Buy Successfully Manages Its Working Capital 512 PUTTING THINGS IN PERSPECTIVE 512 WEB APPENDIX 16B Short-Term Loans and Bank Financing Chapter 17 Financial Planning and Forecasting 552 Forecasting Apple's Future 552 PUTTING THINGS IN PERSPECTIVE 553 Contents xxix 17.1 17.2 17.3 Strategic Planning 553 The Sales Forecast 555 The AFN Equation 556 Key Determinants of External Funds Requirements 558 Excess Capacity Adjustments 558 18.6 18.7 Forward and Futures Contracts 596 Other Types of Derivatives 600 Swaps 600 Structured Notes 601 Inverse Floaters 602 Credit Instruments Create New Opportunities and Risks 603 17.4 17.5 17.6 Forecasted Financial Statements 560 Initial Forecast: "Business as Usual" 560 18.8 Risk Management 603 An Approach to Risk Management 605 Using Regression to Improve Financial Forecasts 563 Using Individual Ratios in the Forecasting Process 565 Modifying Accounts Receivable 565 Modifying Inventories 566 Other "Special Studies" 566 Microsoft's Goal: Manage Every Risk! 606 18.9 Using Derivatives to Reduce Risks 607 Security Price Exposure 607 Commodity Price Exposure 610 The Use and Misuse of Derivatives 610 TYING IT ALL TOGETHER 611 INTEGRATED CASE Tropical Sweets Inc. 613 TYING IT ALL TOGETHER 567 INTEGRATED CASE New World Chemicals Inc. 572 WEB APPENDIX 17A Forecasting Financial Requirements When Financial Ratios Change Chapter 19 Multinational Financial Management 615 U.S. Firms Look Overseas to Enhance Shareholder Value 615 PUTTING THINGS IN PERSPECTIVE 616 Part 7 Special Topics in Financial Management 577 Chapter 18 Derivatives and Risk Management 578 Using Derivatives to Manage Risk 578 PUTTING THINGS IN PERSPECTIVE 579 19.1 19.2 19.3 Multinational or Global Corporations 616 Multinational versus Domestic Financial Management 619 The International Monetary System 621 International Monetary Terminology 621 Current Monetary Arrangements 622 19.4 18.1 18.2 Reasons to Manage Risk 579 Background on Derivatives 582 Global Perspectives: Barings and Sumitomo Suffer Large Losses in the Derivatives Market 583 Foreign Exchange Rate Quotations 623 Cross Rates 624 Interbank Foreign Currency Quotations 625 19.5 19.6 19.7 19.8 19.9 Trading in Foreign Exchange 626 Spot Rates and Forward Rates 626 Interest Rate Parity 627 Purchasing Power Parity 629 Inflation, Interest Rates, and Exchange Rates 630 International Money and Capital Markets 631 International Credit Markets 631 18.3 Options 584 Option Types and Markets 584 Factors That Affect the Value of a Call Option 586 Exercise Value versus Option Price 586 18.4 18.5 Introduction to Option Pricing Models 589 Expensing Executive Stock Options 590 The Black-Scholes Option Pricing Model (OPM) 592 OPM Assumptions and Equations 592 OPM Illustration 594 Hungry for a Big Mac? Go to China! 632 Stock Market Indices Around the World 634 International Stock Markets 635 19.10 International Capital Budgeting 636 xxx Contents 19.11 19.12 International Capital Structures 638 Multinational Working Capital Management 639 Cash Management 639 Credit Management 640 Inventory Management 641 INTEGRATED CASE Fish & Chips, Inc., Part I 681 Fish & Chips, Inc., Part II 681 Chapter 21 Mergers and Acquisitions 683 Procter & Gamble Acquires Gillette 683 PUTTING THINGS IN PERSPECTIVE 684 TYING IT ALL TOGETHER 642 INTEGRATED CASE Citrus Products Inc. 646 21.1 Chapter 20 Hybrid Financing: Preferred Stock, Leasing, Warrants, and Convertibles 648 Taking a Wild Ride with Amazon's Convertible Debt 648 PUTTING THINGS IN PERSPECTIVE 649 Rationale for Mergers 685 Synergy 685 Tax Considerations 685 Purchase of Assets below Their Replacement Cost 686 Diversification 686 Managers' Personal Incentives 686 Breakup Value 687 21.2 21.3 21.4 21.5 21.6 Types of Mergers 687 Level of Merger Activity 687 Hostile versus Friendly Takeovers 689 Merger Regulation 690 Merger Analysis 691 Valuing the Target Firm 692 Setting the Bid Price 695 20.1 Preferred Stock 650 Basic Features 650 Other Types of Preferred Stock 652 Advantages and Disadvantages of Preferred Stock 652 20.2 Leasing 653 Types of Leases 653 Funny-Named Preferred-Like Securities 654 More Than Just Financial Statements 697 Post-Merger Control 698 Financial Statement Effects 656 Evaluation by the Lessee 657 Factors That Affect Leasing Decisions 660 21.7 Financial Reporting for Mergers 699 Purchase Accounting 699 Income Statement Effects 700 20.3 Warrants 661 Initial Market Price of a Bond with Warrants 662 Use of Warrants in Financing 663 Wealth Effects and Dilution Due to Warrants 664 The Component Cost of Bonds with Warrants 666 Problems with Warrant Issues 666 Tempest in a Teapot? 701 21.8 The Role of Investment Bankers 702 Arranging Mergers 702 Developing Defensive Tactics 702 Establishing a Fair Value 703 Financing Mergers 703 Arbitrage Operations 704 21.9 Do Mergers Create Value? The Empirical Evidence 704 The Track Record of Recent Large Mergers 705 20.4 Convertibles 667 Conversion Ratio and Conversion Price 667 The Component Cost of Convertibles 668 Use of Convertibles in Financing 672 Convertibles and Conflicts of Interest 673 21.10 21.11 21.12 Corporate Alliances 706 Leveraged Buyouts 706 Divestitures 707 Types of Divestitures 707 Divestiture Illustrations 707 Global Perspectives: Governments Are Divesting State-Owned Businesses to Spur Economic Efficiency 708 20.5 20.6 A Final Comparison of Warrants and Convertibles 673 Reporting Earnings When Warrants or Convertibles Are Outstanding 674 TYING IT ALL TOGETHER 675 Contents xxxi TYING IT ALL TOGETHER 710 INTEGRATED CASE Smitty's Home Repair Company 713 WEB APPENDIX 21A Holding Companies Cyberproblem CP7-1 Cyberproblem CP8-1 Cyberproblem CP9-1 Appendixes Appendix A Appendix B Appendix C Solutions to Self-Test Questions and Problems A-1 Answers to Selected End-ofChapter Problems A-27 Selected Equations and Data A-30 Cyberproblem CP10-1 Cyberproblem CP11-1 Cyberproblem CP12-1 Cyberproblem CP13-1 Cyberproblem CP14-1 Cyberproblem CP15-1 WEB APPENDIX C Selected Equations and Data Index I-1 Cyberproblem CP16-1 Cyberproblems Cyberproblem CP1-1 Cyberproblem CP2-1 Cyberproblem CP3-1 Cyberproblem CP4-1 Executive Compensation Online Financial Calculators Examining the Financial Report--3M Using Ratio Analysis as a Tool--Brady Corporation World Financial Markets Yield Curves and Interest Rates Cyberproblem CP17-1 Cyberproblem CP18-1 Cyberproblem CP19-1 Cyberproblem CP20-1 Cyberproblem CP21-1 Cyberproblem CP5-1 Cyberproblem CP6-1 BondsOnline Educated Investor Center Evaluating Portfolio Risk and Return Intrinsic Stock Valuation--Emerson Electric Estimating the WACC-- AT&T Capital Expenditures and Investment--IBM Cash Flow Estimation-- Alcoa Real Options Applying the Hamada Equation Dividend Reinvestment Plans Cash Conversion Cycle Using Analyst Reports and Forecasts Option Strategies Multinational Financial Management-- McDonald's Lease Analysis Mergers-- CNNMoney.com Top 25 Deals of the Year INTRODUCTION TO FINANCIAL MANAGEMENT P A R T 1 1 An Overview of Financial Management C H APTE R 1 AN OVERVIEW OF FINANCIAL MANAGEMENT Striking the Right Balance In 1776 Adam Smith described how an "invisible hand" guides companies striving to maximize profits so that they make decisions that also benefit society. Smith's insights led economists to reach two key conclusions: (1) Profit maximization is the proper goal for a business, and (2) the free enterprise system is best for society. However, the world has changed since 1776. Firms then were much smaller, they operated in one country, and they were generally managed by their owners. Firms today are much larger, operate across the globe, have thousands of employees, and are owned by millions of investors. Therefore, the "invisible hand" may no longer provide reliable guidance. If not, how should our giant corporations be managed, and what should their goals be? In particular, should companies try to maximize their owners' interests, or should they strike a balance between profits and actions designed specifically to benefit customers, employees, suppliers, and even society as a whole? Most academics today subscribe to a slightly modified version of Adam Smith's theory: Maximize stockholder wealth, which amounts to maximizing the value of the stock. Stock price maximization requires firms to consider profits, but it also requires them to think about the riskiness of those profits and whether they are paid out as dividends or retained and reinvested in the business. Firms must develop desirable products, produce them efficiently, and sell them at competitive prices, all of which also benefit society. Obviously, some constraints are necessary--firms must not be allowed to pollute the air and water excessively, engage in unfair employment practices, or create monopolies that exploit consumers. So, the view today is that management should try to maximize stock values, but subject to government-imposed constraints. To paraphrase Charles Prince, chairman of Citigroup, in an interview with Fortune: We Citigroup CLARO CORTES IV/REUTERS/CORBIS Chapter 1 An Overview of Financial Management 3 want to grow aggressively, but without breaking the law.1 Citigroup had recently been fined hundreds of millions of dollars for breaking laws in the United States and abroad. The constrained maximization theory does have critics. For example, General Electric (GE) chief executive officer (CEO) Jeffrey Immelt believes that alterations are needed. GE is the world's most valuable company, and it has an excellent reputation.2 Immelt tells his management team that value and reputation go hand in glove--having a good reputation with customers, suppliers, employees, and regulators is essential if value is to be maximized. According to Immelt, "The reason people come to work for GE is that they want to be part of something that is bigger than themselves. They want to work hard, win promotions, and receive stock options. But they also want to work for a company that makes a difference, a company that's doing great things in the world. . . . It's up to GE to be a good citizen. Not only is it a nice thing to do, it's good for business." This is a new position for GE. Immelt's predecessor, Jack Welch, focused on compliance--like Citigroup's Prince, Welch believed in obeying rules pertaining to the environment, employment practices, and the like, but his goal was to maximize shareholder value within those constraints. Immelt, on the other hand, thinks it's necessary to go further, doing some things because they benefit society, not just because they are profitable. But Immelt is not totally altruistic--he thinks that actions to improve world conditions will also enhance GE's reputation, helping it attract top workers and loyal customers, get better cooperation from suppliers, and obtain expedited regulatory approvals for new ventures, all of which would benefit GE's stock price. One could interpret all this as saying that the CEOs of both Citigroup and GE have stock price maximization as their top goal, but Citigroup's CEO focuses quite directly on that goal while GE's CEO takes a somewhat broader view. Putting Things In Perspective This chapter will give you an idea of what financial management is all about. We begin with a brief discussion of the different forms of business organization. For corporations, management's goal should be to maximize shareholder wealth, which means maximizing the value of the stock. When we say "maximizing the value of the stock," we mean the "true, long-run value," which may be different from the current stock price. Good managers understand the importance of ethics, and they recognize that maximizing long-run value is consistent with being socially responsible. We conclude the chapter by describing how finance is related to the overall business and how firms must provide the right incentives if they are to get managers to focus on long-run value maximization. 1 2 "Tough Questions for Citigroup's CEO," Fortune, November 29, 2004, pp. 114122. Marc Gunther, "Money and Morals at GE," Fortune, November 15, 2004, pp. 176182. 4 Part 1 Introduction to Financial Management 1.1 FORMS OF BUSINESS ORGANIZATION The key aspects of financial management are the same for all businesses, large or small, regardless of how they are organized. Still, its legal structure does affect some aspects of a firm's operations and thus must be recognized. There are three main forms of business organization: (1) sole proprietorships, (2) partnerships, and (3) corporations. In terms of numbers, about 80 percent of businesses are operated as sole proprietorships, while most of the remainder are divided equally between partnerships and corporations. However, based on the dollar value of sales, about 80 percent of all business is done by corporations, about 13 percent by sole proprietorships, and about 7 percent by partnerships. Because corporations conduct the most business, and because most successful proprietorships and partnerships eventually convert into corporations, we concentrate on them in this book. Still, it is important to understand the differences among the three types of firms. A proprietorship is an unincorporated business owned by one individual. Going into business as a sole proprietor is easy--merely begin business operations. Proprietorships have three important advantages: (1) They are easily and inexpensively formed, (2) they are subject to few government regulations, and (3) they are subject to lower income taxes than corporations. However, proprietorships also have three important limitations: (1) Proprietors have unlimited personal liability for the business's debts, which can result in losses that exceed the money they have invested in the company; (2) it is difficult for proprietorships to obtain large sums of capital; and (3) the life of a business organized as a proprietorship is limited to the life of the individual who created it. For these reasons, sole proprietorships are used primarily for small businesses. However, businesses are frequently started as proprietorships and then converted to corporations when their growth causes the disadvantages of being a proprietorship to outweigh the advantages. A partnership is a legal arrangement between two or more people who decide to do business together. Partnerships are similar to proprietorships in that they can be established easily and inexpensively, and they are not subject to the corporate income tax. They also have the disadvantages associated with proprietorships: unlimited personal liability, difficulty raising capital, and limited lives. The liability issue is especially important, because under partnership law, each partner is liable for the business's debts. Therefore, if any partner is unable to meet his or her pro rata liability and the partnership goes bankrupt, then the remaining partners are personally responsible for making good on the unsatisfied claims. The partners of a national accounting firm, Laventhol and Horvath, a huge partnership that went bankrupt as a result of suits filed by investors who relied on faulty audit statements, learned all about the perils of doing business as a partnership. Another major accounting firm, Arthur Andersen, suffered a similar fate because the partners who worked with Enron, WorldCom, and a few other clients broke the law and led to the firm's demise. Thus, a Texas partner who audits a business that goes under can bring ruin to a millionaire New York partner who never even went near the client company.3 3 Proprietorship An unincorporated business owned by one individual. Partnership An unincorporated business owned by two or more persons. There are actually a number of types of partnerships, but we focus on "plain vanilla partnerships" and leave the variations to courses on business law. We note, though, that the variations are generally designed to limit the liabilities of some of the partners. For example, a "limited partnership" has a general partner, who has unlimited liability, and limited partners, whose liability is limited to their investment. This sounds great from the standpoint of the limited partners, but they have to cede sole and absolute authority to the general partner, which means that they have no say in the way the firm conducts its business. With a corporation, the owners (stockholders) have limited liability, but they also have the right to vote and thus influence management. Chapter 1 An Overview of Financial Management 5 A corporation is a legal entity created by a state, and it is separate and distinct from its owners and managers. Corporations have unlimited lives, their owners are not subject to losses beyond the amount they have invested in the business, and it is easier to transfer one's ownership interest (stock) in a corporation than one's interest in a nonincorporated business. These three factors make it much easier for corporations to raise the capital necessary to operate large businesses. Thus, growth companies such as Hewlett-Packard and Microsoft generally begin life as proprietorships or partnerships, but at some point find it advantageous to convert to the corporate form. The biggest drawback to incorporation is taxes: Corporate earnings are generally subject to double taxation--the earnings of the corporation are taxed at the corporate level, and then, when after-tax earnings are paid out as dividends, those earnings are taxed again as personal income to the stockholders. However, as an aid to small businesses Congress created S corporations and allowed them to be taxed as if they were proprietorships or partnerships and thus exempt from the corporate income tax. The S designation is based on the section of the Tax Code that deals with S corporations, though it could stand for "small." Larger corporations are known as C corporations. S corporations can have no more than 75 stockholders, which limits their use to relatively small, privately owned firms. The vast majority of small firms elect S status and retain that status until they decide to sell stock to the public and thus expand their ownership beyond 75 stockholders. In deciding on a form of organization, firms must trade off the advantages of incorporation against a possibly higher tax burden. However, the value of any business other than a very small one will probably be maximized if it is organized as a corporation for the following three reasons: 1. Limited liability reduces the risks borne by investors, and, other things held constant, the lower the firm's risk, the higher its value. 2. A firm's value is dependent on its growth opportunities, which, in turn, are dependent on its ability to attract capital. Because corporations can attract capital more easily than can unincorporated businesses, they are better able to take advantage of growth opportunities. 3. The value of an asset also depends on its liquidity, which means the ease of selling the asset and converting it to cash at a "fair market value." Because an investment in the stock of a corporation is much easier to transfer to another investor than are proprietorship or partnership interests, a corporate investment is more liquid than a similar investment in a proprietorship or partnership, and this too enhances the value of a corporation. As we just discussed, most firms are managed with value maximization in mind, and that, in turn, has caused most large businesses to be organized as corporations. Corporation A legal entity created by a state, separate and distinct from its owners and managers, having unlimited life, easy transferability of ownership, and limited liability. S Corporation A special designation that allows small businesses that meet qualifications to be taxed as if they were a proprietorship or partnership rather than as a corporation. What are the key differences between sole proprietorships, partnerships, and corporations? How do some firms get to enjoy the benefits of the corporate form of organization yet avoid corporate income taxes? Why don't all firms--for example, IBM or GE--do this? Why is the value of a business other than a small one generally maximized if it is organized as a corporation? 6 Part 1 Introduction to Financial Management 1.2 STOCK PRICES AND SHAREHOLDER VALUE At the outset, it is important to understand the chief goals of a business. As we will see, the goals of a sole proprietor may be different than the goals of a corporation. Consider first Larry Jackson, a sole proprietor who operates a sporting goods store on Main Street. Jackson is in business to make money, but he also likes to take time off to play golf on Fridays. Jackson also has a few employees who are no longer very productive, but he keeps them on the payroll out of friendship and loyalty. Jackson is clearly running the business in a way that is consistent with his own personal goals--which is perfectly reasonable given that he is a sole proprietor. Jackson knows that he would make more money if he didn't play golf or if he replaced some of his employees, but he is comfortable with the choices he has made, and since it is his business, he is free to make those choices. By contrast, Linda Smith is CEO of a large corporation. Smith manages the company on a day-to-day basis, but she isn't the sole owner of the company. The company is owned primarily by shareholders who purchased its stock because they were looking for a financial return that would help them retire, send their kids to college, or pay for a long-anticipated trip. The shareholders elected a board of directors, who then selected Smith to run the company. Smith and the firm's other managers are working on behalf of the shareholders, and they were hired to pursue policies that enhance shareholder value. Throughout this book we focus primarily on publicly owned companies, hence we operate on the assumption that management's primary goal is stockholder wealth maximization, which translates into maximizing the price of the firm's common stock. If managers are to maximize shareholder wealth, they must know how that wealth is determined. Essentially, a company's shareholder wealth is simply the number of shares outstanding times the market price per share. If you own 100 shares of GE's stock and the price is $35 per share, then your wealth in GE is $3,500. The wealth of all its stockholders can be summed, and that is the value of GE, the item that management is supposed to maximize. The number of shares outstanding is for all intents and purposes a given, so what really determines shareholder wealth is the price of the stock. Therefore, a central issue is this: What determines the stock's price? Throughout this book, we will see that the value of any asset is simply the present value of the cash flows it provides to its owners over time. We discuss stock valuation in depth in Chapter 9, where we will see that a stock's price at any given time depends on the cash flows an "average" investor expects to receive in the future if he or she bought the stock. To illustrate, suppose investors are aware that GE earned $1.58 per share in 2004 and paid out 51 percent of that amount, or $0.80 per share, in dividends. Suppose further that most investors expect earnings, dividends, and the stock price to all increase by about 6 percent per year. Management might run the company so that these expectations are met. However, management might make some wonderful decisions that cause profits to rise at a 12 percent rate, causing the dividends and stock price to increase at that same rate. Of course, management might make some big mistakes, profits might suffer, and the stock price might decline sharply rather than grow. Thus, investors are exposed to more risk if they buy GE stock than if they buy a new U.S. Treasury bond, which offers a guaranteed interest payment every six months plus repayment of the purchase price when the bond matures. We see, then, that if GE's management makes good decisions, the stock price should increase, while if it makes enough bad decisions, the stock price will Stockholder Wealth Maximization The primary goal for managerial decisions; considers the risk and timing associated with expected earnings per share in order to maximize the price of the firm's common stock. Chapter 1 An Overview of Financial Management 7 decrease. Management's goal is to make the set of decisions that leads to the maximum stock price, as that will maximize its shareholders' wealth. Note, though, that factors beyond management's control also affect stock prices. Thus, after the 9/11 terrorist attacks on the World Trade Center and Pentagon, the prices of virtually all stocks fell, no matter how effective their management was. Firms have a number of different departments, including marketing, accounting, production, human resources, and finance. The finance department's principal task is to evaluate proposed decisions and judge how they will affect the stock price and therefore shareholder wealth. For example, suppose the production manager wants to replace some old equipment with new, automated machinery that will enable the firm to reduce labor costs. The finance staff will evaluate that proposal and determine if the savings are worth the cost. Similarly, if marketing wants to sign a contract with Tiger Woods that will cost $10 million per year for five years, the financial staff will evaluate the proposal, looking at the probable increased sales and other related factors, and reach a conclusion as to whether signing Tiger will lead to a higher stock price. Most significant decisions will be evaluated similarly. Note too that stock prices change over time as conditions change and as investors obtain new information about companies' prospects. For example, Apple Computer's stock ranged from a low of $21.18 to $69.57 per share during 2004, rising and falling as good and bad news was released. GE, which is older, more diversified, and consequently more stable, had a narrower price range, from $28.88 to $37.75. Investors can predict future results for GE more accurately than for Apple, hence GE is less risky. Note too that the investment decisions firms make determine their future profits and investors' cash flows. Some corporate projects are relatively straightforward and easy to evaluate, hence not very risky. For example, if Wal-Mart were considering opening a new store, the expected revenues, costs, and profits for this project would be easier to estimate than an Apple Computer project for a new voice-activated computer. The success or lack of success of projects such as these will determine the future stock prices of Wal-Mart, Apple, and other companies. Managers must estimate the probable effects of projects on profitability and thus on the stock price. Stockholders must forecast how successful companies will be, and current stock prices reflect investors' judgments as to that future success. What is management's primary goal? What do investors expect to receive when they buy a share of stock? Do investors know for sure what they will receive? Explain. Based just on the name, which company would you regard as being riskier, General Foods or South Seas Oil Exploration Company? Explain. When a company like Boeing decides to invest $5 billion in a new jet airliner, are its managers positive about the project's effect on Boeing's future profits and stock price? Explain. Would Boeing's managers or its stockholders be better able to judge the effect of a new airliner on profits and the stock price? Explain. Would all Boeing stockholders expect the same outcome from an airliner project, and how would these expectations affect the stock price? Explain. 8 Part 1 Introduction to Financial Management 1.3 INTRINSIC VALUES, STOCK PRICES, AND COMPENSATION PLANS As noted in the preceding section, stock prices are based on cash flows expected in future years, not just in the current year. Thus, stock price maximization requires us to take a long-run view of operations. Academics have always assumed that managers adhere to this long-run focus, but the focus for many companies shifted to the short run during the latter part of the 20th century. To give managers an incentive to focus on stock prices, stockholders (acting through boards of directors) gave executives stock options that could be exercised on a specified future date. An executive could exercise the option on that date, receive stock, sell it immediately, and thereby earn a profit. That led many managers to try to maximize the stock price on the option exercise date, not over the long run. That, in turn, led to some horrible abuses. Projects that looked good in the long run were turned down because they would penalize profits in the short run and thus the stock price on the option exercise day. Even worse, some managers deliberately overstated profits, thus temporarily boosting the stock price. These executives then exercised their options, sold the inflated stock, and left outside stockholders holding the bag when the true situation was revealed. Enron, WorldCom, and Fannie Mae are examples of companies whose managers did this, but there were many others. Many more companies use aggressive but legal accounting practices that boost current profits but will lower profits in future years. For example, management might truly think that an asset should be depreciated over 5 years but will then depreciate it over a 10-year life. This reduces reported costs and raises reported income for the next 5 years but will raise costs and lower income in the following 5 years. Many other legal but questionable accounting procedures were used, all in an effort to boost reported profits and the stock price on the options exercise day, and thus the executives' profits when they exercised their options. Obviously, all of this made it difficult for investors to decide how much stocks were really worth. Figure 1-1 can be used to illustrate the situation. The top box indicates that managerial actions, combined with economic and political conditions, determine investors' returns. Remember too that we don't know for sure what those future returns will be--we can estimate them, but expected and realized returns are often quite different. Investors like high returns but dislike risk, so the larger the expected profits and the lower the perceived risk, the higher the stock price. The second row of boxes differentiates between what we call "true expected returns" and "true risk" versus "perceived" returns and risk. By "true" we mean the returns and risk that most investors would expect if they had all the information that exists about the company. "Perceived" means what investors expect, given the limited information that they actually have. To illustrate, in early 2001 investors thought that Enron was highly profitable and would enjoy high and rising future profits. They also thought that actual results would be close to their expected levels, hence that Enron's risk was low. However, the best true estimates of Enron's profits, which were known by its executives but not the investing public, were negative, and Enron's true situation was extremely risky. The third row of boxes shows that each stock has an intrinsic value, which is an estimate of its "true" value as calculated by a fully informed analyst based Intrinsic Value An estimate of a stock's "true" value based on accurate risk and return data. The intrinsic value can be estimated but not measured precisely. Chapter 1 An Overview of Financial Management 9 FIGURE 1-1 Determinants of Intrinsic Values and Stock Prices Managerial Actions, the Economic Environment, and the Political Climate "True" Investor Returns "True" Risk "Perceived" Investor Returns "Perceived" Risk Stock's Intrinsic Value Stock's Market Price Market Equilibrium: Intrinsic Value = Stock Price Stock Price and Intrinsic Value ($) Stock overvalued Actual stock price Intrinsic value Stock undervalued R&D breakthrough 1980 1985 1990 1995 2000 2005 10 Part 1 Introduction to Financial Management Market Price The stock value based on perceived but possibly incorrect information as seen by the marginal investor. Equilibrium The situation in which the actual market price equals the intrinsic value, so investors are indifferent between buying or selling a stock. on accurate risk and return data, and a market price, which is the value in the market based on perceived but possibly incorrect information as seen by the marginal investor.4 Investors don't all agree, so it is this "marginal" investor who determines the actual price. For example, investors at the margin might expect GE's dividend to be $0.80 per share in 2005 and to grow at a rate of 6 percent per year thereafter, and on that basis they might set a price of $35 per share. However, if they had all the available facts, they might conclude that the best dividend estimate is $0.85 with a 7 percent growth rate, which would lead to a higher price, say, $40 per share. In this example, the actual market price would be $35 versus an intrinsic value of $40. If a stock's actual market price is equal to its intrinsic value, then as shown in the bottom box in Figure 1-1, the stock is said to be in equilibrium. There is no fundamental imbalance, hence no pressure for a change in the stock's price. Market prices can and do differ from intrinsic values. Eventually, though, as the future unfolds, the two values will converge. Actual stock prices are easy to determine--they are published in newspapers every day. However, intrinsic values are strictly estimates, and different analysts with different data and different views of the future will form different estimates of the intrinsic value for any given stock. Indeed, estimating intrinsic values is what security analysis is all about, and something successful investors are good at. Investing would be easy, profitable, and almost riskless if we knew all stocks' intrinsic values, but of course we don't--we can estimate intrinsic values, but we can never be sure that we are right. Note, though, that a firm's managers have the best information about the company's future prospects, so managers' estimates of intrinsic value are generally better than the estimates of outside investors. Even managers, though, can be wrong. The graph in the lower part of Figure 1-1 plots a hypothetical company's actual price and intrinsic value as estimated by management over time.5 The intrinsic value rose because the firm retained and reinvested earnings, which tends to increase profits, and it jumped dramatically in 1997, when a research and development (R&D) breakthrough raised management's estimate of future profits. The actual stock price tended to move up and down with the estimated intrinsic value, but investor optimism and pessimism, along with imperfect knowledge about the intrinsic value, led to deviations between the actual prices and intrinsic values. Intrinsic value is a long-run concept. It reflects both improper actions (Enron's overstating earnings) and proper actions (GE's efforts to improve the environment). Management's goal should be to take actions designed to maximize the firm's intrinsic value, not its current market price. Note, though, that maximizing 4 Investors at the margin are the ones who actually set stock prices. Some stockholders think a stock at its current price is a good deal, and they would buy more if they had more money. Other investors think the stock is priced too high, so they would not buy it unless it dropped sharply. Still other investors think the current stock price is about where it should be, so they would buy more if it fell slightly, sell it if it rose slightly, and maintain their current holdings unless something changes. These are the marginal investors, and it is their view that determines the current stock price. We discuss this point in more depth in Chapter 8, where we discuss the stock market in detail. 5 We emphasize that the intrinsic value is an estimate, and different analysts will have different estimates for a company at any given time. Its managers should also estimate their firm's intrinsic value and then take actions to maximize that value. They should also try to help outside security analysts improve their intrinsic value estimates by providing accurate information about the company's financial position and operations, but without releasing information that would help its competitors. Enron, WorldCom, and a number of other companies tried successfully to deceive analysts and succeeded only too well. Chapter 1 An Overview of Financial Management 11 the intrinsic value will maximize the average price over the long run but not necessarily the current price at each point in time. For example, management might make an investment that will lower profits for the current year but raise future profits substantially. If investors are not aware of the true situation, then the stock price might be held down by the low current profits even though the intrinsic value is actually increased. Management should provide information that helps investors make accurate estimates of the firm's "true" intrinsic value, which will keep the stock price closer to its equilibrium level over time, but there may be times when management cannot divulge the true situation because to do so would provide helpful information to its competitors.6 What's the difference between a stock's current market price and its intrinsic value? Do stocks have a known and "provable" intrinsic value, or might different people reach different conclusions about intrinsic values? Explain. Should a firm's managers estimate its intrinsic value or leave this estimation to outside security analysts? Explain. If an action would maximize either the current market price or the intrinsic value, but not both, which one should stockholders (as a group) want managers to maximize? Explain. Should its managers help investors improve their estimates of a firm's intrinsic value? Explain. 1.4 SOME IMPORTANT TRENDS Three important trends should be noted. First, the points noted in the preceding section have led to profound changes in business practices. Executives at Enron, WorldCom, and other companies lied when they reported financial results, leading to huge stockholder losses. These companies' CEOs later claimed not to have been aware of what was happening. As a result, Congress passed legislation that requires the CEO and chief financial officer (CFO) to certify that their firm's financial statements are accurate, and these executives could be sent to jail if it later turns out that the statements did not meet the required standards. Consequently, published statements in the future are likely to be more accurate and dependable than those in the past. A second trend is the increased globalization of business. Developments in communications technology have made it possible for firms like Wal-Mart to obtain real-time data on sales of hundreds of thousands of items in stores from China to Chicago, and to manage those stores from Bentonville, Arkansas. IBM, Microsoft, and other high-tech companies now have research labs and help desks in China, India, Romania, and the like, and the customers of Home Depot and other retailers have their telephone or e-mail questions answered by call-center operators in countries all around the globe. Moreover, many U.S. companies, 6 As we discuss in Chapter 5, many academics believe that stock prices embody all publicly available information, hence that stock prices are typically reasonably close to their intrinsic values and thus at or close to an equilibrium. However, almost no one doubts that managers have better information than the public at large, that at times stock prices and equilibrium values diverge, and thus that stocks can be temporarily undervalued or overvalued, as we suggest in the graph in Figure 1-1. 12 Part 1 Introduction to Financial Management Is Shareholder Wealth Maximization a Worldwide Goal? Most academics agree that shareholder wealth maximization should be a firm's primary goal, at least in the United States; however, it's not clear that people really know how to implement it. PricewaterhouseCoopers (PWC), a global consulting firm, conducted a survey of 82 Singapore companies to test their understanding and implementation of shareholder value concepts. Ninety percent of the respondents said their firm's primary goal was to enhance shareholder value, but only 44 percent had taken steps to achieve this goal. Moreover, almost half of the respondents who had shareholder value programs in place said they were dissatisfied with the results achieved thus far. Even so, respondents who focused on shareholder value were more likely to believe that their stock was fairly valued than those with other focuses, and 50 percent of those without a specific program said they wanted to learn more and would probably adopt one eventually. The study found that firms measure performance primarily with accounting-based measures such as the returns on assets, on equity, or on invested capital. These measures are easy to understand and thus to implement, even though they might not be the best conceptually. Compensation was tied to shareholder value, but only for mid-level managers and above. It is unclear how closely these results correspond to U.S. firms, but firms from the United States and Singapore would certainly agree on one thing: It is easier to set the goal of shareholder wealth maximization than it is to figure out how to achieve it. Source: Kalpana Rashiwala, "Low Adoption of Shareholder Value Concepts Here," The Business Times (Singapore), February 14, 2002. including Coca-Cola, ExxonMobil, GE, and IBM, generate close to half their sales and income overseas. The trend toward globalization is likely to continue, and companies that resist it will have difficulty competing in the 21st century. A third trend that's having a profound effect on financial management is ever-improving information technology (IT). These improvements are spurring globalization, and they are also changing financial management as it is practiced in the United States. Firms are collecting massive amounts of data and then using it to take much of the guesswork out of financial decisions. For example, when Wal-Mart is considering a potential site for a new store, it can draw on historical results from thousands of other stores to predict results at the proposed site, which lowers the risk of investing in the new store. These trends are reflected in this book, and everyone involved in business should recognize the trends and their implications for decisions of all types. What are three trends that affect business management in general and financial management in particular? 1.5 BUSINESS ETHICS As a result of the Enron and other recent scandals, there has been a strong push to improve business ethics. This is occurring on several fronts, from actions by New York Attorney General Elliot Spitzer and others who are suing companies for improper acts, to Congress, which has passed legislation imposing sanctions Chapter 1 An Overview of Financial Management 13 on executives who do bad things, to business schools trying to inform students about what's right and what's wrong, and about the consequences of their actions once they enter the business world. As we discussed earlier, companies benefit from good reputations and are penalized by bad ones, and the same is true for individuals. Reputations reflect the extent to which firms and people are ethical. Ethics is defined in Webster's Dictionary as "standards of conduct or moral behavior." Business ethics can be thought of as a company's attitude and conduct toward its employees, customers, community, and stockholders. High standards of ethical behavior demand that a firm treat the parties that it deals with in a fair and honest manner. A firm's commitment to business ethics can be measured by the tendency of its employees, from the top down, to adhere to laws, regulations, and moral standards relating to product safety and quality, fair employment practices, fair marketing and selling practices, the use of confidential information for personal gain, community involvement, and illegal payments to obtain business. Business Ethics A company's attitude and conduct toward its employees, customers, community, and stockholders. What Companies Are Doing Most firms today have strong codes of ethical behavior, and they also conduct training programs to ensure that employees understand proper behavior in different situations. When conflicts arise between profits and ethics, ethical considerations sometimes are so obviously important that they clearly dominate. However, in many cases the right choice is not clear. For example, suppose Norfolk Southern's managers know that its coal trains are polluting the air, but the amount of pollution is within legal limits and further reduction would be costly. Are the managers ethically bound to reduce pollution? Similarly, some time ago Merck's own research indicated that its Vioxx pain medicine might be causing heart attacks, but the evidence was not overwhelmingly strong and the product was clearly helping some patients. Over time, additional tests produced stronger and stronger evidence that Vioxx did indeed pose a significant health risk. If the company released negative but still questionable information, this would hurt sales and possibly keep some patients who would benefit from using the product. If it delayed release, more and more patients might suffer irreversible harm. At what point should Merck make the potential problem known to the public? There are no obvious answers to questions such as these, but companies must deal with them, and a failure to handle them properly can lead to severe consequences. Consequences of Unethical Behavior Over the past few years ethical lapses have led to a number of bankruptcies. The recent collapses of Enron and WorldCom, as well as the accounting firm Arthur Andersen, dramatically illustrate how unethical behavior can lead to a firm's rapid decline. In all three cases, top executives came under fire for misleading accounting practices that led to overstated profits. Enron and WorldCom executives were busily selling their stock at the same time they were recommending the stock to employees and outside investors. Thus, senior executives reaped millions before the stock declined, while lower-level employees and outside investors were left holding the bag. Some of these executives are now in jail, and others will probably follow. Moreover, the financial institutions that facilitated these frauds, including Merrill Lynch and Citigroup, have been fined hundreds of millions of dollars, and more lawsuits are on the way. These frauds also contributed to fatal wounds to other companies and even whole industries. For example, WorldCom understated its costs by some $11 billion. It used those artifically low costs when it set prices to its customers, and as 14 Part 1 Introduction to Financial Management a result its prices were the lowest in the industry. This allowed it to increase its market share and growth rate. Its earnings per share were badly overstated, and this caused its stock price to be way too high. Even though WorldCom's results were built on lies, they still had a tremendous effect on the industry. For example, AT&T's top executives, believing WorldCom's numbers, put pressure on their own managers to match WorldCom's costs and prices, but that was not possible without cheating. AT&T cut back on important projects, put far too much stress on its employees, and ended up ruining a wonderful 100-year-old company. A similar situation occurred in the energy industry as a result of Enron's cheating. All of this caused many investors to lose faith in American business and to turn away from the stock market, which made it difficult for firms to raise the capital they needed to grow, create jobs, and stimulate our economy. So, unethical actions can have consequences far beyond the companies that perpetrate them. This raises a question: Are companies unethical, or is it just some of their employees? That issue came up in the case of Arthur Andersen, the accounting firm that audited Enron, WorldCom, and several other companies that committed accounting fraud. Evidence showed that some Andersen accountants helped perpetrate the frauds. Its top managers argued that while some rogue employees did bad things, the firm's 85,000 other employees, and the firm itself, were innocent. The U.S. Justice Department disagreed, concluding that the firm itself was guilty because it fostered a climate where unethical behavior was permitted, and it built an incentive system that made such behavior profitable to both the perpetrators and the firm itself. As a result, Anderson was put out of business, its partners lost millions of dollars, and its 85,000 employees lost their jobs. In most other cases, individuals rather than firms were tried, and while the firms survived, they suffered reputational damage that greatly lowered their future profit potential and value. How Should Employees Deal with Unethical Behavior? Far too often the desire for stock options, bonuses, and promotions drives managers to take unethical actions, including fudging the books to make profits in the manager's division look good, holding back information about bad products that would depress sales, and failing to take costly but needed measures to protect the environment. Generally these acts don't rise to the level of an Enron or WorldCom, but they are still bad. If questionable things are going on, who should take action, and what should that action be? Obviously, in situations like Enron and WorldCom, where fraud was being perpetrated at or close to the top, senior managers knew about it. In other cases, the problem is caused by a midlevel manager trying to boost his unit's profits and thus his bonus. In all cases, though, at least some lower-level employees are aware of what's happening, and they may even be ordered to take fraudulent actions. Should the lower-level employees obey their boss's orders, refuse to obey those orders, or report the situation to a higher authority, such as the company's board of directors, its auditors, or a federal prosecutor? In the WorldCom and Enron cases, it was clear to a number of employees that unethical and illegal acts were being committed, but in cases like Merck's Vioxx product, the situation is less clear. If early evidence that Vioxx led to heart attacks was quite weak but evidence of its pain reduction was strong, then it would probably not be appropriate to sound an alarm. However, as evidence accumulates, at some point the public should be given a strong warning, or the product should be taken off the market. But judgment comes into play when Chapter 1 An Overview of Financial Management 15 Protection for Whistle-Blowers As a result of the recent accounting and other frauds, Congress in 2002 passed the Sarbanes-Oxley Act, which codified certain rules pertaining to corporate behavior. One provision in the bill was designed to protect "whistle-blowers," or lower-level employees who sound an alarm over actions by their superiors. Employees who report improper actions are often fired or otherwise penalized, and this keeps many people from reporting things that should be investigated. The Sarbanes-Oxley provision was designed to alleviate this problem--if someone reports a corporate wrong-doing and is later penalized, he or she can ask the Occupational Safety and Health Administration (OSHA) to investigate the situation, and if the employee was improperly penalized, the company can be required to reinstate the person, along with back pay and a sizable penalty award. According to The Wall Street Journal, some big awards have been handed out, and a National Whistle-Blower Center has been established to help people sue companies.a It's still dangerous to blow a whistle, but less so than before the Sarbanes-Oxley Act was passed. Deborah Solomon and Kara Scannell, "SEC Is Urged to Enforce `Whistle-Blower' Provision," The Wall Street Journal, November 15, 2004, p. A6. a deciding on what action to take and when to take it. If a lower-level employee thinks that the product should be pulled but his or her boss disagrees, what should the employee do? If an employee goes ahead and sounds the alarm, he or she might be in trouble regardless of the merits of the case. If the alarm is false, then the company will have been harmed and nothing will have been gained. In that case, the employee will probably lose his or her job. Even if the employee is correct, his or her career may still be ruined, because some companies, or at least some bosses, don't like "disloyal, troublemaking" employees. Such situations arise frequently, and in contexts ranging from accounting fraud to product liability and environmental cases. Employees jeopardize their jobs if they come forward over their bosses' objections, but if they don't they can suffer emotional problems and also contribute to the downfall of their companies and the accompanying loss of jobs and savings. Moreover, if they obey orders that they know are illegal, they can end up going to jail. Indeed, in most of the scandals that have come to trial, the lower-level people who physically did the bad deeds have received longer jail sentences than the bosses who told them what to do. So, employees can be stuck between a rock and a hard place, that is, doing what they should do and possibly losing their jobs versus going along with the boss and possibly ending up in jail. This discussion shows why ethics is such an important consideration in both business and business schools, and why we are concerned with it in this book. How would you define "business ethics"? Can a firm's incentive compensation plan lead to unethical behavior? Explain. Unethical acts are generally committed by unethical people. What are some things companies can do to help ensure that their employees act ethically? 16 Part 1 Introduction to Financial Management 1.6 CONFLICTS BETWEEN MANAGERS AND STOCKHOLDERS7 It has long been recognized that managers' personal goals may compete with shareholder wealth maximization. In particular, managers might be more interested in maximizing their own wealth rather than their stockholders' wealth, hence pay themselves excessive salaries. For example, Disney paid its former president, Michael Ovitz, $140 million as a severance package after just 14 months on the job--$140 million to go away--because he and Disney CEO Michael Eisner were having disagreements. Eisner himself was also handsomely compensated the year Ovitz was fired--a $750,000 base salary, plus a $9.9 million bonus, plus a $565 million profit from stock options, for a total of just over $575 million. As another example of corporate excesses, Tyco CEO Dennis Kozlowski spent more than $2 million of the company's money on a birthday party for his wife. Neither the Disney executives' pay nor Kozlowski's expenditures seem consistent with shareholder wealth maximization. Still, good executive compensation plans can motivate managers to act in their stockholders' best interests. Useful motivational tools include (1) reasonable compensation packages; (2) direct intervention by shareholders, including firing managers who don't perform well; and (3) the threat of a takeover. The compensation package should be sufficient to attract and retain able managers but not go beyond what is needed. Also, compensation should be structured so that managers are rewarded on the basis of the stock's performance over the long run, not the stock's price on an option exercise date. This means that options (or direct stock awards) should be phased in over a number of years so managers will have an incentive to keep the stock price high over time. If the intrinsic value could be measured in an objective and verifiable manner, then performance pay could be based on changes in intrinsic value. However, because intrinsic value is not observable, compensation must be based on the stock's market price--but the price used should be an average over time rather than on a spot date. Stockholders can intervene directly with managers. Years ago most stock was owned by individuals, but today the majority is owned by institutional investors such as insurance companies, pension funds, and mutual funds. These institutional money managers have the clout to exercise considerable influence over firms' operations. First, they can talk with managers and make suggestions about how the business should be run. In effect, institutional investors such as Calpers (California Public Employees Retirement System, with $165 billion of assets) and TIAACREF (a retirement plan originally set up for professors at private colleges that now has more than $300 billion of assets) act as lobbyists for the body of stockholders. When such large stockholders speak, companies listen. Second, any shareholder who has owned $2,000 of a company's stock for one year can sponsor a proposal that must be voted on at the annual stockholders' meeting, even if management opposes the proposal. Although shareholdersponsored proposals are nonbinding, the results of such votes are clearly heard by top management. Stockholder intervention can range from making suggestions for improving sales to threatening to fire the management team. Until recently, the probability of a large firm's management being ousted by its stockholders was so remote 7 These conflicts are studied under the heading of agency theory in the finance literature. The classic work on agency theory is Michael C. Jensen and William H. Meckling, "Theory of the Firm, Managerial Behavior, Agency Costs, and Ownership Structure," Journal of Financial Economics, October 1976, pp. 305360. Chapter 1 An Overview of Financial Management 17 that it posed little threat. Most firms' shares were so widely distributed, and management had so much control over the voting mechanism, that it was virtually impossible for dissident stockholders to get the votes needed to overthrow a management team. However, that situation has changed. In recent years the top executives of AT&T, Coca-Cola, Fannie Mae, General Motors, IBM, and Xerox, to name a few, have been forced out. Also, Tyco's Kozlowski is gone and Disney's Eisner is under pressure and will soon be leaving. All of these departures were due to their firm's poor performance. If a firm's stock is undervalued, then corporate raiders will see it to be a bargain and will attempt to capture the firm in a hostile takeover. If the raid is successful, the target's executives will almost certainly be fired. This situation gives managers a strong incentive to take actions to maximize their stock's price. In the words of one executive, "If you want to keep your job, never let your stock sell at a bargain price." Again, note that the price managers should be trying to maximize is not the price on a specific day. Rather, it is the average price over the long run, which will be maximized if management focuses on the stock's intrinsic value. However, managers must communicate effectively with stockholders (without divulging information that would aid their competitors) in order to keep the actual price close to the intrinsic value. It's bad for both stockholders and managers for the intrinsic value to be high but the actual price low, because then a raider may swoop in, buy the company at a bargain price, and fire the managers. To repeat our earlier message: Managers should try to maximize their stock's intrinsic value and then communicate effectively with stockholders. That will cause the intrinsic value to be high and the actual stock price to remain close to the intrinsic value over time. Because the intrinsic value cannot be observed, it is impossible to know if it is really being maximized. Still, as we will discuss in Chapter 9, there are procedures for estimating a stock's value. Managers can then use these valuation models to analyze alternative courses of action in terms of how they are likely to affect the estimated value. This type of value-based management is not as precise as we would like, but it is the best way to run a business. Corporate Raider An individual who targets a corporation for takeover because it is undervalued. Hostile Takeover The acquisition of a company over the opposition of its management. What are three techniques stockholders can use to motivate managers to try to maximize their stock's long-run price? Should managers focus directly on the actual stock price, on the stock's intrinsic value, or are both important? Explain. 1.7 THE ROLE OF FINANCE IN THE ORGANIZATION The organizational structure of a typical corporation has the board of directors at the top, and the chairman of the board is the person most responsible for the firm's strategic policies. Under the chairman's guidance, the board sets policy, but implementing that policy is the responsibility of the firm's management. Note too that the boards of most publicly owned corporations have a compensation committee that consists of three outside (nonemployee) directors who set the compensation package for the senior officers. The compensation committee looks at factors such as the firm's stock price performance relative to the market as a whole and other firms in the same industry, the growth rate in earnings per share, and the compensation of executives in other similar firms. Obviously, this is a very important committee. Chairman of the Board The person most responsible for the firm's strategic policies. Compensation Committee A committee that consists of three outside (nonemployee) directors who set the compensation package for senior officers. 18 Part 1 Introduction to Financial Management Chief Executive Officer (CEO) Heads the management team, and ideally is separate from chairman of the board. Chief Operating Officer (COO) In charge of the firm's actual operations. Chief Financial Officer (CFO) Responsible for the accounting system, raising capital, and evaluating major investment decisions and the effectiveness of operations. The management team is headed by the chief executive officer (CEO). Sometimes the chairman of the board is also the CEO, but corporate governance experts, including the New York Stock Exchange, think those two offices should be separated, and there is a clear trend toward separation. Directly below the CEO is the chief operating officer (COO) and the chief financial officer (CFO). The COO is in charge of actual operations, including producing and selling the firm's products. The CFO is responsible for the accounting system, for raising any capital the firm needs, for evaluating the effectiveness of operations in relation to other firms in the industry, and for evaluating all major investment decisions, including proposed new plants, stores, and the like. All of the CFO's duties are important if the firm is to maximize shareholder wealth. The accounting system must provide good information if the firm is to be run efficiently-- management must know the true costs in order to make good decisions. Also, the accounting system must provide investors with accurate and timely information--if investors don't trust the reported numbers, they will avoid the stock and its value won't be maximized. We don't go deeply into accounting mechanics in this text, but we do explain how accounting numbers are used to make good internal decisions and by investors when they value securities. It is also important that the firm be financed in an optimal manner--it should use the value-maximizing mix of debt and equity. Finally, the financial staff must evaluate the various departments and divisions, including their proposed capital expenditures, to make sure the firm is operating efficiently and making investments that will enhance shareholders' wealth. What are the principal responsibilities of the board of directors and the CEO? What are the principal responsibilities of the CFO? Tying It All Together This chapter provides a broad overview of financial management. Management's goal should be to maximize the long-run value of the stock, which means the intrinsic value as measured by the average stock price over time. To maximize value, firms must develop products that consumers want, produce them efficiently, sell them at competitive prices, and observe laws relating to corporate behavior. If they are successful at maximizing the stock's value, they will also be contributing to social welfare and our citizens' well-being. In the 1990s corporations tended to give executives stock options that could be exercised and then sold on a specific date. That led some managers to try to maximize the stock price on the option exercise day, not the long-run price that would be in their stockholders' best interests. This problem can be corrected by giving options that are phased in and can be exercised over time, which will cause managers to focus on the stock's long-run intrinsic value. Chapter 1 An Overview of Financial Management 19 Businesses can be organized as proprietorships, partnerships, or corporations. The vast majority of all business is done by corporations, and the most successful firms end up as corporations. Therefore, we focus on corporations in the book. We also discussed some new developments that are affecting all businesses. The first is the focus on business ethics that resulted from a series of scandals in the late 1990s. The second is the trend toward globalization, which is changing the way companies do business. And the third is the continuing development of new technology, which is also changing the way business is done. The primary tasks of the CFO are (1) to make sure that the accounting system provides "good" numbers for internal decisions and to investors, (2) to ensure that the firm is financed in the proper manner, (3) to evaluate the operating units to make sure they are performing in an optimal manner, and (4) to evaluate all proposed capital expenditures to make sure that they will increase the firm's value. In the balance of the book we discuss exactly how financial managers carry out these tasks. SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) ST-1 Key terms Define each of the following terms: a. Proprietorship; partnership; corporation; S corporation b. Stockholder wealth maximization c. Intrinsic value; market price d. Equilibrium; marginal investor e. Business ethics f. Corporate raider; hostile takeover g. Chairman of the board; compensation committee h. CEO; COO; CFO QUESTIONS 1-1 1-2 1-3 If you bought a share of stock, what would you expect to receive, when would you expect to receive it, and would you be certain that your expectations would be met? Are the stocks of different companies equally risky? If not, what are some factors that would cause a company's stock to be viewed as being relatively risky? If most investors expect the same cash flows from Companies A and B but are more confident that A's cash flows will be close to their expected value, which should have the higher stock price? Explain. Are all corporate projects equally risky, and if not, how do a firm's investment decisions affect the riskiness of its stock? What is a firm's intrinsic value? Its current stock price? Is the stock's "true long-run value" more closely related to its intrinsic value or its current price? When is a stock said to be in equilibrium? At any given time, would you guess that most stocks are in equilibrium as you defined it? Explain. 1-4 1-5 1-6 20 Part 1 Introduction to Financial Management 1-7 Suppose three completely honest individuals gave you their estimates of Stock X's intrinsic value. One is your current girlfriend or boyfriend, the second is a professional security analyst with an excellent reputation on Wall Street, and the third is Company X's CFO. If the three estimates differed, which one would you have the most confidence in? Why? Is it better for a firm's actual stock price in the market to be under, over, or equal to its intrinsic value? Would your answer be the same from the standpoints of both stockholders in general and a CEO who is about to exercise a million dollars in options and then retire? Explain. If a company's board of directors wants management to maximize shareholder wealth, should the CEO's compensation be set as a fixed dollar amount, or should it depend on how well the firm performs? If it is to be based on performance, how should performance be measured? Would it be easier to measure performance by the growth rate in reported profits or the growth rate in the stock's intrinsic value? Which would be the better performance measure? Why? What are the three principal forms of business organization? What are the advantages and disadvantages of each? Should stockholder wealth maximization be thought of as a long-term or a short-term goal--for example, if one action would probably increase the firm's stock price from a current level of $20 to $25 in 6 months and then to $30 in 5 years but another action would probably keep the stock at $20 for several years but then increase it to $40 in 5 years, which action would be better? Can you think of some specific corporate actions that might have these general tendencies? What are some actions stockholders can take to ensure that management's and stockholders' interests are aligned? The president of Southern Semiconductor Corporation (SSC) made this statement in the company's annual report: "SSC's primary goal is to increase the value of our common stockholders' equity." Later in the report, the following announcements were made: a. The company contributed $1.5 million to the symphony orchestra in Birmingham, Alabama, its headquarters city. b. The company is spending $500 million to open a new plant and expand operations in China. No profits will be produced by the Chinese operation for 4 years, so earnings will be depressed during this period versus what they would have been had the decision not been made to expand in that market. c. The company holds about half of its assets in the form of U.S. Treasury bonds, and it keeps these funds available for use in emergencies. In the future, though, SSC plans to shift its emergency funds from Treasury bonds to common stocks. Discuss how SSC's stockholders might view each of these actions, and how they might affect the stock price. 1-8 1-9 1-10 1-11 1-12 1-13 1-14 Investors generally can make one vote for each share of stock they hold. Teacher's Insurance and Annuity AssociationCollege Retirement Equity Fund (TIAACREF) is the largest institutional shareholder in the United States, hence it holds many shares and has more votes than any other organization. Traditionally, this fund has acted as a passive investor, just going along with management. However, back in 1993 it mailed a notice to all 1,500 companies whose stocks it held that henceforth it planned to actively intervene if, in its opinion, management was not performing well. Its goal was to improve corporate performance so as to boost the prices of the stocks it held. It also wanted to encourage corporate boards to appoint a majority of independent (outside) directors, and it stated that it would vote against any directors of firms that "don't have an effective, independent board that can challenge the CEO." In the past, TIAACREF responded to poor performance by "voting with its feet," which means selling stocks that were not doing well. However, by 1993 that position had become difficult for two reasons. First, the fund invested a large part of its assets in "index funds," which hold stocks in accordance with their percentage value in the broad stock market. Furthermore, TIAACREF owns such large blocks of stocks in many companies that if it tried to sell out, this would severely depress the prices of those stocks. Thus, TIAACREF is locked in to a large extent, and that led to its decision to become a more active investor. Chapter 1 An Overview of Financial Management 21 a. b. Is TIAACREF an ordinary shareholder? Explain. Due to its asset size, TIAACREF owns many shares in a number of companies. The fund's management plans to vote those shares. However, TIAACREF is itself owned by many thousands of investors. Should the fund's managers vote its shares, or should it pass those votes, on a pro rata basis, back to its own shareholders? Explain. 1-15 Edmund Enterprises recently made a large investment to upgrade its technology. While these improvements won't have much of an effect on performance in the short run, they are expected to reduce future costs significantly. What effect will this investment have on Edmund Enterprises' earnings per share this year? What effect might this investment have on the company's intrinsic value and stock price? Suppose you were a member of Company X's board of directors and chairman of the company's compensation committee. What factors should your committee consider when setting the CEO's compensation? Should the compensation consist of a dollar salary, stock options that depend on the firm's performance, or a mix of the two? If "performance" is to be considered, how should it be measured? Think of both theoretical and practical (that is, measurement) considerations. If you were also a vice president of Company X, might your actions be different than if you were the CEO of some other company? Suppose you are a director of an energy company that has three divisions--natural gas, oil, and retail (gas stations). These divisions operate independently from one another, but the division managers all report to the firm's CEO. If you were on the compensation committee as discussed in question 1-16 and your committee was asked to set the compensation for the three division managers, would you use the same criteria as you would use for the firm's CEO? Explain your reasoning. 1-16 1-17 Please go to the ThomsonNOW Web site to access the Cyberproblems. FUNDAMENTAL CONCEPTS IN FINANCIAL MANAGEMENT P A R T 2 2 3 4 5 Time Value of Money Financial Statements, Cash Flow, and Taxes Analysis of Financial Statements Financial Markets and Institutions C H APTE R 2 TIME VALUE OF MONEY Will You Be Able to Retire? Your reaction to this question is probably, "First things first! I'm worried about getting a job, not about retiring!" However, understanding the retirement situation could help you land a job, because (1) this is an important issue today, (2) employers like to hire people who know what's happening in the real world, and (3) professors often test on the time value of money with problems related to saving for future purposes, including retirement. A recent Fortune article began with some interesting facts: (1) The U.S. savings rate is the lowest of any industrial nation. (2) The ratio of U.S. workers to retirees, which was 17 to 1 in 1950, is now down to 3 to 1, and it will decline to less than 2 to 1 after 2020. (3) With so few people paying into the Social Security system and so many drawing funds out, Social Security is going to be in serious trouble. The article concluded that even people making $85,000 per year will have trouble maintaining a reasonable standard of living after they retire, and many of today's college students will have to support their parents. This is an important issue for millions of Americans, but many don't know how to deal with it. When Fortune studied the retirement issue, using the tools and techniques described in this chapter, they concluded that most Americans have been putting their heads in the sand, ignoring what is almost certainly going to be a huge personal and social problem. However, if you study this chapter carefully, you can avoid the trap that is likely to catch so many people. Excellent retirement calculators are available at http://www.ssa.gov and http://www .choosetosave.org/ calculators. These calculators allow you to input hypothetical retirement savings information, and the program shows if current retirement savings will be sufficient to meet retirement needs. Putting Things In Perspective DIGITAL VISION/ GETTY IMAGES INC. Time value analysis has many applications, including planning for retirement, valuing stocks and bonds, setting up loan payment schedules, and making corporate decisions regarding investing in new plant and equipment. In fact, of all financial concepts, time value of money is the single most important. Chapter 2 Time Value of Money 25 Indeed, time value analysis is used throughout the book, so it is vital that you understand this chapter before continuing. You need to understand basic time value concepts, but conceptual knowledge will do you little good if you can't do the required calculations. Therefore, this chapter is heavy on calculations. Also, most students studying finance have a financial or scientific calculator, and some also own or have access to a computer. Moreover, one of these tools is necessary to work many finance problems in a "reasonable" length of time. However, when they start on this chapter, many students don't know how to use the time value functions in their calculator or computer. If you are in that situation, you will find yourself simultaneously studying concepts and trying to learn to use your calculator, and you will need more time to cover this chapter than you might expect.1 2.1 TIME LINES The first step in time value analysis is to set up a time line, which will help you visualize what's happening in a particular problem. To illustrate, consider the following diagram, where PV represents $100 that is on hand today and FV is the value that will be in the account on a future date: Periods Cash 0 5% 1 2 3 FV = ? Time Line An important tool used in time value analysis; it is a graphical representation used to show the timing of cash flows. PV = $100 The intervals from 0 to 1, 1 to 2, and 2 to 3 are time periods such as years or months. Time 0 is today, and it is the beginning of Period 1; Time 1 is one period from today, and it is both the end of Period 1 and the beginning of Period 2; and so on. Although the periods are often years, periods can also be quarters or months or even days. Note that each tick mark corresponds to both the end of one period and the beginning of the next one. Thus, if the periods are years, the tick mark at Time 2 represents both the end of Year 2 and the beginning of Year 3. Cash flows are shown directly below the tick marks, and the relevant interest rate is shown just above the time line. Unknown cash flows, which you are trying to find, are indicated by question marks. Here the interest rate is 5 percent; a single cash outflow, $100, is invested at Time 0; and the Time 3 value is an unknown inflow. In this example, cash flows occur only at Times 0 and 3, with no flows at Times 1 or 2. Note that in our example the interest rate is constant for all three years. That condition is generally true, but if it were not then we would show different interest rates for the different periods. Time lines are essential when you are first learning time value concepts, but even experts use them to analyze complex finance problems, and we use them throughout the book. We begin each problem by setting up a time line to show what's happening, after which we provide an equation that must be solved to find the answer, and then we explain how to use a regular calculator, a financial calculator, and a spreadsheet to find the answer. 1 Calculator manuals tend to be long and complicated, partly because they cover a number of topics that aren't required in the basic finance course. Therefore, we provide, on the ThomsonNOW Web site, tutorials for the most commonly used calculators. The tutorials are keyed to this chapter, and they show exactly how to do the required calculations. If you don't know how to use your calculator, go to the ThomsonNOW Web site, get the relevant tutorial, and go through it as you study the chapter. 26 Part 2 Fundamental Concepts in Financial Management Do time lines deal only with years or could other periods be used? Set up a time line to illustrate the following situation: You currently have $2,000 in a three-year certificate of deposit (CD) that pays a guaranteed 4 percent annually. 2.2 FUTURE VALUES Future Value (FV) The amount to which a cash flow or series of cash flows will grow over a given period of time when compounded at a given interest rate. Present Value (PV) The value today of a future cash flow or series of cash flows. Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when compound interest is applied. A dollar in hand today is worth more than a dollar to be received in the future because, if you had it now, you could invest it, earn interest, and end up with more than a dollar in the future. The process of going to future values (FVs) from present values (PVs) is called compounding. To illustrate, refer back to our three-year time line and assume that you plan to deposit $100 in a bank that pays a guaranteed 5 percent interest each year. How much would you have at the end of Year 3? We first define some terms, after which we set up a time line and show how the future value is calculated. PV FVN Present value, or beginning amount. In our example, PV $100. Future value, or ending amount, of your account after N periods. Whereas PV is the value now, or the present value, FVN is the value N periods into the future, after the interest earned has been added to the account. Cash flow. Cash flows can be positive or negative. The cash flow for a particular period is often given a subscript, CFt, where t is the period. Thus, CF0 PV the cash flow at Time 0, whereas CF3 would be the cash flow at the end of Period 3. Interest rate earned per year. Sometimes a lowercase "i" is used. Interest earned is based on the balance at the beginning of each year, and we assume that it is paid at the end of the year. Here I 5%, or, expressed as a decimal, 0.05. Throughout this chapter, we designate the interest rate as I because that symbol (or I/YR, for interest rate per year) is used on most financial calculators. Note, though, that in later chapters we use the symbol "r" to denote rates because r (for rate of return) is used more often in the finance literature. Note too that in this chapter we generally assume that interest payments are guaranteed by the U.S. government, hence they are certain. In later chapters we will consider risky investments, where the interest rate actually earned might differ from its expected level. Dollars of interest earned during the year Beginning amount I. In our example, INT $100(0.05) $5. Number of periods involved in the analysis. In our example N 3. Sometimes the number of periods is designated with a lowercase "n," so both N and n indicate number of periods. CFt I INT N We can use four different procedures to solve time value problems.2 These methods are described in the following sections. 2 A fifth procedure, using tables that show "interest factors," was used before financial calculators and computers became available. Now, though, calculators and spreadsheets such as Excel are programmed to calculate the specific factor needed for a given problem and then to use it to find the FV. This is much more efficient than using the tables. Moreover, calculators and spreadsheets can handle fractional periods and fractional interest rates, like the FV of $100 after 3.75 years when the interest rate is 5.375 percent, whereas tables provide numbers only for specific periods and rates. For these reasons, tables are not used in business today; hence we do not discuss them in the text. Chapter 2 Time Value of Money 27 Simple versus Compound Interest As noted in the text, when interest is earned on the interest earned in prior periods, as was true in our example and is always true when we apply Equation 2-1, this is called compound interest. If interest is not earned on interest, then we have simple interest. The formula for FV with simple interest is FV = PV + PV(I)(N), so in our example FV would have been $100 + $100(0.05)(3) = $100 + $15 = $115 based on simple interest. Most financial contracts are based on compound interest, but in legal proceedings the law often specifies that simple interest must be used. For example, Maris Distributing, a company founded by home run king Roger Maris, won a lawsuit against Anheuser-Busch (A-B) because A-B had breached a contract and taken away Maris's franchise to sell Budweiser beer. The judge awarded Maris $50 million plus interest at 10 percent from 1997 (when A-B breached the contract) until the payment is actually made. The interest award was based on simple interest, which as of 2004 had raised the total from $50 million to $50 million + 0.10($50 million)(7 years) = $85 million. If the law had allowed compound interest, the award would have totaled ($50 million)(1.10)7 = $97.44 million, or $12.44 million more. This legal procedure dates back to the days before we had calculators and computers. The law moves slowly! 1. Step-by-Step Approach The time line used to find the FV of $100 compounded for three years at 5 percent, along with some calculations, is shown below: Multiply the initial amount, and each succeeding amount, by (1 Time Amount at beginning of period 0 $100.00 5% Compound Interest Occurs when interest is earned on prior periods' interest. Simple Interest Occurs when interest is not earned on interest. I) (1.05): 3 $115.76 1 $105.00 2 $110.25 0: You start with $100 in the account--this is shown at t You earn $100(0.05) $5 of interest during the first year, so the amount at the end of Year 1 (or t 1) is $100 $5 $105. You begin the second year with $105, earn 0.05($105) $5.25 on the now larger beginning-of-period amount, and end the year with $110.25. Interest during Year 2 is $5.25, and it is higher than the first year's interest, $5, because you earned $5(0.05) $0.25 interest on the first year's interest. This is called "compounding," and when interest is earned on interest, this is called "compound interest." This process continues, and because the beginning balance is higher in each successive year, the interest earned each year increases. The total interest earned, $15.76, is reflected in the final balance, $115.76. The step-by-step approach is useful because it shows exactly what is happening. However, this approach is time-consuming, especially if a number of years are involved, so streamlined procedures have been developed. 2. Formula Approach In the step-by-step approach, we multiply the amount at the beginning of each period by (1 I) (1.05). If N 3, then we multiply by (1 I) three different times, which is the same as multiplying the beginning amount by (1 I)3. This concept can be extended, and the result is this key equation: 28 Part 2 Fundamental Concepts in Financial Management FVN FV3 PV(1 I)N $115.76 (2-1) We can apply Equation 2-1 to find the FV in our example: $100(1.05)3 Equation 2-1 can be used with any calculator that has an exponential function, making it easy to find FVs, no matter how many years are involved. 3. Financial Calculators Financial calculators are extremely helpful when working time value problems. Their manuals explain calculators in detail, and we provide summaries of the features needed to work the problems in this book for several popular calculators on the ThomsonNOW Web site. Also, see the box entitled "Hints on Using Financial Calculators" for suggestions that will help you avoid some common mistakes. If you are not yet familiar with your calculator, we recommend that you go through our tutorial as you study this chapter. First, note that financial calculators have five keys that correspond to the five variables in the basic time value equations. We show the inputs for our example above the keys and the output, the FV, below its key. Because there are no periodic payments, we enter 0 for PMT. We describe the keys in more detail below the diagram. 3 5 100 0 N I/YR PV PMT FV 115.76 N I/YR PV PMT FV Number of periods. Some calculators use n rather than N. Interest rate per period. Some calculators use i or I rather than I/YR. Present value. In our example we begin by making a deposit, which is an outflow, so the PV should be entered with a negative sign. On most calculators you must enter the 100, then press the / key to switch from 100 to 100. If you enter 100 directly, this will subtract 100 from the last number in the calculator and give you an incorrect answer. Payment. This key is used if we have a series of equal, or constant, payments. Because there are no such payments in our illustrative problem, we enter PMT 0. We will use the PMT key when we discuss annuities later in this chapter. Future value. In this example, the FV is positive because we entered the PV as a negative number. If we had entered the 100 as a positive number, then the FV would have been negative. As noted in our example, you first enter the known values (N, I/YR, PMT, and PV) and then press the FV key to get the answer, 115.76. Again, note that if you entered the PV as 100 without a minus sign, the FV would be given as a negative. The calculator assumes that either the PV or the FV is negative. This should not be confusing if you think about what you are doing. 4. Spreadsheets3 Students generally use calculators for homework and exam problems, but in business people generally use spreadsheets for problems that involve the time 3 If you have never worked with spreadsheets, you might want to skip this section. However, you might want to go through it and refer to this chapter's Excel model to get an idea of how spreadsheets work. Chapter 2 Time Value of Money 29 Hints on Using Financial Calculators When using a financial calculator, make sure your machine is set up as indicated below. Refer to your calculator manual or to our calculator tutorial on the ThomsonNOW Web site for information on setting up your calculator. One payment per period. Many calculators "come out of the box" assuming that 12 payments are made per year; that is, they assume monthly payments. However, in this book we generally deal with problems where only one payment is made each year. Therefore, you should set your calculator at one payment per year and leave it there. See our tutorial or your calculator manual if you need assistance. End mode. With most contracts, payments are made at the end of each period. However, some contracts call for payments at the beginning of each period. You can switch between "End Mode" and "Begin Mode," depending on the problem you are solving. Because most of the problems in this book call for end-of-period payments, you should return your calculator to End Mode after you work a problem where payments are made at the beginning of periods. Negative sign for outflows. Outflows must be entered as negative numbers. This generally means typing the outflow as a positive number and then pressing the +/ key to convert from + to before hitting the enter key. Decimal places. With most calculators, you can specify from 0 to 11 decimal places. When working with dollars, we generally specify two decimal places. When dealing with interest rates, we generally specify two places if the rate is expressed as a percentage, like 5.25 percent, but we specify four places if the rate is expressed as a decimal, like 0.0525. Interest rates. For arithmetic operations with a nonfinancial calculator, the 0.0525 must be used, but with a financial calculator you must enter 5.25, not .0525, because financial calculators assume that rates are stated as percentages. value of money (TVM). Spreadsheets show in detail what is happening, and they help us reduce both conceptual and data-entry errors. The spreadsheet discussion can be skipped without loss of continuity, but if you understand the basics of Excel and have access to a computer, we recommend that you go through this section. Even if you aren't familiar with spreadsheets, our discussion will still give you an idea of how they operate. We used Excel to create Table 2-1, which summarizes the four methods for finding the FV and shows the spreadsheet formulas toward the bottom. Note that spreadsheets can be used to do calculations, but they can also be used like a word processor to create exhibits like Table 2-1, which includes text, drawings, and calculations. The letters across the top designate columns, the numbers to the left designate rows, and the rows and columns jointly designate cells. Thus, C14 is the cell where we specify the $100 investment, C15 shows the interest rate, and C16 shows the number of periods. We then created a time line on Rows 17 to 19, and on Row 21 we have Excel go through the step-by-step calculations, multiplying the beginning-of-year values by (1 I) to find the compounded value at the end of each period. Cell G21 shows the final result. Then, on Row 23, we illustrate the formula approach, using Excel to solve Equation 2-1 and find the FV, $115.76. Next, on Rows 25 to 27, we show a picture of the calculator solution. Finally, on Rows 29 and 30 we use Excel's built-in FV function to find the answers given in Cells G29 and G30. The G29 answer is based on fixed inputs while the G30 answer is based on cell references, which makes it easy to change inputs and see the effects on the output. Table 2-1 demonstrates that all four methods get the same result, but they use different calculating procedures. It also shows that with Excel all the inputs 30 Part 2 Fundamental Concepts in Financial Management TA B L E 2 - 1 Summary of Future Value Calculations are shown in one place, which makes checking data entries relatively easy. Finally, it shows that Excel can be used to create exhibits, which are quite important in the real world. In business, it's often as important to explain what you are doing as it is to "get the right answer," because if decision makers don't understand your analysis, they may well reject your recommendations. Graphic View of the Compounding Process Figure 2-1 shows how a $1 investment grows over time at different interest rates. We made the curves by solving Equation 2-1 with different values for N and I. The interest rate is a growth rate: If a sum is deposited and earns 5 percent interest per year, then the funds on deposit will grow by 5 percent per year. Note also that time value concepts can be applied to anything that grows--sales, population, earnings per share, or your future salary. Explain why this statement is true: "A dollar in hand today is worth more than a dollar to be received next year." What is compounding? What's the difference between simple interest and compound interest? What would the future value of $100 be after five years at 10 percent compound interest? At 10 percent simple interest? ($161.05; $150.00) Suppose you currently have $2,000 and plan to purchase a threeyear certificate of deposit (CD) that pays 4 percent interest compounded annually. How much will you have when the CD matures? Chapter 2 Time Value of Money 31 FIGURE 2-1 Growth of $1 at Various Interest Rates and Time Periods Future Value of $1 6.00 5.00 4.00 3.00 2.00 1.00 I = 0% 0 1 2 3 4 5 6 7 8 9 10 Periods I = 10% I = 5% I = 20% How would your answer change if the interest rate were 5 percent, or 6 percent, or 20 percent? ($2,249.73; $2,315.25; $2,382.03; $3,456.00) Hint: With a calculator, enter N 3, I/YR 4, PV 2000, and PMT 0, then press FV to get 2,249.73. Then, enter I/YR 5 to override the 4 percent and press FV again to get the second answer. In general, you can change one input at a time to see how the output changes. A company's sales in 2005 were $100 million. If sales grow at 8 percent, what will they be 10 years later, in 2015? ($215.89 million) How much would $1, growing at 5 percent per year, be worth after 100 years? What would FV be if the growth rate were 10 percent? ($131.50; $13,780.61) 2.3 PRESENT VALUES Finding a present value is the reverse of finding a future value. Indeed, we simply solve Equation 2-1, the formula for the future value, for the PV to produce the basic present value equation, 2-2: Future value Present value FVN PV PV(1 I)N (2-1) (2-2) FVN 11 I2 N We illustrate PVs with the following example. A broker offers to sell you a Treasury bond that three years from now will pay $115.76. Banks are currently 32 Part 2 Fundamental Concepts in Financial Management Opportunity Cost The rate of return you could earn on an alternative investment of similar risk. Discounting The process of finding the present value of a cash flow or a series of cash flows; discounting is the reverse of compounding. offering a guaranteed 5 percent interest on three-year certificates of deposit (CDs), and if you don't buy the bond you will buy a CD. The 5 percent rate paid on the CDs is defined as your opportunity cost, or the rate of return you could earn on an alternative investment of similar risk. Given these conditions, what's the most you should pay for the bond? We answer this question using the four methods we discussed in the last section--step-by-step, formula, calculator, and spreadsheet. Table 2-2 summarizes our results. First, recall from the future value example in the last section that if you invested $100 at 5 percent it would grow to $115.76 in three years. You would also have $115.76 after three years if you bought the T-bond. Therefore, the most you should pay for the bond is $100--this is its "fair price." If you could buy the bond for less than $100, you should buy it rather than invest in the CD. Conversely, if its price were more than $100, you should buy the CD. If the bond's price were exactly $100, you should be indifferent between the T-bond and the CD. The $100 is defined as the present value, or PV, of $115.76 due in three years when the appropriate interest rate is 5 percent. In general, the present value of a cash flow due N years in the future is the amount which, if it were on hand today, would grow to equal the given future amount. Because $100 would grow to $115.76 in three years at a 5 percent interest rate, $100 is the present value of $115.76 due in three years at a 5 percent rate. Finding present values is called discounting, and as noted above, it is the reverse of compounding--if you know the PV, you can compound to find the FV, while if you know the FV, you can discount to find the PV. The top section of Table 2-2 calculates the PV using the step-by-step approach. When we found the future value in the previous section, we worked from left to right, multiplying the initial amount and each subsequent amount TA B L E 2 - 2 Summary of Present Value Calculations Chapter 2 Time Value of Money 33 by (1 I). To find present values, we work backward, or from right to left, dividing the future value and each subsequent amount by (1 I). This procedure shows exactly what's happening, and that can be quite useful when you are working complex problems. However, it's inefficient, especially if you are dealing with a number of years. With the formula approach we use Equation 2-2, simply dividing the future value by (1 I)N. This is more efficient than the step-by-step approach, and it gives the same result. Equation 2-2 is built into financial calculators, and as shown in Table 2-2, we can find the PV by entering values for N, I/YR, PMT, and FV, and then pressing the PV key. Finally, spreadsheets have a function that's essentially the same as the calculator, which also solves Equation 2-2. The fundamental goal of financial management is to maximize the firm's value, and the value of a business (or any asset, including stocks and bonds) is the present value of its expected future cash flows. Because present value lies at the heart of the valuation process, we will have much more to say about it in the remainder of this chapter and throughout the book. Graphic View of the Discounting Process Figure 2-2 shows that the present value of a sum to be received in the future decreases and approaches zero as the payment date is extended further and further into the future and also that the present value falls faster the higher the interest rate. At relatively high rates, funds due in the future are worth very little today, and even at relatively low rates present values of sums due in the very distant future are quite small. For example, at a 20 percent discount rate, $1 million due in 100 years would be worth only $0.0121 today. This is because $0.0121 would grow to $1 million in 100 years when compounded at 20 percent. FIGURE 2-2 Present Value of $1 at Various Interest Rates and Time Periods Present Value of $1 I = 0% 1.00 0.80 I = 5% 0.60 I = 10% 0.40 I = 20% 0.20 0 10 20 30 40 50 Periods 34 Part 2 Fundamental Concepts in Financial Management What is "discounting," and how is it related to compounding? How is the future value equation (2-1) related to the present value equation (2-2)? How does the present value of a future payment change as the time to receipt is lengthened? As the interest rate increases? Suppose a U.S. government bond promises to pay $2,249.73 three years from now. If the going interest rate on three-year government bonds is 4 percent, how much is the bond worth today? How would your answer change if the bond matured in five rather than three years? What if the interest rate on the five-year bond were 6 percent rather than 4 percent? ($2,000; $1,849.11; $1,681.13) How much would $1,000,000 due in 100 years be worth today if the discount rate were 5 percent? If the discount rate were 20 percent? ($7,604.49; $0.0121) 2.4 FINDING THE INTEREST RATE, I Thus far we have used Equations 2-1 and 2-2 to find future and present values. Those equations have four variables, and if we know three of them, we can solve for the fourth. Thus, if we know PV, I, and N, then we can solve 2-1 for FV, while if we know FV, I, and N we can solve 2-2 to find PV. That's what we did in the preceding two sections. Now suppose we know PV, FV, and N, and we want to find I. For example, suppose we know that a given bond has a cost of $100 and that it will return $150 after 10 years. Thus, we know PV, FV, and N, and we want to find the rate of return we will earn if we buy the bond. Here's the situation: FV $150 $150/$100 1.5 PV(1 $100(1 (1 (1 I)N I)10 I)10 I)10 Unfortunately, we can't factor I out to produce as simple a formula as we could for FV and PV--we can solve for I, but it requires a bit more algebra.4 However, financial calculators and spreadsheets can find interest rates almost instantly. Here's the calculator setup: 10 100 0 150 N I/YR 4.14 PV PMT FV Enter N 10, PV 100, PMT 0 because there are no payments until the security matures, and FV 150. Then, when you press the I/YR key, the calculator gives the answer, 4.14 percent. You would get this same answer with a spreadsheet. 4 Raise the left side of the equation, the 1.5, to the power 1/N number is 1 plus the interest rate, so the interest rate is 0.0414 1/10 0.1, getting 1.0414. That 4.14%. Chapter 2 Time Value of Money 35 The U.S. Treasury offers to sell you a bond for $585.43. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond for $585.43? What rate would you earn if you could buy the bond for $550? For $600? (5.5%; 6.16%; 5.24%) Microsoft earned $0.12 per share in 1994. Ten years later, in 2004, it earned $1.04. What was the growth rate in Microsoft's earnings per share (EPS) over the 10-year period? If EPS in 2004 had been $0.65 rather than $1.04, what would the growth rate have been? (24.1%; 18.41%) 2.5 FINDING THE NUMBER OF YEARS, N We sometimes need to know how long it will take to accumulate a given sum of money, given our beginning funds and the rate we will earn on those funds. For example, suppose we believe that we could retire comfortably if we had $1 million, and we want to find how long it will take us to have $1 million, assuming we now have $500,000 invested at 4.5 percent. We cannot use a simple formula-- the situation is like that with interest rates. We could set up a formula that uses logarithms, but calculators and spreadsheets can find N very quickly. Here's the calculator setup: 4.5 500000 0 1000000 N 15.7473 I/YR PV PMT FV Enter I/YR 4.5, PV 500000, PMT 0, and FV 1000000. Then, when we press the N key, we get the answer, 15.7473 years. If you plug N 15.7473 into the FV formula, you can prove that this is indeed the correct number of years: FV PV(1 I)N $500,000(1.045)15.7473 $1,000,000 We would also get N 15.7473 with a spreadsheet. How long would it take $1,000 to double if it were invested in a bank that pays 6 percent per year? How long would it take if the rate were 10 percent? (11.9 years; 7.27 years) Microsoft's 2004 earnings per share were $1.04, and its growth rate during the prior 10 years was 24.1 percent per year. If that growth rate were maintained, how long would it take for Microsoft's EPS to double? (3.21 years) 2.6 ANNUITIES Thus far we have dealt with single payments, or "lump sums." However, many assets provide a series of cash inflows over time, and many obligations like auto, student, and mortgage loans require a series of payments. If the payments are equal and are made at fixed intervals, then the series is an annuity. For example, Annuity A series of equal payments at fixed intervals for a specified number of periods. 36 Part 2 Fundamental Concepts in Financial Management Ordinary (Deferred) Annuity An annuity whose payments occur at the end of each period. Annuity Due An annuity whose payments occur at the beginning of each period. $100 paid at the end of each of the next three years is a three-year annuity. If the payments occur at the end of each year, then we have an ordinary (or deferred) annuity. If the payments are made at the beginning of each year, then we have an annuity due. Ordinary annuities are more common in finance, so when we use the term "annuity" in this book, assume that the payments occur at the ends of the periods unless otherwise noted. Here are the time lines for a $100, three-year, 5 percent, ordinary annuity and for the same annuity on an annuity due basis. With the annuity due, each payment is shifted back to the left by one year. A $100 deposit will be made each year, so we show the payments with minus signs: Ordinary Annuity: Periods Payments 0 5% 1 $100 2 $100 3 $100 Annuity Due: Periods Payments 0 $100 5% 1 $100 2 $100 3 As we demonstrate in the following sections, we can find an annuity's future and present values, the interest rate built into annuity contracts, and how long it takes to reach a financial goal using an annuity. Keep in mind that annuities must have constant payments and a fixed number of periods. If these conditions don't hold, then we don't have an annuity. What's the difference between an ordinary annuity and an annuity due? Why should you rather receive an annuity due for $10,000 per year for 10 years than an otherwise similar ordinary annuity? 2.7 FUTURE VALUE OF AN ORDINARY ANNUITY The future value of an annuity can be found using the step-by-step approach or with a formula, a financial calculator, or a spreadsheet. To illustrate, consider the ordinary annuity diagrammed earlier, where you deposit $100 at the end of each year for three years and earn 5 percent per year. How much will you have at the end of the third year? The answer, $315.25, is defined as the future value of the annuity, FVAN, and it is shown in Table 2-3. As shown in the step-by-step section of the table, we compound each payment out to Time 3, then sum those compounded values to find the annuity's FV, FVA3 $315.25. The first payment earns interest for two periods, the second for one period, and the third earns no interest at all because it is made at the end of the annuity's life. This approach is straightforward, but if the annuity extends out for many years, it is cumbersome and time-consuming. FVAN The future value of an annuity over N periods. Chapter 2 Time Value of Money 37 As you can see from the time line diagram, with the step-by-step approach we apply the following equation, with N 3 and I 5%: FVAN PMT(1 $315.25 I)N-1 PMT(1 $100(1.05)1 I)N-2 PMT(1 I)N-3 $100(1.05)2 $100(1.05)0 We can generalize and streamline the equation as follows: FVAN PMT(1 I)N-1 PMT(1 PMT(1 I)N-3 . . . PMT c 11 I2 N I 1 d I)N-2 PMT(1 I)0 (2-3) The first line shows the equation in its long form, and it can be transformed to the second form, which can be used to solve annuity problems with a nonfinancial calculator.5 This equation is also built into financial calculators and TA B L E 2 - 3 Summary: Future Value of an Ordinary Annuity 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 Payment amount = PMT = Interest rate = I = Number of periods = N = Periods: Cash Flow Time Line: Step-By-Step Approach. . Multiply each payment by (1+I)N-t and sum these FVs to find FVAN : Formula Approach: FVAN = $100.00 5.00% 3 0 | 1 | $100 2 | $100 3 | $100 $100.00 $105. 5.00 $110.25 $315.25 PMT x (1+ I )N - 1 I 5 I/YR = $315.25 Calculator Approach: 3 N $0 PV $100.00 PMT FV $315.25 = = $315.25 $315.25 Excel Function Approach: Fixed inputs: Cell references: FVAN = FVAN = =FV(0.05,3, 100,0) =FV(C132,C133, C131,0) = 5 The long form of the equation is a geometric progression that can be reduced to the second form. 38 Part 2 Fundamental Concepts in Financial Management spreadsheets. With an annuity, we have recurring payments, hence the PMT key is used. Here's the calculator setup for our illustrative annuity: 3 5 0 100 End Mode N I/YR PV PMT FV 315.25 We enter PV 0 because we start off with nothing, and we enter PMT 100 because we plan to deposit this amount in the account at the end of each year. When we press the FV key we get the answer, FVA3 315.25. Because this is an ordinary annuity, with payments coming at the end of each year, we must set the calculator appropriately. As noted earlier, calculators "come out of the box" set to assume that payments occur at the end of each period, that is, to deal with ordinary annuities. However, there is a key that enables us to switch between ordinary annuities and annuities due. For ordinary annuities, the designation is "End Mode" or something similar, while for annuities due the designator is "Begin" or "Begin Mode" or "Due" or something similar. If you make a mistake and set your calculator on Begin Mode when working with an ordinary annuity, then each payment would earn interest for one extra year. That would cause the compounded amounts, and thus the FVA, to be too large. The last approach in Table 2-3 shows the spreadsheet solution, using Excel's built-in function. We could put in either fixed values for N, I, and PMT or set up an Input Section, where we assign values to those variables, and then to input values into the function as cell references. Using cell references makes it easy to change the inputs to see the effects of changes on the output. For an ordinary annuity with five annual payments of $100 and a 10 percent interest rate, how many years will the first payment earn interest, and what will this payment's value be at the end? Answer this same question for the fifth payment. (4 years, $146.41; 0 years, $100) Assume that you plan to buy a condo five years from now, and you estimate that you can save $2,500 per year. You plan to deposit the money in a bank that pays 4 percent interest, and you will make the first deposit at the end of the year. How much will you have after five years? How would your answer change if the interest rate were increased to 6 percent, or lowered to 3 percent? ($13,540.81; $14,092.73; $13,272.84) 2.8 FUTURE VALUE OF AN ANNUITY DUE Because each payment occurs one period earlier with an annuity due, the payments will all earn interest for one additional year. Therefore, the FV of an annuity due will be greater than that of a similar ordinary annuity. If you went through the step-by-step procedure, you would see that our illustrative annuity due has an FV of $331.01 versus $315.25 for the ordinary annuity. With the formula approach, we first use Equation 2-3, but since each payment occurs one period earlier, we multiply the Equation 2-3 result by (1 I): FVAdue FVAordinary(1 I) (2-4) Chapter 2 Time Value of Money 39 Thus, for the annuity due, FVAdue $315.25(1.05) $331.01, which is the same result as found using the period-by-period approach. With a calculator we input the variables just as we did with the ordinary annuity, but now we set the calculator to Begin Mode to get the answer, $331.01. Why does an annuity due always have a higher future value than an ordinary annuity? If you calculated the value of an ordinary annuity, how could you find the value of the corresponding annuity due? Assume that you plan to buy a condo five years from now, and you need to save for a down payment. You plan to save $2,500 per year, with the first payment made immediately, and you will deposit the funds in a bank account that pays 4 percent. How much will you have after five years? How much would you have if you made the deposits at the end of each year? ($14,082.44; $13,540.81) 2.9 PRESENT VALUE OF AN ORDINARY ANNUITY The present value of an annuity, PVAN, can be found using the step-by-step, formula, calculator, or spreadsheet methods. Look back at Table 2-3. To find the FV of the annuity, we compounded the deposits. To find the PV, we discount them, dividing each payment by (1 I). The step-by-step procedure is diagrammed below: Periods Payments 0 5% PVAN The present value of an annuity of N periods. 1 $100 2 $100 3 $100 $ 95.24 $ 90.70 $ 86.38 $272.32 = Present value of the annuity (PVAN) Equation 2-5 expresses the step-by-step procedure in a formula. The bracketed form of the equation can be used with a scientific calculator, and it is helpful if the annuity extends out for a number of years: PVAN PMT/(1 PMT $100 1 I)1 11 I PMT/(1 1 I2 N I)2 ... PMT/(1 I)N (2-5) [1 1/(1.05)3]/0.05 $272.32 Calculators are programmed to solve Equation 2-5, so we merely input the variables and press the PV key, being sure the calculator is set to End Mode. The calculator setup is shown below for both an ordinary annuity and an annuity due. Note that the PV of the annuity due is larger because each payment is discounted 40 Part 2 Fundamental Concepts in Financial Management back one less year. Note too that you could just find the PV of the ordinary annuity and then multiply by (1 I) 1.05, getting $272.32(1.05) $285.94, the PV of the annuity due. 3 5 100 0 End Mode (Ordinary Annuity) N I/YR PV 272.32 PMT FV 3 5 100 0 N I/YR PV 285.94 PMT FV Begin Mode (Annuity Due) Why does an annuity due have a higher present value than an ordinary annuity? If you know the present value of an ordinary annuity, how could you find the PV of the corresponding annuity due? What is the PVA of an ordinary annuity with 10 payments of $100 if the appropriate interest rate is 10 percent? What would PVA be if the interest rate were 4 percent? What if the interest rate were 0 percent? How would the PVA values differ if we were dealing with annuities due? ($614.46; $811.09; $1,000.00; $675.90; $843.53; $1,000) Assume that you are offered an annuity that pays $100 at the end of each year for 10 years. You could earn 8 percent on your money in other investments with equal risk. What is the most you should pay for the annuity? If the payments began immediately, how much would the annuity be worth? ($671.01; $724.69) 2.10 FINDING ANNUITY PAYMENTS, PERIODS, AND INTEREST RATES We can find payments, periods, and interest rates for annuities. Here five variables come into play: N, I, PMT, FV, and PV. If we know any four, we can find the fifth. Finding Annuity Payments, PMT Suppose we need to accumulate $10,000 and have it available five years from now. Suppose further that we can earn a return of 6 percent on our savings, which are currently zero. Thus, we know that FV 10,000, PV 0, N 5, and I/YR 6. We can enter these values in a financial calculator and then press the PMT key to find how large our deposits must be. The answer will, of course, depend on whether we make deposits at the end of each year (ordinary annuity) or at the beginning (annuity due). Here are the results for each type of annuity: 5 6 0 10000 End Mode (Ordinary Annuity) N I/YR PV PMT 1,773.96 FV Chapter 2 Time Value of Money 41 5 6 0 10000 N I/YR PV PMT 1,673.55 FV Begin Mode (Annuity Due) Thus, you must save $1,773.96 per year if you make payments at the end of each year, but only $1,673.55 if the payments begin immediately. Note that the required payment for the annuity due is the ordinary annuity payment divided by (1 I): $1,773.96/1.06 $1,673.55. Spreadsheets can also be used to find annuity payments. Finding the Number of Periods, N Suppose you decide to make end-of-year deposits, but you can only save $1,200 per year. Again assuming that you would earn 6 percent, how long would it take you to reach your $10,000 goal? Here is the calculator setup: 6 0 1200 10000 End Mode N 6.96 I/YR PV PMT FV With these smaller deposits, it would take 6.96 years to reach the $10,000 target. If you began the deposits immediately, then you would have an annuity due and N would be a bit less, 6.63 years. Finding the Interest Rate, I Now suppose you can only save $1,200 annually, but you still want to have the $10,000 in five years. What rate of return would enable you to achieve your goal? Here is the calculator setup: 5 0 1200 10000 End Mode N I/YR 25.78 PV PMT FV You would need to earn a whopping 25.78 percent. About the only way to get such a high return would be to invest in speculative stocks or head to Las Vegas and the casino. Of course, speculative stocks and gambling aren't like making deposits in a bank with a guaranteed rate of return, so there's a good chance you'd end up with nothing. We'd recommend that you change your plans--save more, lower your $10,000 target, or extend your time horizon. It might be appropriate to seek a somewhat higher return, but trying to earn 25.78 percent in a 6 percent market would require taking on more risk than would be prudent. It's easy to find rates of return with a financial calculator or a spreadsheet. However, without one of these tools you would have to go through a trial-anderror process, and that would be very time-consuming if many years were involved. Suppose you inherited $100,000 and invested it at 7 percent per year. How much could you withdraw at the end of each of the next 10 years? How would your answer change if you made withdrawals at the beginning of each year? ($14,237.75; $13,306.31) 42 Part 2 Fundamental Concepts in Financial Management If you had $100,000 that was invested at 7 percent and you wanted to withdraw $10,000 at the end of each year, how long would your funds last? How long would they last if you earned 0 percent? How long would they last if you earned the 7 percent but limited your withdrawal to $7,000 per year? (17.8 years; 10 years; forever) Your rich uncle named you as the beneficiary of his life insurance policy. The insurance company gives you a choice of $100,000 today or a 12-year annuity of $12,000 at the end of each year. What rate of return is the insurance company offering? (6.11%) Assume that you just inherited an annuity that will pay you $10,000 per year for 10 years, with the first payment being made today. A friend of your mother offers to give you $60,000 for the annuity. If you sell it, what rate of return would your mother's friend earn on his investment? If you think a "fair" return would be 6 percent, how much should you ask for the annuity? (13.70%; $78,016.92) 2.11 PERPETUITIES In the last section we dealt with annuities whose payments continue for a specific number of periods--for example, $100 per year for 10 years. However, some securities promise to make payments forever. For example, in 1749 the British government issued some bonds whose proceeds were used to pay off other British bonds, and since this action consolidated the government's debt, the new bonds were called consols. Because consols promise to pay interest forever, they are "perpetuities." The interest rate on the consols was 2.5 percent, so a bond with a face value of $1,000 would pay $25 per year in perpetuity.6 A perpetuity is simply an annuity with an extended life. Because the payments go on forever, you couldn't apply the step-by-step approach. However, it's easy to find the PV of a perpetuity with a formula found by solving Equation 2-5 with N set at infinity:7 Consol A perpetual bond issued by the British government to consolidate past debts; in general, any perpetual bond. Perpetuity A stream of equal payments at fixed intervals expected to continue forever. PV of a perpetuity PMT I (2-6) Now we can use Equation 2-6 to find the value of a British consol with a face value of $1,000 that pays $25 per year in perpetuity. The answer depends on the interest rate. In 1888, the "going rate" as established in the financial marketplace was 2.5 percent, so at that time the consol's value was $1,000: Consol value1888 $25/0.025 $1,000 In 2004, 116 years later, the annual payment was still $25, but the going interest rate had risen to 5.2 percent, causing the consol's value to fall to $480.77: Consol value2004 $25/0.052 $480.77 Note, though, that if interest rates decline in the future, say, to 2 percent, the value of the consol will rise: Consol value if rates decline to 2% $25/0.02 $1,250.00 6 7 The consols actually pay interest in pounds, but we discuss them in dollar terms for simplicity. Equation 2-6 was found by letting N in Equation 2-5 approach infinity. The result is Equation 2-6. Chapter 2 Time Value of Money 43 These examples demonstrate an important point: When interest rates change, the prices of outstanding bonds also change. Bond prices decline if rates rise and increase if rates fall. We will discuss this point in more detail in Chapter 7, where we cover bonds in depth. Figure 2-3 gives a graphic picture of how much each payment contributes to the value of an annuity. Here we analyze an annuity that pays $100 per year when the market interest rate is 10 percent. We found the PV of each payment for the first 100 years and graphed those PVs. We also found the value of the annuity if it had a 25-year, 50-year, 100-year, and infinite life. Here are some points to note: 1. The value of an ordinary annuity is the sum of the present values of its payments. 2. We could construct graphs for annuities of any length--for 3 years, or 25 years, or 50 years, or any other period. The fewer the years, the fewer the bars in the graph. 3. As the years increase, the PV of each additional payment--which represents the amount the payment contributes to the annuity's value--decreases. This occurs because each payment is divided by (1 I)t, and that term increases exponentially with t. Indeed, in our graph the payments after 62 years are too small to be noticed. 4. The data below the graph show the value of a $100 annuity when the interest rate is 10 percent if the annuity lasts for 25, 50, and 100 years, and forever. The difference between these values shows how much the additional years contribute to the annuity's value. The payments for distant years are worth very little today, so the value of the annuity is determined largely by the FIGURE 2-3 PV of Additional Payments in an Annuity ($) 100 Contribution of Payments to Value of $100 Annuity at 10% Interest Rate 50 0 10 20 30 40 50 60 70 80 90 100 Years (N) Value of 25-year annuity: Value of 50-year annuity: Value of 100-year annuity: Value of perpetuity: Amount added: Years 125 2650 51100 $907.70 $991.48 $999.93 $1,000.00 $907.70 $83.78 $8.45 44 Part 2 Fundamental Concepts in Financial Management payments to be received in the near term. Note, though, that the discount rate affects the values of distant cash flows and thus the graph. The higher the discount rate, the steeper the decline and thus the smaller the values of the distant flows. Figure 2-3 highlights some important implications for financial issues. For example, if you win a "$10 million lottery" that actually pays $500,000 per year for 20 years, beginning immediately, the lottery is really worth a lot less than $10 million. Each cash flow must be discounted, and their sum is much less than $10 million. At a 10 percent discount rate, the "$10 million" is worth only $4,682,460, and that's before taxes. Not bad, but not $10 million. What's the present value of a perpetuity that pays $1,000 per year, beginning one year from now, if the appropriate interest rate is 5 percent? What would the value be if the annuity began its payments immediately? ($20,000, $21,000. Hint: Just add the $1,000 to be received immediately to the value of the annuity.) Would distant payments contribute more to the value of an annuity if interest rates were high or low? (Hint: When answering conceptual questions, it often helps to make up an example and use it to help formulate your answer. PV of $100 at 5 percent after 25 years $29.53; PV at 20 percent $1.05. So, distant payments contribute more at low rates.) 2.12 UNEVEN CASH FLOWS The definition of an annuity includes the words constant payment--in other words, annuities involve payments that are equal in every period. Although many financial decisions do involve constant payments, many others involve nonconstant, or uneven, cash flows. For example, the dividends on common stocks typically increase over time, and investments in capital equipment almost always generate uneven cash flows. Throughout the book, we reserve the term payment (PMT) for annuities with their equal payments in each period and use the term cash flow (CFt) to denote uneven cash flows, where the t designates the period in which the cash flow occurs. There are two important classes of uneven cash flows: (1) a stream that consists of a series of annuity payments plus an additional final lump sum and (2) all other uneven streams. Bonds represent the best example of the first type, while stocks and capital investments illustrate the other type. Here are numerical examples of the two types of flows: 1. Annuity plus additional final payment: Periods 0 I = 12% 1 2 Cash flows $0 $100 $100 Uneven (Nonconstant) Cash Flows A series of cash flows where the amount varies from one period to the next. Payment (PMT) This term designates equal cash flows coming at regular intervals. Cash Flow (CFt) This term designates a cash flow that's not part of an annuity. 3 $100 4 $100 5 $ 100 $ 1,000 $1,100 2. Irregular cash flows: Periods Cash flows 0 $0 I = 12% 1 $100 2 $300 3 $300 4 $300 5 $500 Chapter 2 Time Value of Money 45 We can find the PV of either stream by using Equation 2-7 and following the step-by-step procedure, where we discount each cash flow and then sum them to find the PV of the stream: PV CF1 11 I2 1 11 CF2 I2 2 ... CFN 11 I2 N N CFt a 11 I2 t t 1 (2-7) If we did this, we would find the PV of Stream 1 to be $927.90 and the PV of Stream 2 to be $1,016.35. The step-by-step procedure is straightforward, but if we have a large number of cash flows it is time-consuming. However, financial calculators speed up the process considerably. First, consider Stream 1, and notice that here we have a five-year, 12 percent, ordinary annuity plus a final payment of $1,000. We could find the PV of the annuity, then find the PV of the final payment, and then sum them to get the PV of the stream. Financial calculators do this in one simple step--use the five TVM keys, enter the data as shown below, and then press the PV key to get the answer, $927.90. 5 12 100 1000 N I/YR PV 927.90 PMT FV The solution procedure is different for the second uneven stream. Here we must use the step-by-step approach as shown in Figure 2-4. Even calculators and spreadsheets solve the problem using the step-by-step procedure, but they do it quickly and efficiently. First, you enter all the cash flows and the interest rate, then the calculator or computer discounts each cash flow to find its present value and sums these PVs to produce the PV of the stream. You must enter the cash flows in the calculator's "cash flow register," then enter the interest rate, and then press the NPV key to find the PV of the stream. NPV stands for net present value. We cover the calculator mechanics in the tutorial, and we discuss the process in more detail in Chapters 9 and 11, where we use the NPV calculation to analyze stocks and proposed capital budgeting projects. If you don't FIGURE 2-4 PV of an Uneven Cash Flow Stream 0 1 2 3 4 5 Periods I = 12% Cash flows $0 $100 $300 $300 $300 $500 PV of CFs $ 89.29 $ 239.16 $ 213.53 $ 190.66 $ 283.71 $1,016.35 = PV of cash flow stream = Value of the asset 46 Part 2 Fundamental Concepts in Financial Management know how to do the calculation with your calculator, it would be worthwhile to go to our tutorial or your calculator manual, learn the steps, and be sure you can make this calculation. You will have to learn to do it eventually, and now is a good time. Could you use Equation 2-2, once for each cash flow, to find the PV of an uneven stream of cash flows? What's the present value of a five-year ordinary annuity of $100 plus an additional $500 at the end of Year 5 if the interest rate is 6 percent? What would the PV be if the $100 payments occurred in Years 1 through 10 and the $500 came at the end of Year 10? ($794.87; $1,015.21) What's the present value of the following uneven cash flow stream: $0 at Time 0, $100 in Year 1 (or at Time 1), $200 in Year 2, $0 in Year 3, and $400 in Year 4 if the interest rate is 8 percent? ($558.07) Would a typical common stock provide cash flows more like an annuity or more like an uneven cash flow stream? Explain. 2.13 FUTURE VALUE OF AN UNEVEN CASH FLOW STREAM We find the future value of uneven cash flow streams by compounding rather than discounting. Consider Cash Flow Stream 2 in the preceding section. We discounted those cash flows to find the PV, but we would compound them to find the FV. Figure 2-5 illustrates the procedure for finding the FV of the stream, using the step-by-step approach. The values of all financial assets--stocks, bonds, or business capital investments--are found as the present values of their expected future cash flows. Therefore, we need to calculate present values very often, far more often than future values. As a result, all financial calculators provide automated functions FIGURE 2-5 FV of an Uneven Cash Flow Stream Periods Cash flows 0 $0 I = 12% 1 $100 2 $300 3 $300 4 $300 5 $500 $ 500.00 $ 336.00 $ 376.32 $ 421.48 $ 157.35 $ 0.00 $1,791.15 Chapter 2 Time Value of Money 47 for finding PVs, but they generally do not provide automated FV functions. On the relatively few occasions when we need to find the FV of an uneven cash flow stream, we generally use the step-by-step procedure as shown in Figure 2-5. That approach works for any cash flow stream, even those where some cash flows are zero or negative. Why are we more likely to need to calculate the PV of cash flow streams than the FV of streams? What is the future value of this cash flow stream: $100 at the end of one year, $150 due after two years, and $300 due after three years if the appropriate interest rate is 15 percent? ($604.75) 2.14 SOLVING FOR I WITH UNEVEN CASH FLOWS8 Before financial calculators and spreadsheets existed, it was extremely difficult to find I if the cash flows were uneven. With spreadsheets and financial calculators, though, it's relatively easy to find I. If you have an annuity plus a final lump sum, you can input values for N, PV, PMT, and FV into the calculator's TVM registers and then press the I/YR key. Here is the setup for Stream 1 from Section 2.12, assuming we must pay $927.90 to buy the asset. The rate of return on the $927.90 investment is 12 percent. 5 927.90 100 1000 N I/YR 12.00 PV PMT FV Finding the interest rate for an uneven cash flow stream such as Stream 2 is a bit more complicated. First, note that there is no simple procedure--finding the rate requires a trial-and-error process, which means that a financial calculator or a spreadsheet is needed. With a calculator, we would enter the CFs into the cash flow register and then press the IRR key to get the answer. IRR stands for "internal rate of return," and it is the rate of return the investment provides. The investment is the cash flow at Time 0, and it must be entered as a negative. To illustrate, consider the cash flows given below, where CF0 $1,000 is the cost of the asset: Periods Cash flows IRR I 0 $1,000 12.55% 1 $100 2 $300 3 $300 4 $300 5 $500 When we enter those cash flows in the calculator's cash flow register and press the IRR key, we get the rate of return on the $1,000 investment, 12.55 percent. You would get the same answer using Excel's IRR function. The process is covered in our calculator tutorial, and it is also discussed in Chapter 11, where we study capital budgeting. 8 This section is relatively technical. It can be deferred at this point, but the calculations will be required in Chapter 11. 48 Part 2 Fundamental Concepts in Financial Management An investment costs $465 and is expected to produce cash flows of $100 at the end of each of the next four years, then an extra lump sum payment of $200 at the end of the fourth year. What is the expected rate of return on this investment? (9.05%) An investment costs $465 and is expected to produce cash flows of $100 at the end of Year 1, $200 at the end of Year 2, and $300 at the end of Year 3. What is the expected rate of return on this investment? (11.71%) 2.15 SEMIANNUAL AND OTHER COMPOUNDING PERIODS Annual Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when interest is added once a year. Semiannual Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when interest is added twice a year. In all of our examples thus far we assumed that interest is compounded once a year, or annually. This is called annual compounding. Suppose, however, that you deposited $100 in a bank that pays a 5 percent annual interest rate but credits interest each six months, so in the second six-month period you earn interest on your original $100 plus interest on the interest earned during the first six months. This is called semiannual compounding. Note that banks generally pay interest more than once a year, virtually all bonds pay interest semiannually, and most mortgages, student loans, and auto loans require monthly payments. Therefore, it is important to understand how to deal with nonannual compounding. To illustrate semiannual compounding, assume that we deposit $100 in an account that pays 5 percent and leave it there for 10 years. First, consider again what the future value would be under annual compounding: FVN PV(1 I)N $100(1.05)10 $162.89 We would, of course, get this same answer using a financial calculator or a spreadsheet. How would things change in this example if interest were paid semiannually rather than annually? First, whenever payments occur more than once a year, you must make two conversions: (1) Convert the stated interest rate into a "periodic rate," and (2) convert the number of years into "number of periods." The conversions are done as follows, where I is the stated annual rate, M is the number of compounding periods per year, and N is the number of years: Periodic rate (IPER) Stated annual rate/Number of payments per year I/M (2-8) With a stated annual rate of 5 percent, compounded semiannually, the periodic rate is 2.5 percent: Periodic rate 5%/2 2.5% The number of compounding periods per year is found with Equation 2-9: Number of periods (Number of years)(Periods per year) NM (2-9) With 10 years and semiannual compounding, there are 20 periods: Number of periods 10(2) 20 periods Under semiannual compounding, our $100 investment will earn 2.5 percent every six months for 20 semiannual periods, not 5 percent per year for 10 years. Chapter 2 Time Value of Money 49 The periodic rate and number of periods, not the annual rate and number of years, must be shown on time lines and entered into the calculator or spreadsheet whenever you are working with nonannual compounding.9 With this background, we can find the value of $100 after 10 years if it is held in an account that pays a stated annual rate of 5.0 percent but with semiannual compounding. Here's the time line and the future value: Periods Cash flows 0 $100 1 2 19 20 I = 2.5% PV (1 + I)N = $100(1.025)20 = FV = $163.86 With a financial calculator, we would get the same result, using the periodic rate and number of periods: 20 2.5 100 0 N I/YR PV PMT FV 163.86 The future value under semiannual compounding, $163.86, exceeds the FV under annual compounding, $162.89, because interest starts accruing sooner and thus you earn more interest on interest. How would things change in our example if interest were compounded quarterly, or monthly, or daily? With quarterly compounding, there would be NM 10(4) 40 periods, and the periodic rate would be I/M 5%/4 1.25% per quarter. Using those values, we would find FV $164.36. If we used monthly compounding, we would have 10(12) 120 periods, the monthly rate would be 5%/12 0.416667%, and the FV would rise to $164.70. If we went to daily compounding, we would have 10(365) 3,650 periods, the daily rate would be 5%/365 0.0136986% per day, and the FV would be $164.87, based on a 365-day year. The same logic applies when we find present values under semiannual compounding. Again, we use Equation 2-8 to convert the stated annual rate to the periodic (semiannual) rate and Equation 2-9 to find the number of semiannual periods. We then use the periodic rate and number of periods in the calculations. For example, we can find the PV of $100 due after 10 years when the stated annual rate is 5 percent, with semiannual compounding: Periodic rate Number of periods PV of $100 5%/2 10(2) 2.5% per period 20 periods $61.03 $100/(1.025)20 We would get this same result with a financial calculator: 20 2.5 0 100 N I/YR PV 61.03 PMT FV 9 With some financial calculators, you can enter the annual (nominal) rate and the number of compounding periods per year rather than make the conversions we recommend. We prefer the conversions because they must be used on time lines and also because it is easy to forget to reset your calculator after you change its settings, which may lead to an error on your next problem. 50 Part 2 Fundamental Concepts in Financial Management If we increased the number of compounding periods from 2 (semiannual) to 12 (monthly), the PV would decline to $60.72, and if we went to daily compounding, it would fall to $60.66. Would you rather invest in an account that pays 7 percent with annual compounding or 7 percent with monthly compounding? Would you rather borrow at 7 percent and make annual or monthly payments? Why? What's the future value of $100 after three years if the appropriate interest rate is 8 percent, compounded annually? Compounded monthly? ($125.97; $127.02) What's the present value of $100 due in three years if the appropriate interest rate is 8 percent, compounded annually? Compounded monthly? ($79.38; $78.73) 2.16 COMPARING INTEREST RATES Different compounding periods are used for different types of investments. For example, bank accounts generally pay interest daily; most bonds pay interest semiannually; stocks pay dividends quarterly; and mortgages, auto loans, and other instruments require monthly payments.10 If we are to compare investments or loans with different compounding periods properly, we need to put them on a common basis. Here are some terms you need to understand: Nominal (Quoted, or Stated) Interest Rate, INOM The contracted, or quoted, or stated, interest rate. Annual Percentage Rate (APR) The periodic rate times the number of periods per year. Effective (Equivalent) Annual Rate (EFF % or EAR) The annual rate of interest actually being earned, as opposed to the quoted rate. Also called the "equivalent annual rate." The nominal rate (INOM), also called the annual percentage rate (or APR), or stated, or quoted rate, is the rate that banks, credit card companies, student loan officers, auto dealers, and so on, tell you they are charging on loans or paying on deposits. Note that if two banks offer loans with a stated rate of 8 percent but one requires monthly payments and the other quarterly payments, then they are not charging the same "true" rate--the one that requires monthly payments is really charging more than the one with quarterly payments because it will get your money sooner. So, to compare loans across lenders, or interest rates earned on different securities, you should calculate effective annual rates as described here.11 The effective annual rate, abbreviated EFF%, is also called the equivalent annual rate (EAR). This is the rate that would produce the same future value under annual compounding as would more frequent compounding at a given nominal rate. If a loan or investment uses annual compounding, then its nominal rate is also its effective rate. However, if compounding occurs more than once a year, the EFF% is higher than INOM. To illustrate, a nominal rate of 10 percent, with semiannual compounding, is equivalent to a rate of 10.25 percent with annual compounding because both of those rates will cause $100 to grow to the same amount after one year. Some banks even pay interest compounded continuously. Continuous compounding is discussed in Web Appendix 2A. 11 Note, though, if you are comparing two bonds that both pay interest semiannually, then it's OK to compare their nominal rates. Similarly, you can compare the nominal rates on two money funds that pay interest daily. But don't compare the nominal rate on a semiannual bond with the nominal rate on a money fund that compounds daily, because that will make the money fund look worse than it really is. 10 Chapter 2 Time Value of Money 51 The top line in the following diagram shows that $100 will grow to $110.25 at a nominal rate of 10.25 percent. The lower line shows the situation if the nominal rate is 10 percent but semiannual compounding is used. 0 1 $110.25 Nom = EFF% = 10.25% $100.00 0 Nom = 10.00% semi; EFF% = 10.25% 1 $105 2 $110.25 $100.00 We can find the effective annual rate, given the nominal rate and the number of compounding periods per year, with this equation: Effective annual rate (EFF%) a1 INOM M b M 1.0 (2-10) Here INOM is the nominal rate expressed as a decimal and M is the number of compounding periods per year. In our example, the nominal rate is 10 percent but with semiannual compounding, hence INOM 10% 0.10 and M 2. This results in EFF% 10.25%:12 Effective annual rate 1EFF% 2 a1 0.10 2 b 2 1 0.1025 10.25% Thus, if one investment promises to pay 10 percent with semiannual compounding and an equally risky investment promises 10.25 percent with annual compounding, we would be indifferent between the two. Define the terms "annual percentage rate, or APR," "effective annual rate, or EFF%," and "nominal interest rate, INOM." A bank pays 5 percent with daily compounding on its savings accounts. Should it advertise the nominal or effective rate if it is seeking to attract new deposits? Credit card issuers must by law print their annual percentage rate on their monthly statements. A common APR is 18 percent, with interest paid monthly. What is the EFF% on such a loan? [EFF% (1 0.18/12)12 1 0.1956 19.56%.] Some years ago banks didn't have to reveal the rate they charged on credit cards. Then Congress passed a "truth in lending" law that required them to publish their APR. Is the APR really the "most truthful" rate, or would the EFF% be "more truthful"? 12 Most financial calculators are programmed to find the EFF% or, given the EFF%, to find the nominal rate. This is called "interest rate conversion." You enter the nominal rate and the number of compounding periods per year and then press the EFF% key to find the effective annual rate. However, we generally use Equation 2-10 because it's as easy to use as the interest conversion feature is, and the equation reminds us of what we are really doing. If you use the interest rate conversion feature on your calculator, don't forget to reset your calculator settings. Interest conversion is discussed in the calculator tutorials. 52 Part 2 Fundamental Concepts in Financial Management 2.17 FRACTIONAL TIME PERIODS Thus far we have assumed that payments occur at either the beginning or the end of periods, but not within periods. However, we often encounter situations that require compounding or discounting over fractional periods. For example, suppose you deposited $100 in a bank that pays a nominal rate of 10 percent but adds interest daily, based on a 365-day year. How much would you have after 9 months? The answer is $107.79, found as follows:13 Periodic rate Number of days Ending amount IPER 0.10/365 0.000273973 per day 273.75 rounded to 274 $107.79 (9/12)(365) 0.75(365) $100(1.000273973)274 Now suppose you borrow $100 from a bank whose nominal rate is 10 percent per year "simple interest," which means that interest is not earned on interest. If the loan is outstanding for 274 days, how much interest would you have to pay? Here we would calculate a daily interest rate, IPER, as above, but multiply it by 274 rather than use the 274 as an exponent: Interest owed $100(0.000273973)(274) $7.51 You would owe the bank a total of $107.51 after 274 days. This is the procedure most banks actually use to calculate interest on loans, except that they require borrowers to pay the interest on a monthly basis rather than after 274 days. Suppose a company borrowed $1 million at a rate of 9 percent, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would the firm have to pay in a 30-day month? What would the interest be if the bank used a 365-day year? [(0.09/360)(30)($1,000,000) $7,500 interest for the month. For the 365-day year, (0.09/365)(30)($1,000,000) $7,397.26 of interest. The use of a 360-day year raises the interest cost by $102.74. That's why banks like to use it on loans.] Suppose you deposited $1,000 in a credit union that pays 7 percent with daily compounding and a 365-day year. What is the EFF%, and how much could you withdraw after seven months, assuming this is seven-twelfths of a year? [EFF% (1 0.07/365)365 1 0.07250098 7.250098%. Thus, your account would grow from $1,000 to $1,000(1.07250098)0.583333 $1,041.67, and you could withdraw that amount.] 2.18 AMORTIZED LOANS14 Amortized Loan A loan that is repaid in equal payments over its life. An important application of compound interest involves loans that are paid off in installments over time. Included are automobile loans, home mortgage loans, student loans, and many business loans. A loan that is to be repaid in equal amounts on a monthly, quarterly, or annual basis is called an amortized loan.15 13 Bank loan contracts specifically state whether they are based on a 360- or a 365-day year. If a 360-day year is used, then the daily rate is higher, so the effective rate is also higher. Here we assumed a 365-day year. Also, note that in real-world calculations, banks' computers have built-in calendars, so they can calculate the exact number of days, taking account of 30-day, 31-day, and 28- or 29-day months. 14 Amortized loans are important, but this section can be omitted without loss of continuity. 15 The word amortized comes from the Latin mors, meaning "death," so an amortized loan is one that is "killed off" over time. Chapter 2 Time Value of Money 53 Table 2-4 illustrates the amortization process. A homeowner borrows $100,000 on a mortgage loan, and the loan is to be repaid in five equal payments at the end of each of the next five years.16 The lender charges 6 percent on the balance at the beginning of each year. Our first task is to determine the payment the homeowner must make each year. Here's a picture of the situation: 0 $100,000 I = 6% 1 PMT 2 PMT 3 PMT 4 PMT 5 PMT The payments must be such that the sum of their PVs equals $100,000: $100,000 PMT (1.06)1 PMT (1.06)2 PMT (1.06)3 PMT (1.06)4 PMT (1.06)5 5 t=1 PMT (1.06)t We could insert values into a calculator as shown below to get the required payments, $23,739.64:17 5 6 100000 0 N I/YR PV PMT 23,739.64 FV Therefore, the borrower must pay the lender $23,739.64 per year for the next five years. TA B L E 2 - 4 Loan Amortization Schedule, $100,000 at 6% for 5 Years Amount borrowed: $100,000 Years: 5 Rate: 6% PMT: $23,739.64 Beginning Amount (1) $100,000.00 82,260.36 63,456.34 43,524.08 22,395.89 Payment (2) $23,739.64 23,739.64 23,739.64 23,739.64 23,739.64 Interesta (3) $6,000.00 4,935.62 3,807.38 2,611.44 1,343.75 Repayment of Principalb (4) $17,739.64 18,804.02 19,932.26 21,128.20 22,395.89 Ending Balance (5) $82,260.36 63,456.34 43,524.08 22,395.89 0.00 Year 1 2 3 4 5 a Interest in each period is calculated by multiplying the loan balance at the beginning of the year by the interest rate. Therefore, interest in Year 1 is $100,000.00(0.6) $6,000; in Year 2 it is $4,935.62; and so on. b Repayment of principal is equal to the payment of $23,739.64 minus the interest charge for the year. Most mortgage loans call for monthly payments over 10 to 30 years, but we use a shorter period to reduce the calculations. 17 You could also factor out the PMT term, find the value of the remaining summation term (it's 4.212364), and then divide it into the $100,000 to find the payment, $23,739.64. 16 54 Part 2 Fundamental Concepts in Financial Management Amortization Schedule A table showing precisely how a loan will be repaid. It gives the required payment on each payment date and a breakdown of the payment, showing how much is interest and how much is repayment of principal. Each payment will consist of two parts--interest and repayment of principal. This breakdown is shown on an amortization schedule such as the one in Table 2-4. The interest component is relatively high in the first year, but it declines as the loan balance decreases. For tax purposes, the borrower would deduct the interest component while the lender would report the same amount as taxable income. Suppose you borrowed $30,000 on a student loan at a rate of 8 percent and now must repay it in three equal installments at the end of each of the next three years. How large would your payments be, how much of the first payment would represent interest, how much would be principal, and what would your ending balance be after the first year? (PMT $11,641.01; Interest $2,400; Principal $9,241.01; Balance at end of Year 1 $20,758.99) Tying It All Together In this chapter we worked with single payments, ordinary annuities, annuities due, perpetuities, and uneven cash flow streams. There is one fundamental equation, Equation 2-1, which is used to calculate the future value of a given amount. The equation can be transformed to Equation 2-2 and then used to find the present value of a given future amount. We used time lines to show when cash flows occur, and we saw that time value problems can be solved in a step-by-step manner where we work with individual cash flows, with formulas that streamline the approach, with financial calculators, and with spreadsheets. As we noted at the outset, TVM is the single most important concept in finance, and the procedures developed in Chapter 2 are used throughout the book. Time value analysis is used to find the values of stocks, bonds, and capital budgeting projects. It is also used to analyze personal finance problems, like the retirement issue set forth in the opening vignette. You will become more familiar with time value analysis as you go through the book, but we strongly recommend that you get a good handle on Chapter 2 before you continue. SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) ST-1 Key terms Define each of the following terms: a. Time line b. FVN; PV; I; INT; N; FVAN; PMT; PVAN c. Compounding; discounting d. Simple interest; compound interest Chapter 2 Time Value of Money 55 e. f. g. h. i. j. k. Opportunity cost Annuity; ordinary (deferred) annuity; annuity due Consol; perpetuity Uneven cash flow; payment; cash flow (CFt) Annual compounding; semiannual compounding Nominal (quoted) interest rate; annual percentage rate (APR); effective (equivalent) annual rate (EAR or EFF%) Amortized loan; amortization schedule ST-2 Future value It is now January 1, 2006. You will deposit $1,000 today into a savings account that pays 8 percent. a. If the bank compounds interest annually, how much will you have in your account on January 1, 2009? b. What would your January 1, 2009, balance be if the bank used quarterly compounding? c. Suppose you deposit $1,000 in 3 payments of $333.333 each on January 1 of 2007, 2008, and 2009. How much would you have in your account on January 1, 2009, based on 8 percent annual compounding? d. How much would be in your account if the 3 payments began on January 1, 2006? e. Suppose you deposit 3 equal payments in your account on January 1 of 2007, 2008, and 2009. Assuming an 8 percent interest rate, how large must your payments be to have the same ending balance as in part a? Time value of money It is now January 1, 2006, and you will need $1,000 on January 1, 2010, in 4 years. Your bank compounds interest at an 8 percent annual rate. a. How much must you deposit today to have a balance of $1,000 on January 1, 2010? b. If you want to make 4 equal payments on each January 1 from 2007 through 2010 to accumulate the $1,000, how large must each payment be? (Note that the payments begin a year from today.) c. If your father were to offer either to make the payments calculated in part b ($221.92) or to give you $750 on January 1, 2007 (a year from today), which would you choose? Explain. d. If you have only $750 on January 1, 2007, what interest rate, compounded annually for 3 years, must you earn to have $1,000 on January 1, 2010? e. Suppose you can deposit only $200 each January 1 from 2007 through 2010 (4 years). What interest rate, with annual compounding, must you earn to end up with $1,000 on January 1, 2010? f. Your father offers to give you $400 on January 1, 2007. You will then make 6 additional equal payments each 6 months from July 2007 through January 2010. If your bank pays 8 percent, compounded semiannually, how large must each payment be for you to end up with $1,000 on January 1, 2010? g. What is the EAR, or EFF%, earned on the bank account in part f? What is the APR earned on the account? Effective annual rates Bank A offers loans at an 8 percent nominal rate (its APR), but requires that interest be paid quarterly; that is, it uses quarterly compounding. Bank B wants to charge the same effective rate on its loans, but it wants to collect interest on a monthly basis, that is, use monthly compounding. What nominal rate must Bank B set? ST-3 ST-4 QUESTIONS 2-1 2-2 What is an opportunity cost? How is this concept used in TVM analysis, and where is it shown on a time line? Is a single number used in all situations? Explain. Explain whether the following statement is true or false: $100 a year for 10 years is an annuity, but $100 in Year 1, $200 in Year 2, and $400 in Years 3 through 10 does not constitute an annuity. However, the second series contains an annuity. If a firm's earnings per share grew from $1 to $2 over a 10-year period, the total growth would be 100 percent, but the annual growth rate would be less than 10 percent. True or false? Explain. (Hint: If you aren't sure, plug in some numbers and check it out.) Would you rather have a savings account that pays 5 percent interest compounded semiannually or one that pays 5 percent interest compounded daily? Explain. 2-3 2-4 56 Part 2 Fundamental Concepts in Financial Management 2-5 To find the present value of an uneven series of cash flows, you must find the PVs of the individual cash flows and then sum them. Annuity procedures can never be of use, even if some of the cash flows constitute an annuity because the entire series is not an annuity. True or false? Explain. The present value of a perpetuity is equal to the payment on the annuity, PMT, divided by the interest rate, I: PV PMT/I. What is the future value of a perpetuity of PMT dollars per year? (Hint: The answer is infinity, but explain why.) Banks and other lenders are required to disclose a rate called the APR. What is this rate? Why did Congress require that it be disclosed? Is it the same as the effective annual rate? If you were comparing the costs of loans from different lenders, could you use their APRs to determine the one with the lowest effective interest rate? Explain. What is a loan amortization schedule, and what are some ways these schedules are used? 2-6 2-7 2-8 PROBLEMS Easy Problems 18 2-1 2-2 2-3 Future value If you deposit $10,000 in a bank account that pays 10 percent interest annually, how much would be in your account after 5 years? Present value What is the present value of a security that will pay $5,000 in 20 years if securities of equal risk pay 7 percent annually? Finding the required interest rate Your parents will retire in 18 years. They currently have $250,000, and they think they will need $1,000,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Time for a lump sum to double If you deposit money today in an account that pays 6.5 percent annual interest, how long will it take to double your money? Time to reach a financial goal You have $42,180.53 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $250,000. You expect to earn 12 percent annually on the account. How many years will it take to reach your goal? Future value: annuity versus annuity due What's the future value of a 7 percent, 5-year ordinary annuity that pays $300 each year? If this were an annuity due, what would its future value be? Present and future values of a cash flow stream An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal risk earn 8 percent annually, what is its present value? Its future value? Loan amortization and EAR You want to buy a car, and a local bank will lend you $20,000. The loan would be fully amortized over 5 years (60 months), and the nominal interest rate would be 12 percent, with interest paid monthly. What would be the monthly loan payment? What would be the loan's EAR? Present and future values for different periods Find the following values, using the equations and then a financial calculator. Compounding/discounting occurs annually. a. An initial $500 compounded for 1 year at 6 percent. b. An initial $500 compounded for 2 years at 6 percent. c. The present value of $500 due in 1 year at a discount rate of 6 percent. d. The present value of $500 due in 2 years at a discount rate of 6 percent. Present and future values for different interest rates Find the following values. Compounding/discounting occurs annually. a. An initial $500 compounded for 10 years at 6 percent. b. An initial $500 compounded for 10 years at 12 percent. c. The present value of $500 due in 10 years at 6 percent. d. The present value of $1,552.90 due in 10 years at 12 percent and also at 6 percent. e. Define present value, and illustrate it using a time line with data from part d. How are present values affected by interest rates? 2-4 2-5 2-6 2-7 2-8 Intermediate Problems 926 2-9 2-10 Chapter 2 Time Value of Money 57 2-11 Growth rates Shalit Corporation's 2005 sales were $12 million. Its 2000 sales were $6 million. a. At what rate have sales been growing? b. Suppose someone made this statement: "Sales doubled in 5 years. This represents a growth of 100 percent in 5 years, so, dividing 100 percent by 5, we find the growth rate to be 20 percent per year." Is the statement correct? Effective rate of interest Find the interest rates earned on each of the following: a. You borrow $700 and promise to pay back $749 at the end of 1 year. b. You lend $700 and the borrower promises to pay you $749 at the end of 1 year. c. You borrow $85,000 and promise to pay back $201,229 at the end of 10 years. d. You borrow $9,000 and promise to make payments of $2,684.80 at the end of each year for 5 years. Time for a lump sum to double How long will it take $200 to double if it earns the following rates? Compounding occurs once a year. a. 7 percent. b. 10 percent. c. 18 percent. d. 100 percent. Future value of an annuity Find the future values of these ordinary annuities. Compounding occurs once a year. a. $400 per year for 10 years at 10 percent. b. $200 per year for 5 years at 5 percent. c. $400 per year for 5 years at 0 percent. d. Rework parts a, b, and c assuming that they are annuities due. Present value of an annuity Find the present values of these ordinary annuities. Discounting occurs once a year. a. $400 per year for 10 years at 10 percent. b. $200 per year for 5 years at 5 percent. c. $400 per year for 5 years at 0 percent. d. Rework parts a, b, and c assuming that they are annuities due. Present value of a perpetuity What is the present value of a $100 perpetuity if the interest rate is 7 percent? If interest rates doubled to 14 percent, what would its present value be? Effective interest rate You borrow $85,000; the annual loan payments are $8,273.59 for 30 years. What interest rate are you being charged? Uneven cash flow stream a. Find the present values of the following cash flow streams at 8 percent, compounded annually. 2-12 2-13 2-14 2-15 2-16 2-17 2-18 0 Stream A Stream B b. 1 $100 $300 2 $400 $400 3 $400 $400 4 $400 $400 5 $300 $100 $0 $0 What are the PVs of the streams at 0 percent, compounded annually? 2-19 Future value of an annuity Your client is 40 years old, and she wants to begin saving for retirement, with the first payment to come one year from now. She can save $5,000 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 9 percent in the future. a. If she follows your advice, how much money would she have at 65? b. How much would she have at 70? c. If she expects to live for 20 years in retirement if she retires at 65 and for 15 years at 70, and her investments continue to earn the same rate, how much could she withdraw at the end of each year after retirement at each retirement age? PV of a cash flow stream A rookie quarterback is negotiating his first NFL contract. His opportunity cost is 10 percent. He has been offered three possible 4-year contracts. 2-20 58 Part 2 Fundamental Concepts in Financial Management Payments are guaranteed, and they would be made at the end of each year. Terms of each contract are listed below: 1 Contract 1 Contract 2 Contract 3 $3,000,000 $2,000,000 $7,000,000 2 $3,000,000 $3,000,000 $1,000,000 3 $3,000,000 $4,000,000 $1,000,000 4 $3,000,000 $5,000,000 $1,000,000 As his advisor, which would you recommend that he accept? 2-21 Evaluating lump sums and annuities Crissie just won the lottery, and she must choose between three award options. She can elect to receive a lump sum today of $61 million, to receive 10 end-of-year payments of $9.5 million, or 30 end-of-year payments of $5.5 million. a. If she thinks she can earn 7 percent annually, which should she choose? b. If she expects to earn 8 percent annually, which is the best choice? c. If she expects to earn 9 percent annually, which would you recommend? d. Explain how interest rates influence the optimal choice. Loan amortization Jan sold her house on December 31 and took a $10,000 mortgage as part of the payment. The 10-year mortgage has a 10 percent nominal interest rate, but it calls for semiannual payments beginning next June 30. Next year, Jan must report on Schedule B of her IRS Form 1040 the amount of interest that was included in the 2 payments she received during the year. a. What is the dollar amount of each payment Jan receives? b. How much interest was included in the first payment? How much repayment of principal? How do these values change for the second payment? c. How much interest must Jan report on Schedule B for the first year? Will her interest income be the same next year? d. If the payments are constant, why does the amount of interest income change over time? Future value for various compounding periods Find the amount to which $500 will grow under each of these conditions: a. 12 percent compounded annually for 5 years. b. 12 percent compounded semiannually for 5 years. c. 12 percent compounded quarterly for 5 years. d. 12 percent compounded monthly for 5 years. e. 12 percent compounded daily for 5 years. f. Why does the observed pattern of FVs occur? Present value for various compounding periods Find the present value of $500 due in the future under each of these conditions: a. 12 percent nominal rate, semiannual compounding, discounted back 5 years. b. 12 percent nominal rate, quarterly compounding, discounted back 5 years. c. 12 percent nominal rate, monthly compounding, discounted back 1 year. d. Why do the differences in the PVs occur? Future value of an annuity Find the future values of the following ordinary annuities: a. FV of $400 paid each 6 months for 5 years at a nominal rate of 12 percent, compounded semiannually. b. FV of $200 paid each 3 months for 5 years at a nominal rate of 12 percent, compounded quarterly. c. These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. Why does this occur? PV and loan eligibility You have saved $4,000 for a down payment on a new car. The largest monthly payment you can afford is $350. The loan would have a 12 percent APR based on end-of-month payments. What is the most expensive car you could afford if you finance it for 48 months? For 60 months? Effective versus nominal interest rates Bank A pays 4 percent interest, compounded annually, on deposits, while Bank B pays 3.5 percent, compounded daily. 2-22 2-23 2-24 2-25 2-26 Challenging Problems 2740 2-27 Chapter 2 Time Value of Money 59 a. b. Based on the EAR (or EFF%), which bank should you use? Could your choice of banks be influenced by the fact that you might want to withdraw your funds during the year as opposed to at the end of the year? Assume that your funds must be left on deposit during an entire compounding period in order to receive any interest. 2-28 Nominal interest rate and extending credit As a jewelry store manager, you want to offer credit, with interest on outstanding balances paid monthly. To carry receivables, you must borrow funds from your bank at a nominal 6 percent, monthly compounding. To offset your overhead, you want to charge your customers an EAR (or EFF%) that is 2 percent more than the bank is charging you. What APR rate should you charge your customers? Building credit cost into prices Your firm sells for cash only, but it is thinking of offering credit, allowing customers 90 days to pay. Customers understand the time value of money, so they would all wait and pay on the 90th day. To carry these receivables, you would have to borrow funds from your bank at a nominal 12 percent, daily compounding based on a 360-day year. You want to increase your base prices by exactly enough to offset your bank interest cost. To the closest whole percentage point, by how much should you raise your product prices? Reaching a financial goal Erika and Kitty, who are twins, just received $30,000 each for their 25th birthdays. They both have aspirations to become millionaires. Each plans to make a $5,000 annual contribution to her "early retirement fund" on her birthday, beginning a year from today. Erika opened an account with the Safety First Bond Fund, a mutual fund that invests in high-quality bonds whose investors have earned 6 percent per year in the past. Kitty invested in the New Issue Bio-Tech Fund, which invests in small, newly issued bio-tech stocks and whose investors on average have earned 20 percent per year in the fund's relatively short history. a. If the two women's funds earn the same returns in the future as in the past, how old will each be when she becomes a millionaire? b. How large would Erika's annual contributions have to be for her to become a millionaire at the same age as Kitty, assuming their expected returns are realized? c. Is it rational or irrational for Erika to invest in the bond fund rather than in stocks? Required lump sum payment You need $10,000 annually for 4 years to complete your education, starting next year. (One year from today you would withdraw the first $10,000.) Your uncle will deposit an amount today in a bank paying 5 percent annual interest, which would provide the needed $10,000 payments. a. How large must the deposit be? b. How much will be in the account immediately after you make the first withdrawal? Reaching a financial goal Six years from today you need $10,000. You plan to deposit $1,500 annually, with the first payment to be made a year from today, in an account that pays an 8 percent effective annual rate. Your last deposit will be for less than $1,500 if less is needed to have the $10,000 in 6 years. How large will your last payment be? FV of uneven cash flow You want to buy a house within 3 years, and you are currently saving for the down payment. You plan to save $5,000 at the end of the first year, and you anticipate that your annual savings will increase by 10 percent annually thereafter. Your expected annual return is 7 percent. How much would you have for a down payment at the end of Year 3? Amortization schedule a. Set up an amortization schedule for a $25,000 loan to be repaid in equal installments at the end of each of the next 3 years. The interest rate is 10 percent, compounded annually. b. What percentage of the payment represents interest and what percentage represents principal for each of the 3 years? Why do these percentages change over time? Amortization schedule with a balloon payment You want to buy a house that costs $100,000. You have $10,000 for a down payment, but your credit is such that mortgage companies will not lend you the required $90,000. However, the realtor persuades the seller to take a $90,000 mortgage (called a seller take-back mortgage) at a rate of 7 percent, provided the loan is paid off in full in 3 years. You expect to inherit $100,000 in 3 years, but right now all you have is $10,000, and you can only afford to make payments 2-29 2-30 2-31 2-32 2-33 2-34 2-35 60 Part 2 Fundamental Concepts in Financial Management of no more than $7,500 per year given your salary. (The loan would really call for monthly payments, but assume end-of-year annual payments to simplify things.) a. If the loan were amortized over 3 years, how large would each annual payment be? Could you afford those payments? b. If the loan were amortized over 30 years, what would each payment be, and could you afford those payments? c. To satisfy the seller, the 30-year mortgage loan would be written as a "balloon note," which means that at the end of the 3rd year you would have to make the regular payment plus the remaining balance on the loan. What would the loan balance be at the end of Year 3, and what would the balloon payment be? 2-36 Nonannual compounding a. You plan to make 5 deposits of $1,000 each, one every 6 months, with the first payment being made in 6 months. You will then make no more deposits. If the bank pays 4 percent nominal interest, compounded semiannually, how much would be in your account after 3 years? b. One year from today you must make a payment of $10,000. To prepare for this payment, you plan to make 2 equal quarterly deposits, in 3 and 6 months, in a bank that pays 4 percent nominal interest, compounded quarterly. How large must each of the 2 payments be? Paying off credit cards Simon recently received a credit card with an 18 percent nominal interest rate. With the card, he purchased a new stereo for $350.00. The minimum payment on the card is only $10 per month. a. If he makes the minimum monthly payment and makes no other charges, how long will it be before he pays off the card? Round to the nearest month. b. If he makes monthly payments of $30, how long will it take him to pay off the debt? Round to the nearest month. c. How much more in total payments will he make under the $10-a-month plan than under the $30-a-month plan? PV and a lawsuit settlement It is now December 31, 2005, and a jury just found in favor of a woman who sued the city for injuries sustained in a January 2004 accident. She requested recovery of lost wages, plus $100,000 for pain and suffering, plus $20,000 for her legal expenses. Her doctor testified that she has been unable to work since the accident and that she will not be able to work in the future. She is now 62, and the jury decided that she would have worked for another 3 years. She was scheduled to have earned $34,000 in 2004, and her employer testified that she would probably have received raises of 3 percent per year. The actual payment will be made on December 31, 2006. The judge stipulated that all dollar amounts are to be adjusted to a present value basis on December 31, 2006, using a 7 percent annual interest rate, using compound, not simple, interest. Furthermore, he stipulated that the pain and suffering and legal expenses should be based on a December, 31, 2005, date. How large a check must the city write on December 31, 2006? Required annuity payments Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $40,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today; and he will then receive 24 additional annual payments. Annual inflation is expected to be 5 percent. He currently has $100,000 saved, and he expects to earn 8 percent annually on his savings. How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Required annuity payments A father is now planning a savings program to put his daughter through college. She is 13, she plans to enroll at the university in 5 years, and she should graduate in 4 years. Currently, the annual cost (for everything--food, clothing, tuition, books, transportation, and so forth) is $15,000, but these costs are expected to increase by 5 percent annually. The college requires that this amount be paid at the start of the year. She now has $7,500 in a college savings account that pays 6 percent annually. The father will make 6 equal annual deposits into her account; the 1st deposit today and the 6th on the day she starts college. How large must each of the 6 payments be? [Hint: Calculate the cost (inflated at 5 percent) for each year of college, then find the 2-37 2-38 2-39 2-40 Chapter 2 Time Value of Money 61 total present value of those costs, discounted at 6 percent, as of the day she enters college. Then find the compounded value of her initial $7,500 on that same day. The difference between the PV costs and the amount that would be in the savings account must be made up by the father's deposits, so find the 6 equal payments (starting immediately) that will compound to the required amount.] COMPREHENSIVE/SPREADSHEET PROBLEM 2-41 Time value of money Answer the following questions: a. Find the FV of $1,000 after 5 years earning a rate of 10 percent annually. b. What would the investment's FV be at rates of 0 percent, 5 percent, and 20 percent after 0, 1, 2, 3, 4, and 5 years? c. Find the PV of $1,000 due in 5 years if the discount rate is 10 percent. d. What is the rate of return on a security that costs $1,000 and returns $2,000 after 5 years? e. Suppose California's population is 30 million people, and its population is expected to grow by 2 percent annually. How long would it take for the population to double? f. Find the PV of an ordinary annuity that pays $1,000 each of the next 5 years if the interest rate is 15 percent. What is the annuity's FV? g. How would the PV and FV of the above annuity change if it were an annuity due? h. What would the FV and the PV be for $1,000 due in 5 years if the interest rate were 10 percent, semiannual compounding? i. What would the annual payments be for an ordinary annuity for 10 years with a PV of $1,000 if the interest rate were 8 percent? What would the payments be if this were an annuity due? j. Find the PV and the FV of an investment that pays 8 percent annually and makes the following end-of-year payments: 0 1 $100 2 $200 3 $400 k. l. Five banks offer nominal rates of 6 percent on deposits, but A pays interest annually, B pays semiannually, C quarterly, D monthly, and E daily. (1) What effective annual rate does each bank pay? If you deposited $5,000 in each bank today, how much would you have at the end of 1 year? 2 years? (2) If the banks were all insured by the government (the FDIC) and thus equally risky, would they be equally able to attract funds? If not, and the TVM were the only consideration, what nominal rate would cause all the banks to provide the same effective annual rate as Bank A? (3) Suppose you don't have the $5,000 but need it at the end of 1 year. You plan to make a series of deposits, annually for A, semiannually for B, quarterly for C, monthly for D, and daily for E, with payments beginning today. How large must the payments be to each bank? (4) Even if the 5 banks provided the same effective annual rate, would a rational investor be indifferent between the banks? Suppose you borrowed $15,000. The loan's annual interest rate is 8 percent, and it requires 4 equal end-of-year payments. Set up an amortization schedule that shows the annual payments, interest payments, principal repayments, and beginning and ending loan balances. 62 Part 2 Fundamental Concepts in Financial Management Integrated Case First National Bank 2-42 Time value of money analysis You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money analysis covering the following questions. a. Draw time lines for (1) a $100 lump sum cash flow at the end of Year 2, (2) an ordinary annuity of $100 per year for 3 years, and (3) an uneven cash flow stream of $50, $100, $75, and $50 at the end of Years 0 through 3. b. (1) What's the future value of $100 after 3 years if it earns 10 percent, annual compounding? (2) What's the present value of $100 to be received in 3 years if the interest rate is 10 percent, annual compounding? c. What annual interest rate would cause $100 to grow to $125.97 in 3 years? d. If a company's sales are growing at a rate of 20 percent annually, how long will it take sales to double? e. What's the difference between an ordinary annuity and an annuity due? What type of annuity is shown here? How would you change it to the other type of annuity? 0 0 f. g. 1 $100 2 $100 3 $100 h. i. (1) What is the future value of a 3-year, $100 ordinary annuity if the annual interest rate is 10 percent? (2) What is its present value? (3) What would the future and present values be if it were an annuity due? A 5-year $100 ordinary annuity has an annual interest rate of 10 percent. (1) What is its present value? (2) What would the present value be if it was a 10-year annuity? (3) What would the present value be if it was a 25-year annuity? (4) What would the present value be if this was a perpetuity? A 20-year-old student wants to save $3 a day for her retirement. Every day she places $3 in a drawer. At the end of each year, she invests the accumulated savings ($1,095) in a brokerage account with an expected annual return of 12 percent. (1) If she keeps saving in this manner, how much will she have accumulated at age 65? (2) If a 40-year-old investor began saving in this manner, how much would he have at age 65? (3) How much would the 40-year-old investor have to save each year to accumulate the same amount at 65 as the 20-year-old investor? What is the present value of the following uneven cash flow stream? The annual interest rate is 10 percent. 0 0 j. 1 $100 2 $300 3 $300 4 Years $50 k. (1) Will the future value be larger or smaller if we compound an initial amount more often than annually, for example, semiannually, holding the stated (nominal) rate constant? Why? (2) Define (a) the stated, or quoted, or nominal, rate, (b) the periodic rate, and (c) the effective annual rate (EAR or EFF%). (3) What is the EAR corresponding to a nominal rate of 10 percent compounded semiannually? Compounded quarterly? Compounded daily? (4) What is the future value of $100 after 3 years under 10 percent semiannual compounding? Quarterly compounding? When will the EAR equal the nominal (quoted) rate? Chapter 2 Time Value of Money 63 l. (1) What is the value at the end of Year 3 of the following cash flow stream if interest is 10 percent, compounded semiannually? (Hint: You can use the EAR and treat the cash flows as an ordinary annuity or use the periodic rate and compound the cash flows individually.) 0 0 2 $100 4 $100 6 Periods $100 (2) What is the PV? (3) What would be wrong with your answer to parts l(1) and l(2) if you used the nominal rate, 10 percent, rather than either the EAR or the periodic rate, INOM/2 10%/2 5% to solve them? m. (1) Construct an amortization schedule for a $1,000, 10 percent annual interest loan with 3 equal installments. (2) What is the annual interest expense for the borrower, and the annual interest income for the lender, during Year 2? Please go to the ThomsonNOW Web site to access the Cyberproblems. C H APTE R 3 FINANCIAL STATEMENTS, CASH FLOW, AND TAXES Doing Your Homework with Financial Statements Suppose you are a small investor who knows a little about finance and accounting. Could you compete successfully against large institutional investors with armies of analysts, high-powered computers, and state-of-the-art trading strategies? The answer, according to one Wall Street legend, is a resounding yes! Peter Lynch, who had an outstanding track record as manager of the $10 billion Fidelity Magellan fund and then went on to become the best-selling author of One Up on Wall Street and Beating the Street, has long argued that small investors can beat the market by using common sense and information available to all of us as we go about our day-to-day lives. For example, a college student may be more adept at scouting out the new and interesting products that will become tomorrow's success stories than is an investment banker who works 75 hours a week in a New York office. Parents of young children are likely to know which baby foods will succeed or which diapers are best. Couch potatoes may have the best feel for which tortilla chips have the brightest future or whether a new remote control is worth its price. The trick is to find a product that will boom, yet whose manufacturer's stock is undervalued. If this sounds too easy, you are right. Lynch argues that once you have discovered a good product, you still have a lot of homework to do. This involves combing through the vast amount of financial information that companies regularly provide. It also requires taking a closer and more critical look at how the company conducts its business--Lynch refers to this as "kicking the tires." To illustrate his point, Lynch relates his experience with Dunkin' Donuts. As a consumer, Lynch was impressed with the quality of the product. This impression led him to take a closer look at the company's financial statements and operations. He liked what he saw, and Dunkin' Donuts became one of the best investments in his portfolio. The next two chapters discuss what financial statements are and how they are analyzed. Once you have identified a good product as a possible investment, the principles discussed in these chapters will help you "kick the tires." Fidelity JAMES SCHNEPF/LIAISON/GETTY IMAGES INC. Chapter 3 Financial Statements, Cash Flow, and Taxes 65 Putting Things In Perspective A manager's primary goal is to maximize the value of his or her firm's stock. Value is based on the firm's future cash flows. But how does an investor estimate future cash flows, and how does a manager decide which actions are most likely to increase those flows? The answers to both questions lie in a study of the financial statements that publicly traded firms must provide to investors. Here "investors" include both institutions (banks, insurance companies, pension funds, and the like) and individuals like you. This chapter begins with a discussion of what the basic financial statements are, how they are used, and what kinds of financial information users need. As we discussed in Chapter 1, the value of any business asset-- whether it's a financial asset such as a stock or a bond, or a real (physical) asset such as land, buildings, and equipment--depends on the usable, aftertax cash flows the asset is expected to produce. Therefore, the chapter also explains the difference between accounting income and cash flow. Finally, because it is after-tax cash flow that is important, the chapter provides an overview of the federal income tax system. Much of the material in the chapter deals with concepts covered in basic accounting courses. However, the information is important enough to warrant a review. Accounting is used to "keep score," and if a firm's managers do not know the score, they won't know if their actions are appropriate. If you took midterm exams but were not told how you were doing, you would have a difficult time improving your grades. The same thing holds in business. If a firm's managers--whether they are in marketing, personnel, production, or finance--do not understand financial statements, they will not be able to judge the effects of their actions, and that will make it hard for the firm to be successful. Only accountants need to know how to make financial statements, but everyone involved with business needs to know how to interpret and use them. Our focus is on interpretation and use. 3.1 A BRIEF HISTORY OF ACCOUNTING AND FINANCIAL STATEMENTS Financial statements are pieces of paper with numbers written on them, but it is important to also think about the real assets behind those numbers. If you understand how and why accounting began, and how financial statements are used, you can better visualize what is going on and why accounting information is so important. Thousands of years ago, individuals (or families) were self-contained, meaning that they gathered their own food, made their own clothes, and built their own shelters. Then specialization began--some people became good at making pots, others at making arrowheads, others at making clothing, and so on. Are you interested in learning more about the history of accounting? If so, take a tour through the "History of Accounting" organized by the Association of Chartered Accountants in the United States and located at http://www.acaus.org/ acc_his.html. 66 Part 2 Fundamental Concepts in Financial Management Annual Report A report issued annually by a corporation to its stockholders. It contains basic financial statements as well as management's analysis of the firm's past operations and future prospects. As specialization began, so did trading, initially in the form of barter. At first, each artisan worked alone, and trade was strictly local. Eventually, though, master craftsmen set up small factories and employed workers, money (first in the form of clamshells and later gold) began to be used, and trade expanded beyond the local area. As these developments occurred, a primitive form of banking began, with wealthy merchants lending profits from past dealings to enterprising factory owners who needed capital to expand or to young traders who needed money to buy wagons, ships, and merchandise. When the first loans were made, lenders could physically inspect borrowers' assets and judge the likelihood that the loans would be repaid. Eventually, though, things became more complex--borrowers were developing larger factories, traders were acquiring fleets of ships and wagons, and loans were being made to develop distant mines and trading posts. As this occurred, it became increasingly difficult for lenders to personally inspect the assets that backed their loans, so they needed a way to verify that borrowers actually had the assets they claimed to have. Also, some investments were made on a share-of-the-profits basis, and that meant that profits had to be determined. At the same time, factory owners and large merchants needed reports to see how effectively their managers were operating the businesses, and governments needed information for use in assessing taxes. For all these reasons, a need arose for financial statements, for accountants to prepare those statements, and for auditors to verify the accuracy of the accountants' work. The economic system has grown enormously since its beginning, and accounting has become quite complex. However, the original reasons for financial statements still apply: Bankers and investors need accounting information to make intelligent decisions, managers need it to operate their businesses efficiently, and taxing authorities need it to assess taxes in a reasonable way. It should be intuitively clear that it is not easy to translate physical assets into numbers, as accountants must do when they construct financial statements. The numbers shown in the assets section of a balance sheet generally represent the historical costs of the assets, less depreciation. However, inventories may be spoiled, obsolete, or even missing; fixed assets such as machinery and buildings may have higher or lower values than their depreciated historical costs; and accounts receivable may be uncollectible. On the liabilities side, some legitimate claims may not even appear on the balance sheet--obligations to pay retirees' medical costs are a good example. Similarly, some costs as reported on the income statement may be understated, as would be true if a plant with a useful life of 10 years were being depreciated over 40 years. When you examine a set of financial statements, you should keep in mind that a physical reality lies behind the numbers, and you should also realize that the translation from physical assets to "correct" numbers is far from precise. As mentioned previously, it is important for accountants to be able to generate financial statements, while others involved in the business need to know how to interpret them. To be effective, both investors and general managers must have a working knowledge of financial statements and what they reveal. Providing this background is the purpose of this chapter. 3.2 FINANCIAL STATEMENTS AND REPORTS The annual report is the most important report corporations issue to stockholders, and it contains two types of information. First, there is a verbal section, often presented as a letter from the chairman, that describes the firm's operating results during the past year and then discusses new developments that will Chapter 3 Financial Statements, Cash Flow, and Taxes 67 affect future operations. Second, the report provides four basic financial statements--the balance sheet, the income statement, the statement of cash flows, and the statement of retained earnings. Taken together, these statements give an accounting picture of the firm's operations and financial position. Detailed data are provided for the two or three most recent years, along with historical summaries of key operating statistics for the past 5 or 10 years.1 The quantitative and verbal materials are equally important. The financial statements report what has actually happened to assets, earnings, and dividends over the past few years, whereas the verbal statements attempt to explain why things turned out the way they did and what might happen in the future. For illustrative purposes, we use data for Allied Food Products, a processor and distributor of a wide variety of staple foods, to discuss the basic financial statements. Allied was formed in 1978, when several regional firms merged, and it has grown steadily while earning a reputation as one of the best firms in its industry. Allied's earnings dropped a bit in 2005, to $117.5 million versus $121.8 million in 2004. Management reported that the drop resulted from losses associated with a drought as well as increased costs due to a three-month strike. However, management then went on to paint a more optimistic picture for the future, stating that full operations had been resumed, that several unprofitable businesses had been eliminated, and that 2006 profits were expected to rise sharply. Of course, an increase in profitability may not occur, and analysts should compare management's past statements with subsequent results. In any event, the information contained in an annual report can be used to help forecast future earnings and dividends. Therefore, investors are very much interested in this report. We should note that Allied's financial statements are relatively simple and straightforward. It finances with only debt and common stock--no preferred stock, convertibles, and no complex derivative securities. It has had no acquisitions that resulted in goodwill that must be carried on the balance sheet. And all of its assets are used in its basic business operations, hence no nonoperating assets must be stripped out to analyze its operating performance. We deliberately chose such a company because this is an introductory text, and as such we want to explain the basics of financial analysis, not wander into an arcane accounting discussion that is best left to accounting and security analysis courses. We point out some of the pitfalls that can be encountered when trying to interpret accounting statements, but we leave it to advanced courses to cover the intricacies of accounting. For an excellent example of a corporate annual report, take a look at 3M's annual report, found at http://www.3m.com/ index.jhtml. Then, click on investor relations at the bottom of the screen and then you can find 3M's most recent annual report in Adobe Acrobat format. A source for links to many companies' annual reports is http:// www.annualreportservice .com. What is the annual report, and what two types of information does it provide? What four financial statements are typically included in the annual report? Why is the annual report of great interest to investors? 1 Firms also provide quarterly reports, but these are much less comprehensive. In addition, larger firms file even more detailed statements, giving breakdowns for each major division or subsidiary, with the Securities and Exchange Commission (SEC). These reports, called 10-K reports, are made available to stockholders upon request to a company's corporate secretary. Finally, many larger firms also publish statistical supplements, which give financial statement data and key ratios for the last 10 to 20 years, and these reports are available on the World Wide Web. 68 Part 2 Fundamental Concepts in Financial Management 3.3 THE BALANCE SHEET Balance Sheet A statement of the firm's financial position at a specific point in time. The balance sheet represents a "snapshot" of the firm's position at a specific point in time. Figure 3-1 provides a simple illustration of a typical balance sheet. The left side of the statement shows the assets that the company owns. The right side shows the firm's liabilities and equity, which represent claims against the assets. As Figure 3-1 indicates, assets are divided into two major categories: current and long term. Current assets include cash plus other items that should be converted to cash within one year, and they include cash and equivalents, accounts receivable, and inventory.2 Long-term assets are those whose useful lives exceed one year, and they include physical assets such as plant and equipment and intellectual property such as patents and copyrights. Plant and equipment is generally reported net of accumulated depreciation. Allied's long-term assets consist entirely of net plant and equipment, and we often refer to them as "net fixed assets" for convenience. The claims against assets are of two types--liabilities (or money the company owes creditors) and stockholders' equity, which represents ownership FIGURE 3-1 A Typical Balance Sheet Total Assets Total Liabilities and Equity Current Assets Cash and equivalents Accounts receivable Inventory Current Liabilities Accrued wages and taxes Accounts payable Notes payable Long-Term (Fixed) Assets Net plant and equipment Other long-term assets Long-Term Debt Stockholders' Equity Common stock Retained earnings Net Working Capital = Current Assets Current Liabilities 2 Allied and most other companies hold some cash in bank checking accounts, and they also hold short-term, interest-bearing securities that can be sold and thus converted to cash immediately with a simple telephone call. Those securities are reported as "cash equivalents" and are included with checking account balances for financial reporting purposes. If a company has other marketable securities, they will be shown as "Marketable securities" in the Current Assets section if they mature in less than a year; otherwise, they will be shown in the Long-Term Assets section. Chapter 3 Financial Statements, Cash Flow, and Taxes 69 much like a homeowner's equity, which is the value of the house less the amount of any outstanding mortgage loan. Corporate liabilities are further divided into two major categories: current liabilities and long-term debt. Current liabilities are obligations that are due to be paid off within a year, and they include accounts payable, accruals (the total of accrued wages and accrued taxes), and notes payable that are due within one year. Long-term debt includes long-term loans and bonds that have maturities longer than a year. Allied's stockholders' equity section is divided into two accounts--"common stock" and "retained earnings." The amount shown as common stock is, essentially, the amount of cash that stockholders paid to the company when it originally issued stock for use in acquiring assets. The retained earnings account is built up over time as the firm "saves" a part of its earnings rather than paying them all out as dividends. The breakdown of the stockholders' equity accounts is important for some purposes but not for others. For example, a potential stockholder might want to know whether the company actually earned the funds reported in its equity account or whether they came mainly from selling stock. A potential creditor, on the other hand, would be primarily interested in the total equity provided by the firm's owners and not with its source. We generally aggregate the two stockholders' equity accounts and call this sum common equity, or net worth. Notice that the balance sheet items are listed in order of their "liquidity," or the length of time it takes to convert them to cash (current assets) or their expected useful lives (fixed assets). Similarly, the claims are listed in the order in which they must be paid: Accounts payable must generally be paid within 30 days, notes payable within 90 days, and so on, down to the stockholders' equity accounts, which represent ownership and need never be "paid off." A firm needs enough cash and other liquid assets to pay its bills as they come due, so its lenders, suppliers, and bond rating agencies keep an eye on its liquidity. Net working capital, which is defined as current assets minus current liabilities, is a frequently used measure of liquidity. Table 3-1 shows Allied's year-end balance sheets for 2005 and 2004. From the 2005 statement we see that it had $2 billion of assets--half current and half long term. The $2 billion of assets were financed by $310 million of current liabilities, $750 million of long-term debt, and $940 million of common equity represented by 50 million shares outstanding. Its 2005 net working capital was $690 million (the $1 billion of current assets less the $310 million of current liabilities). Comparing the balance sheets for 2005 and 2004, we see that Allied's assets grew by $320 million, or slightly more than 19 percent. Several additional points about the balance sheet are worth noting: 1. Cash and equivalents versus other assets. Although the assets are all stated in dollar terms, only the cash and equivalents account represents actual spendable money. Accounts receivable represent credit sales that have not yet been collected. Inventories show the investment in raw materials, work-inprocess, and finished goods. Finally, net plant and equipment reflects the amount Allied paid for its fixed assets, less accumulated depreciation. Allied has $10 million of cash and equivalents, hence it can write checks totaling that amount (versus current liabilities of $310 million due within a year). The noncash assets should generate cash over time, but they do not represent cash in hand, and the cash they would bring if they were sold today could be higher or lower than their values as reported on the balance sheet. 2. Inventory accounting. Allied uses the FIFO (first-in, first-out) method to determine the inventory value shown on its balance sheet ($615 million), but it could have used LIFO (last-in, first-out) or an average cost method. During a period of rising prices, by assuming that old, low-cost inventory is sold first and new, high-cost items are kept in stock, FIFO results in a relatively high Retained Earnings That portion of the firm's earnings that has been saved rather than paid out as dividends. Common Equity (Net Worth) The capital supplied by common stockholders: common stock, paid-in capital, retained earnings, and, occasionally, certain reserves. Net Working Capital Defined as current assets minus current liabilities. It is a frequently used measure of liquidity. 70 Part 2 Fundamental Concepts in Financial Management TA B L E 3 - 1 Allied Food Products: December 31 Balance Sheets (Millions of Dollars) 2005 2004 Assets Cash and equivalents Accounts receivable Inventories Total current assets Net plant and equipment Total assets Liabilities and Equity Accounts payable Notes payable Accruals Total current liabilities Long-term bonds Total debt Common stock (50,000,000 shares) Retained earnings Total common equity Total liabilities and equity Book value per share $940/50 $ 10 375 615 $1,000 1,000 $2,000 80 315 415 $ 810 870 $1,680 30 60 130 $ 220 580 $ 800 130 750 $ 880 $1,680 $ $ 60 110 140 $ 310 750 $1,060 130 810 $ 940 $2,000 $18.80 $ Notes: 1. The bonds have a sinking fund requirement of $20 million a year. Sinking funds are discussed in Chapter 7, but in brief, a sinking fund is used to help ensure the repayment of long-term debt. Thus, Allied was required to pay off $20 million of its mortgage bonds during 2005. We include the current portion of the long-term debt in notes payable, but in a more detailed balance sheet it would be shown as a separate item under current liabilities. 2. Also, note that a relatively few firms use preferred stock, which we discuss in Chapter 9. Preferred can take several different forms, but it is generally like debt in the sense that it pays a fixed amount each year. However, it is like common stock in the sense that a failure to pay the preferred dividend does not expose the firm to bankruptcy. If a firm does use preferred, it is shown on the balance sheet between Total debt and Common stock. There is no set rule on how preferred should be treated when financial ratios are calculated--it could be considered as debt or as equity--but as long as one is consistent in the treatment, either choice is appropriate. balance sheet inventory value, a low cost of goods sold on the income statement, and thus relatively high reported profits. (This is strictly accounting; companies actually use older items first.) Allied uses FIFO, and because inflation is present, (a) its balance sheet inventories are higher than they would have been had it used LIFO, (b) its cost of goods sold is lower than it would have been under LIFO, and (c) its reported profits are higher. In Allied's case, if the company had used LIFO in 2005, its balance sheet figure for inventories would have been $585 million rather than $615 million, and its earnings (which will be discussed in the next section) would have been reduced by $18 million. Thus, the inventory valuation method can have a significant effect on financial statements. This is important when an analyst is comparing different companies, and the method used must be reported in the notes to the financial statements. 3. Other sources of funds. Most companies (including Allied) finance their assets with a combination of current liabilities, long-term debt, and common Chapter 3 Financial Statements, Cash Flow, and Taxes 71 equity. As we noted earlier, some companies also use hybrid (combination) securities such as preferred stock, convertible bonds, and long-term leases. Preferred stock is a hybrid between common stock and debt, while convertible bonds are debt securities that give the bondholder an option to exchange bonds for shares of common stock. In the event of bankruptcy, preferred stock ranks below debt but above common stock. When a firm has issued preferred stock, its total equity includes common equity plus preferred stock. Most firms do not use any preferred stock, and those that do generally do not use much of it. Therefore, when we use the term "equity," we mean "common equity" unless otherwise noted. 4. Depreciation methods. Most companies prepare two sets of financial statements--one for tax purposes and one for stockholder reporting. Generally, they use the most accelerated depreciation method permitted under the law for tax purposes but straight line for stockholder reporting. Accelerated depreciation results in high depreciation charges, thus low taxable income and therefore relatively low taxes, whereas straight-line depreciation results in lower depreciation charges and high reported profits.3 Thus, accelerated depreciation results in lower taxes in the current year while straight line results in relatively high reported profits. However, Allied is a relatively conservative company, and it uses accelerated depreciation for both stockholder reporting and tax purposes. Had Allied elected to use straight-line depreciation for stockholder reporting, its 2005 depreciation expense would have been $25 million less, so the $1 billion shown for "net plant" on its balance sheet would have been $25 million higher. More importantly, its reported net income also would have been higher. 5. Market values versus book values. Companies use generally accepted accounting principles (GAAP) to determine the values reported on their balance sheets. In most cases, these accounting numbers (often referred to as book values) are different from the corresponding market values. For example, Allied purchased its headquarters building in Chicago in 1979. Under GAAP, the company must report the value of this asset at its historical cost (what it originally paid for the asset in 1979) less accumulated depreciation. Given that Chicago real estate prices have increased over the past 25 years, the current market value of the building is much higher than its book value. Other assets might also differ substantially from their values as based on historical costs. The book and market values of liabilities are normally fairly close to one another, but this is not always true. When a company issues long-term debt, the balance sheet reflects its par value. As we demonstrate in Chapter 7, if interest rates change after debt was issued, its market value will be different from its book value. Finally, the book value of the company's common equity is simply the reported book value of the assets minus the book value of the liabilities. Looking at Table 3-1, we see that the book value of Allied's common equity was $940 million in 2005. Because there were 50 million shares outstanding, the book value per share was $18.80. By contrast, the market value of the company's common stock is its current price, $23, multiplied by the number of shares outstanding, or $23 50 $1,150 million. As is true for most companies in 2006, shareholders are willing to pay more than book value for the firm's stock in part because the values of its fixed assets have increased due 3 Depreciation charges over an asset's life are equal to the asset's cost basis. Accelerated depreciation results in relatively high depreciation in the early years, hence low taxes, then lower depreciation and higher taxes later in the asset's life. This is advantageous due to the time value of money. 72 Part 2 Fundamental Concepts in Financial Management to inflation and in part because shareholders expect the company's future earnings to grow. Allied, like most other companies, has learned how to make investments that are expected to add to future profits. Apple Computer provides an excellent example of this "growth opportunity" phenomenon. When Apple first introduced the iPod, its balance sheet showed very little value for this product, but investors recognized that it was a great product and would lead to high profits in spite of its low book value. They then bid Apple's stock up well above its book value. 6. The time dimension. The balance sheet may be thought of as a snapshot of the firm's financial position at a point in time--for example, on December 31, 2005. Thus, we see that on December 31, 2004, Allied had $80 million of cash and equivalents, but that balance fell to $10 million by year-end 2005. The balance sheet changes every day as inventories are increased or decreased, as fixed assets are added or retired, as bank loans are increased or decreased, and so on. Companies whose business is seasonal experience especially large balance sheet changes over the year. For example, Allied's inventories are low just before the harvest season, but they are high just after the fall crops have been harvested and processed. Similarly, most retailers have large inventories just before Christmas but low inventories and high accounts receivable just after Christmas. Therefore, firms' balance sheets change during the year, depending on the date at which the statement is constructed. What is the balance sheet, and what information does it provide? How is the order of the items shown on the balance sheet determined? A company has $2 million of cash and equivalents, $2 million of inventory, $3 million of accounts receivable, $3 million of accounts payable, $1 million of accruals, and $2 million of notes payable. What is its net working capital? ($1 million) Why might Allied's December 31 balance sheet differ from its June 30 statement? 3.4 THE INCOME STATEMENT Income Statement A report summarizing the firm's revenues and expenses during an accounting period, generally a quarter or a year. Table 3-2 gives Allied's 2005 and 2004 income statements. Net sales are shown at the top of the statement, after which operating costs, interest, and taxes are subtracted to obtain the net income available to common shareholders, which is generally referred to as "net income." Earnings and dividends per share are given at the bottom of the income statement. Earnings per share (EPS) is called "the bottom line," denoting that of all the items on the income statement, EPS is generally the most important to stockholders. Allied earned $2.35 per share in 2005, down from $2.44 in 2004, but it still increased the dividend from $1.06 to $1.15.4 Note that different firms have different financial structures, different tax situations, and different amounts of nonoperating assets. These differences can cause two companies with similar operations to report different levels of net income. For example, suppose two companies have identical operations--their sales, operating costs, and assets are identical. However, one finances with debt 4 Companies must report "comprehensive income" as well as net income. Comprehensive income is equal to net income adjusted to include several additional items, such as unrealized gains or losses on marketable securities, classified as available for sale, when they are marked-to-market. For our purposes in this introductory text, we assume that there are no such items. Chapter 3 Financial Statements, Cash Flow, and Taxes 73 TA B L E 3 - 2 Allied Food Products: Income Statements for Years Ending December 31 (Millions of Dollars, Except for Per-Share Data) 2005 2004 $2,850.0 2,497.0 $ 353.0 90.0 $ 263.0 60.0 $ 203.0 81.2 $ 121.8 $ 53.0 $ 68.8 $ 26.00 $ 2.44 $ 1.06 $ 17.60 $ 4.24 Net sales Operating costs except depreciationa Earnings before interest, taxes, and depreciation (EBITDA)b Depreciation Earnings before interest and taxes (EBIT) Less interest Earnings before taxes (EBT) Taxes Net income Common dividends Addition to retained earnings Per-share data: Common stock price Earnings per share (EPS)c Dividends per share (DPS)c Book value per share (BVPS)c Cash flow per share (CFPS)c $3,000.0 2,616.2 $ 383.8 100.0 $ 283.8 88.0 $ 195.8 78.3 $ 117.5 $ 57.5 $ 60.0 $ 23.00 $ 2.35 $ 1.15 $ 18.80 $ 4.35 Notes: a Operating costs include lease payments of $28 million. b Allied has no amortization charges. c Allied has 50 million shares of common stock outstanding. Note that EPS is based on net income available to common stockholders. Calculations of EPS, DPS, BVPS, and CFPS for 2005 are as follows: Earnings per share EPS Net income Common shares outstanding $117,500,000 50,000,000 $2.35 Dividends per share DPS Dividends paid to common stockholders Common shares outstanding Total common equity Common shares outstanding Net income Depreciation $57,500,000 50,000,000 $18.80 $1.15 Book value per share BVPS $940,000,000 50,000,000 Cash flow per share CFPS Amortization Common shares outstanding $217,500,000 50,000,000 $4.35 If a firm has options or convertibles outstanding, or if it recently issued new common stock, then EPS calculations become a bit more complicated. See any financial accounting text for a discussion. and the other uses only common equity. Despite the fact their operating performances are identical, the company with no debt (and therefore no interest expense) would report higher net income because no interest is deducted from its operating income. Consequently, if you want to compare companies' operating performances, it is essential to focus on their earnings before deducting taxes and interest payments. This is called earnings before interest and taxes (EBIT), and it is often referred to as operating income: EBIT Sales revenues Operating costs (3-1) From Allied's income statement, we see that its operating income increased from $263.0 million in 2004 to $283.8 million in 2005, yet the company's 2005 net 74 Part 2 Fundamental Concepts in Financial Management Depreciation The charge to reflect the cost of assets used up in the production process. Depreciation is not a cash outlay. Tangible Assets Physical assets such as plant and equipment. Amortization A noncash charge similar to depreciation except that it is used to write off the costs of intangible assets. Intangible Assets Assets such as patents, copyrights, trademarks, and goodwill. EBITDA Earnings before interest, taxes, depreciation, and amortization. income declined. This discrepancy occurred because Allied increased its debt in 2005, and the increased interest expense reduced its net income despite its higher operating income. Taking a closer look at the income statement, we see that depreciation and amortization are important components of operating costs.5 Recall from accounting that depreciation is an annual charge against income that reflects the estimated dollar cost of the capital equipment and other tangible assets that were used up in the production process. Amortization amounts to the same thing, except represents the decline in value of intangible assets such as patents, copyrights, trademarks, and goodwill. Because they are so similar, depreciation and amortization are generally lumped together for purposes of financial analysis on the income statement and for other purposes. They both write off, or allocate, the costs of assets over their useful lives. Even though depreciation and amortization are reported as costs on the income statements, they are not cash expenses--cash was spent in the past, when the assets being written off were acquired, but no cash is paid out to cover depreciation. Therefore, managers, security analysts, and bank loan officers who are concerned with the amount of cash a company is generating often calculate EBITDA, defined as earnings before interest, taxes, depreciation, and amortization. Allied has no amortization charges, so the depreciation and amortization on the income statement shown in Table 3-2 is all depreciation. In 2005, EBITDA was $383.8 million. Subtracting the $100 million of depreciation from EBITDA left the company with $283.8 million of operating income (EBIT). After subtracting $88 million in interest and $78.3 million in taxes, Allied had $117.5 million in net income. While the balance sheet can be thought of as a snapshot in time, the income statement reports on operations over a period of time, for example, during the calendar year 2005. Allied's 2005 sales were $3 billion, and its net income was $117.5 million. Income statements can cover any period of time, but most companies prepare them monthly, quarterly, and annually. The quarterly and annual statements are released to investors, while the monthly statements are used internally for planning and control purposes, comparing actual results with forecasted (or "budgeted") results. If revenues drop below or costs rise above the forecasted levels, management should find out why and take corrective steps before the problem becomes serious. What is an income statement, and what information does it provide? Why is earnings per share called "the bottom line"? Differentiate between amortization and depreciation. What are EBIT, operating income, and EBITDA? Which is like a snapshot of the firm's operations--the balance sheet or the income statement--and which is more like a movie? Explain. 5 Industrial companies like Allied generally have few intangible assets, hence little if any amortization. High-tech companies like Microsoft, which spend billions developing new products, and media companies, when they produce movies like The Aviator, do have sizable intangible assets, hence amortization is important for them. Actually, life would be simpler, and financial statements just as informative, if the accountants just applied the term "depreciation" to the periodic write-off of all assets, tangible and intangible alike. But until they change, we must continue using both terms. We should note that prior to 2002 amortization was very important for companies that engaged in mergers. If a company pays more than book value when it acquires another firm, the excess is called "goodwill." Prior to 2002, firms were required to amortize goodwill, and the annual amortization charge reduced reported income by a like amount. After 2002, GAAP no longer required that goodwill be amortized, and that greatly reduced amortization charges for companies in general. Chapter 3 Financial Statements, Cash Flow, and Taxes 75 3.5 NET CASH FLOW As we discussed in Chapter 1, management's goal should be to maximize the stock price. Because the value of any asset, including a share of stock, depends on the cash flows the asset is expected to produce, this means that managers should strive to maximize the cash flows available to investors over the long run. A business's net cash flow differs from its accounting profit because some of the revenues and expenses listed on the income statement are not paid in cash during the year. Allied and many other companies have zero noncash revenues, and depreciation and amortization are the only noncash charges.6 Under these conditions, the relationship between net cash flow and net income can be expressed as follows: Net Cash Flow The actual net cash, as opposed to accounting profit (net income), that a firm generates during a specified period. Accounting Profit A firm's net income as reported on its income statement. Net cash flow Net income Depreciation and amortization (3-2) We can illustrate Equation 3-2 with Allied's 2005 data from Table 3-2: Net cash flow $117.5 $100.0 $217.5 million Depreciation is an important source of cash for Allied and most other companies, and it is important that you understand its financial implications. We discuss depreciation in more depth in Chapter 12, but for a quick illustration, suppose a machine with a life of five years and a zero salvage value was purchased in 2005 for $100,000 and placed in service in 2006. The $100,000 purchase price was paid in cash in 2005, but it does not show up as an expense in 2005; rather, a portion of it is charged as a cost of production over each year of the machine's life. If the $100,000 were taken as an expense in 2005, then profits in that year would be understated, but profits in each of the following five years would be overstated. So, under accrual accounting rules an annual depreciation charge is deducted from sales revenues when determining income in 2006 through 2010. However, the $100,000 cost of the machine was actually paid in cash in 2005, and the depreciation charged against income from 2006 through 2010 does not involve a cash payment. Because depreciation is a noncash charge, it must be added back to net income to obtain net cash flow. If we assume that all other noncash items sum to zero, Equation 3-2 will hold and net cash flows are equal to net income plus depreciation and amortization. How do we estimate net cash flow, and how does it differ from accounting profit? In accounting, the emphasis is on net income. In finance, the primary emphasis is on cash flow. Why is this so? 3.6 STATEMENT OF CASH FLOWS Its net cash flow represents the cash a business generates in a given year. However, the fact that a company generates a high cash flow does not necessarily mean that the cash reported on its balance sheet is also high. Cash flow is not 6 Allied and most other companies have little if any noncash revenues, but this item can be important for construction companies that work on multiyear projects, report income on a percentage of completion basis, and then are paid only after the project is completed. Also, if a company has a substantial amount of deferred taxes, which means that taxes actually paid are less than that reported in the income statement, then this amount could also be added to net income when estimating the net cash flow. Other adjustments could also be made, but a discussion of these details would go beyond the scope of this text and is best left for advanced finance and accounting courses. 76 Part 2 Fundamental Concepts in Financial Management normally used just to build up the cash account. Rather, it is used in a variety of ways, including paying dividends, increasing inventories, financing accounts receivable, investing in fixed assets, retiring debt, and buying back common stock. Here is a quick summary to the key factors that affect a company's cash balance: 1. Cash flow. Other things held constant, a positive net cash flow leads to more cash in the bank. However, other things are generally not held constant, and cash flow is used for other things. 2. Changes in working capital. Increases in working capital (inventories and receivables) are paid for with cash, so such increases decrease cash. On the other hand, decreases in working capital increase cash. For example, if inventories are to increase, the firm must use cash to purchase the additional inventory, whereas if inventories decrease, this generally means the firm is selling inventories and not replacing them, hence generating cash. Similarly, increases in current liabilities such as accounts payable increase cash, whereas decreases in payables reduce it. This occurs because, if payables increase, the firm has received additional credit from its suppliers, which saves cash, while if payables decrease, the firm has used cash to pay its suppliers. 3. Fixed assets. If a company invests in fixed assets, its cash position is reduced, whereas if it sells fixed assets, this increases cash. 4. Security transactions and dividend payments. If a company issues stock or bonds during the year, the funds raised will enhance its cash position. On the other hand, if it uses cash to pay off outstanding debt, to buy back some of its stock, or to pay dividends to shareholders, this will reduce cash. Statement of Cash Flows A statement reporting the impact of a firm's operating, investing, and financing activities on cash flows over an accounting period. Each of these factors is reflected in the statement of cash flows, which summarizes the changes in a company's cash position. The statement separates activities into three categories: 1. Operating activities, which include net income, depreciation, and changes in working capital other than cash and short-term debt. 2. Investing activities, which include purchases or sales of fixed assets. 3. Financing activities, which include raising cash by issuing short-term debt, long-term debt, or stock, or using cash to pay dividends or to buy back outstanding stock or bonds. Accounting texts explain how to prepare the statement of cash flows; however, in finance we're concerned with questions the statement can answer: Is the firm generating enough cash to acquire the assets needed to support its growth? Is it generating any extra cash that can be used to repay debt or to invest in new products? Will internally generated cash be sufficient, or will the company have to issue more common stock? This type of information is useful for both managers and investors, so the statement of cash flows is an important instrument. This statement, along with the cash budget, is used to help forecast a company's cash position. Table 3-3 shows Allied's statement of cash flows as it would appear in the company's annual report. The top section is most important, as it shows the cash flows that were generated by and used in operations. Allied's operations lost cash flow--it was minus $2.5 million. This indicates that the company, in the normal course of business, was running a cash deficit. Its day-to-day operations brought in $257.5 million, but the increase in receivables and inventories more than offset this inflow, resulting in a negative $2.5 million cash flow from operations. Successful companies have large, positive cash flows from operations, as this is what gives them value. Allied clearly had an operating problem in 2005. Chapter 3 Financial Statements, Cash Flow, and Taxes 77 TA B L E 3 - 3 Allied Food Products: Statement of Cash Flows for 2005 (Millions of Dollars) 2005 I. OPERATING ACTIVITIES Net Income before dividends Additions (Sources of Cash) Depreciation and amortizationa Increase in accounts payable Increase in accruals Subtractions (Uses of Cash) Increase in accounts receivable Increase in inventories Net cash provided by operating activities II. LONG-TERM INVESTING ACTIVITIES Cash used to acquire fixed assetsb III. FINANCING ACTIVITIES Increase in notes payable Increase in bonds Payment of dividends Net cash provided by financing activities Net decrease in cash and equivalents Cash and equivalents at beginning of the year IV. CASH AND EQUIVALENTS AT END OF THE YEAR $117.5 100.0 30.0 10.0 (60.0) (200.0) ($ 2.5) ($230.0) $ 50.0 170.0 (57.5) $162.5 ($ 70.0) 80.0 $ 10.0 Notes: Depreciation and amortization are noncash charges, so they must be added back to net income to show the actual cash flow from operations. b The net increase in fixed assets was $130 million, but this is a net amount after deducting the year's depreciation expense. Depreciation must be added to the $130 million to show the actual amount spent to purchase fixed assets. From the income statement, we see that the 2005 depreciation expense was $100 million, so we show expenditures on fixed assets as $230 million. a The second section shows Allied's long-term investing activities. The company purchased fixed assets totaling $230 million; this was the only long-term investment it made during 2005. When we add the results of Sections I and II, we see that Allied had a cash deficit of $232.5 million in 2005. How was that deficit financed? This information is provided in Section III, Financing Activities. Here we see that Allied borrowed from banks (notes payable) and issued new bonds to bring in a total of $220 million, but it paid out $57.5 million in dividends to its stockholders, resulting in a net inflow of $162.5 million from financing activities. Allied's deficit from operations and investment activities totaled $232.5 million, and it raised a net $162.5 million from financing activities, leaving a net deficit of $70 million. How was this $70 million shortfall covered? It was covered by drawing down the cash and equivalents account. The company started the year with $80 million of cash and cash equivalents (marketable securities), ended the year with only $10 million, hence used $70 million of its initial cash holdings to cover its operating deficit and fixed assets investments. Allied's statement of cash flows should worry its managers and investors. It was able to cover the operating deficit and the investments by heavy borrowing and by drawing down its stockpile of cash and equivalents, but that obviously can't continue on into the future. In the long run, Section I should show good 78 Part 2 Fundamental Concepts in Financial Management Massaging the Cash Flow Statement Profits as reported on the income statement can be "massaged" by changes in depreciation methods, inventory valuation procedures, and so on, but "cash is cash," so management can't mess with the cash flow statement, right? Nope--wrong. A recent article in The Wall Street Journal described how Ford, General Motors, and several other companies overstated their operating cash flows, the most interesting section of the cash flow statement. Indeed, GM reported more than twice as much cash from operations as it really had, $7.6 billion versus a true $3.5 billion. When GM sold cars to a dealer on credit, it created an account receivable, which should be shown in the "Operating Activities" section as a use of cash. However, GM classified these receivables as loans to dealers and reported them as a financing activity. That decision more than doubled the reported cash flow from operations. It didn't effect the end-of-year cash, but it made operations look stronger than they really were. If Allied Foods, in Table 3-3, had done this, the $60 million increase in receivables, which is correctly shown as a use of cash, would have been shifted to the "Financing Activities" section, causing Allied's cash provided by operations to rise from $2.5 million to $57.5 million. That would have made Allied look better to investors and credit analysts, but it would have been just smoke, mirrors, and accounting. GM's treatment was uncovered by Professor Charles Mulford of Georgia Tech. The SEC then sent GM a letter that basically required GM to change its procedures. The company issued a statement that it thought at the time it was acting in accordance with GAAP, but that it would reclassify its accounts in the future. GM's action was certainly not in the league of WorldCom's or Enron's, but it does show that companies sometimes do things to make their statements look better than they really are. Source: Diya Gullapalli, "Little Campus Lab Shakes Big Firms," The Wall Street Journal, March 1, 2005, p. C3. operating cash flows; Section II should show spending on fixed assets that is about equal to depreciation charges (to replace worn out fixed assets) plus a bit more to support growth; and Section III should show relatively little net borrowing along with a "reasonable" amount of dividends (for an average company, dividends amount to about 50 percent of net income). Finally, Section IV should show a reasonably stable cash and equivalents balance from year to year. These conditions obviously do not hold for Allied, so something should be done to right the ship. We will go into this more deeply in Chapter 4, when we move on to a more detailed financial analysis of the financial statements. Statement of Retained Earnings A statement reporting how much of the firm's earnings were retained in the business rather than paid as dividends. The balance sheet number reported for retained earnings is the sum of the annual retained earnings for each year of the firm's history. What is the statement of cash flows, and what are some questions it is designed to answer? If a company has high cash flows, does this mean that its cash and equivalents will also be high? Explain. Identify and briefly explain the three types of activities shown in the statement of cash flows. 3.7 STATEMENT OF RETAINED EARNINGS The change in retained earnings between balance sheet dates is reported in the statement of retained earnings. Table 3-4 shows that Allied earned $117.5 million during 2005, paid out $57.5 million in common dividends, and plowed $60 Chapter 3 Financial Statements, Cash Flow, and Taxes 79 TA B L E 3 - 4 Allied Food Products: Statement of Retained Earnings for Year Ending December 31, 2005 (Millions of Dollars) 2005 Balance of Retained Earnings, December 31, 2004 Add: Net Income, 2005 Less: Dividends to common stockholders Balance of Retained Earnings, December 31, 2005 $750.0 117.5 (57.5)a $810.0 Note: a Here, and throughout the book, parentheses are sometimes used to denote negative numbers. million back into the business. Thus, the balance sheet item "Retained earnings" increased from $750 million at year-end 2004 to $810 million at year-end 2005. Note that "retained earnings" represents a claim against assets, not assets per se. Moreover, firms retain earnings for reinvestment in the business, which means investing in plant and equipment, in inventories, and so on, not to pile up cash in a bank account. Changes in retained earnings occur because common stockholders allow management to reinvest funds that otherwise could be distributed as dividends. Thus, the retained earnings account reported on the balance sheet does not represent cash and is not "available" for dividends or anything else.7 What is the statement of retained earnings, and what information does it provide? Why do changes in retained earnings occur? Explain why the following statement is true: "The retained earnings account reported on the balance sheet does not represent cash and is not `available' for dividend payments or anything else." 3.8 USES AND LIMITATIONS OF FINANCIAL STATEMENTS The financial statements provide investors with a lot of useful information. You can look through the statements and answer a number of important questions such as these: How large is the company? Is it growing? Is it making or losing money? Does it have a high percentage of current assets versus fixed assets? To what extent does the firm use debt or equity to finance its assets? Does it rely more on short-term or long-term debt? Has it issued any new debt or equity in recent years? Has it made significant capital expenditures in recent years? Does it have a lot of cash on hand or is a shortage looming, and has the cash balance been rising or falling over time? 7 The amount reported in the retained earnings account is not an indication of the cash the firm has. Cash (as of the balance sheet date) is found in the cash account, an asset account. A positive number in the retained earnings account indicates only that the firm has in the past earned some income and not paid out all of those earnings as dividends. Even though a company reports record earnings and shows an increase in retained earnings, it still may be short of cash. The same situation holds for individuals. You might own a new BMW (no loan), lots of clothes, and an expensive stereo, hence have a high net worth, but if you had only 23 cents in your pocket plus $5 in your checking account, you would still be short of cash. 80 Part 2 Fundamental Concepts in Financial Management Financial Analysis on the Internet A wide range of valuable financial information is available on the Internet. With just a couple of clicks, an investor can find the key financial statements for most publicly traded companies. Suppose you are considering the purchase of Disney stock, and you want to analyze its recent performance. Here's a partial (but by no means a complete) list of places you could go to get started: One source is Yahoo!'s finance Web site, finance .yahoo.com.a Here you will find updated market information along with links to a variety of interesting research sites. Enter a stock's ticker symbol, click on Go, and you will see the stock's current price, along with recent news about the company. Click on Key Statistics and you will find a report on the company's key financial ratios. Links to the company's financials (income statement, balance sheet, and statement of cash flows) can also be found. The Yahoo! site also has a list of insider transactions, so you can tell if a company's CEO and other key insiders are buying or selling the company's stock. In addition, there is a message board where investors share opinions about the company, and there is a link to the company's filings with the Securities and Exchange Commission (SEC). Note also that, in most cases, a more complete listing of SEC filings can be found at www.sec.gov or at www.edgar-online.com. Another Web site with similar information is MSN Money (moneycentral.msn.com). After clicking the Investing and Stocks tabs, you enter the stock's ticker symbol. Then, you will see the current stock price and a list of recent news stories. Here you will also find links to the company's financial statements and key ratios (under Financial Results), as well as other information including analyst ratings, historical charts, earnings estimates, and a summary of insider transactions. Both MSN Money and Yahoo! Finance allow you to export the financial statements and historical prices to an Excel spreadsheet. Other sources for up-to-date market information are money.cnn.com and www.marketwatch.com/ news/. These sites also have areas where you can obtain stock quotes along with company financials, links to Wall Street research and SEC filings, company profiles, and charts of the firm's stock price plotted over time. After accumulating all of this information, you may be looking for sites that provide opinions regarding the direction of the overall market and views regarding the individual stock. Two popular sites in this category are The Motley Fool's Web site, www.fool.com, and the site for TheStreet.com, www.thestreet.com. Keep in mind that this list is just a small subset of the information available online. You should also realize that sites come and go, and also change their content over time. New and interesting sites are constantly being added to the Internet. a To avoid redundancy, we have intentionally left off http:// in all Web addresses given here. A quick way to change an address is to highlight the portion of the address that is different and type in the appropriate letters of the new address. Once you're finished just press Enter. At the same time, investors need to be cautious when they review financial statements. While companies are required to follow GAAP, managers still have quite a lot of discretion in deciding how and when to report certain transactions--see the box in Section 3.6 on GM's treatment of accounts receivable from its dealers. Consequently, two firms in exactly the same operating situation may report financial statements that convey different impressions about their financial strength. Some variations may stem from legitimate differences of opinion about the correct way to record transactions. In other cases, managers may choose to report numbers in a way that helps them present either higher earnings or more stable earnings over time. As long as they follow GAAP, such actions are not illegal, but these differences make it harder for investors to compare companies and gauge their true performances. Unfortunately, as we noted in Chapter 1, there have also been cases where managers overstepped the bounds and reported fraudulent statements. Indeed, Chapter 3 Financial Statements, Cash Flow, and Taxes 81 a number of high-profile executives have faced criminal charges because of their misleading accounting practices. For example, in June 2002 it was discovered that WorldCom (now called MCI) had committed the most massive accounting fraud of all time by recording more than $11 billion of ordinary operating costs as capital expenditures, thus overstating net income by the same amount. WorldCom's published financial statements fooled most investors--investors bid the stock price up to $64.50, and banks and other lenders provided the company with more than $30 billion of loans. Arthur Andersen, the firm's auditor, was faulted for not detecting the fraud. Their defense was that WorldCom's management had lied. WorldCom's CFO pleaded guilty and was sentenced to 5 years in prison, while its CEO was sentenced to 25 years in prison. In the wake of this and other recent accounting scandals, regulators and accounting professionals are issuing new standards to make financial statements more transparent for investors and to create an environment where managers have strong incentives to report truthful numbers. Also, keep in mind that even if investors are provided with accurate accounting data, it is really cash flow, not accounting income, that matters. Similarly, when managers decide on which projects to accept, their focus should be on cash flow. Therefore, when it comes to effective decision making, managers and investors generally need to modify even the most accurate and transparent financial statements to determine the relevant cash flows. We discuss this in the next section. Can an investor have complete confidence that the financial statements of different companies are accurate and that the data reported by one company are truly comparable to the data provided by another? Why might different companies account for similar transactions in different ways? 3.9 MODIFYING ACCOUNTING DATA FOR INVESTOR AND MANAGERIAL DECISIONS Thus far in the chapter we have focused on financial statements as they are prepared by accountants and presented in the annual report. However, these statements are designed more for use by creditors and tax collectors than for managers and stock analysts. Therefore, certain modifications are helpful for corporate decision-making and stock valuation purposes. Recall from Chapter 1 that the firm's primary financial objective is to maximize shareholder value. Investors provide companies with capital, and managers create value for shareholders by investing this capital in productive assets. In the following sections we discuss how financial managers and analysts use accounting data to measure and evaluate corporate performance. Operating Assets and Operating Capital Companies raise funds from a variety of sources. The primary source is investors, including stockholders, bondholders, and lenders such as banks. Investors must be paid for the use of their money, with payment coming as interest for bonds and other debt and as dividends plus capital gains for stock. 82 Part 2 Fundamental Concepts in Financial Management Net Operating Working Capital (NOWC) Operating working capital less accounts payable and accruals. It is the working capital acquired with investorsupplied funds. So, if a company obtains more assets than it actually needs, it will have raised too much capital and thus have unnecessarily high capital costs. Not all of the capital used to acquire assets is provided by investors--some of the funds normally come from suppliers and are reported as accounts payable, while other funds as reported on the balance sheet come as accrued wages and accrued taxes, which amount to short-term loans from workers and tax authorities. Generally, both accounts payable and accruals are "free" because no explicit fee is charged for their use. These funds are commonly referred to as spontaneously generated, non-interest-bearing current liabilities. They are called "spontaneous" because they are generated spontaneously through normal business operations, not by a specific act such as going to a bank and borrowing money. When evaluating a company's overall position and value, analysts often focus on net operating working capital (NOWC), defined as follows:8 Net operating working capital NOWC All current assets required in operations All non-interestbearing current liabilities (3-3) Allied's net operating working capital for 2005 was NOWC All current assets required in operations a Cash and cash equivalents A$10 $800 million Accounts receivable $375 $615B Inventories b a All non-interestbearing current liabilities Accounts payable A$60 Accruals b $140B For 2004, Allied's net operating working capital (NOWC) was Net operating working capital A$80 $315 $415B A$30 $130B $650 million Thus, Allied's NOWC increased by $150 million during 2005. Working capital is important for several reasons. First, all companies must carry some cash to "grease the wheels" of their operations. They continuously receive checks from customers and write checks to suppliers, employees, and so on. Because inflows and outflows do not coincide perfectly, firms must keep some cash (and cash equivalents) in their bank accounts to conduct operations without periodic disruptions. The same is true for most other current assets, such as inventory and accounts receivable. Allied and most other companies try to hold only as much cash and marketable securities as is required under normal operations--they don't try to operate like a bank and hold excess amounts of these assets. However, in some 8 Allied and many other companies have essentially zero nonoperating assets, but a number of companies do have significant amounts of nonoperating assets, often held as marketable securities, and report them on their balance sheets. Therefore, finance professionals typically differentiate operating from nonoperating assets and use the term NOWC as we do. Chapter 3 Financial Statements, Cash Flow, and Taxes 83 instances companies do accumulate more cash and marketable securities than are needed in operations. Perhaps these funds are on hand because the firm just sold a large bond issue and has not yet deployed the funds, or perhaps it is saving up funds for a specific purpose such as a merger or a major capital investment program. In these situations, the excess cash and marketable securities should not be viewed as part of operating working capital--it is nonoperating capital and is analyzed separately. Also, as noted, accounts payable and accruals arise in the normal course of operations, and each dollar of these current liabilities is a dollar that the company does not have to raise from investors to fund its current assets. Therefore, we deduct these current liabilities from the operating current assets when calculating net operating working capital. However, those current liabilities that charge interest, such as notes payable to banks, are investor-supplied capital, and are not deducted when we calculate NOWC. We see, then, that a company's assets can be divided into two groups, operating assets (or operating capital) and nonoperating assets (or nonoperating capital). Operating capital includes those current and net fixed assets that are necessary to operate the business, while nonoperating assets include items like land held for future use, stock in other companies, and marketable securities in excess of those held for liquidity purposes.9 Moreover, firm's holdings of nonoperating assets are always based on unique, special conditions, and decisions regarding them are similarly unique. Typically, the vast majority of assets are operating as opposed to nonoperating, and the firm's value is based on the cash flows that those operating assets provide. Therefore, our focus in the book is on operating, not on nonoperating, assets. Companies typically use a combination of investor-supplied capital and noninterest-bearing, spontaneous current liabilities to finance their required operating assets. For example, when Allied opens a new plant, it needs to acquire fixed assets (land, building, and equipment) and current assets (inventory and receivables). However, the suppliers who ship materials to Allied generally expect to be paid 30 or so days later, so accounts payable, which are non-interest-bearing current liabilities, help finance the new operations. Accrued wages and taxes similarly reduce the amount of funds Allied's investors must provide to acquire the new operating assets. The amount of operating capital supplied by Allied's investors over the years, through December 31, 2005, is found as follows: Total operating capital, 2005 Net operating working capital $800 $1,000 Net fixed assets (3-4) $1,800 million In the prior year, 2004, Allied's total operating capital was Total operating capital, 2004 $650 $870 $1,520 million Therefore, Allied's operating capital increased from $1,520 to $1,800 million during 2005, or by $280 million. 9 To value a firm, analysts typically use the techniques we describe in the text to value the firm's operations and then add to that value the value of the nonoperating assets. To keep things simple, we illustrate concepts with Allied Foods, which has only operating assets. 84 Part 2 Fundamental Concepts in Financial Management Operating Cash Flows Financial managers create value by obtaining funds and investing them in operating assets, and the cash flow generated through operations determines the firm's value. These cash flows are found as follows: Operating cash flow EBIT(1 Tax rate) Depreciation and amortization (3-5) Net Operating Profit After Taxes (NOPAT) The profit a company would generate if it had no debt and held only operating assets. Recall that EBIT is the firm's operating income--it is what remains after subtracting from sales all operating costs, including depreciation and amortization, but before subtracting taxes and interest. Investors are interested in after-tax cash flows, which are found by multiplying EBIT by one minus the tax rate. We add back depreciation and amortization when calculating the cash flow because they are noncash expenses. EBIT(1 Tax rate) is often referred to as NOPAT, or net operating profit after taxes, and it is the profit a company would generate if it had no debt and held only operating assets.10 Thus, we can rewrite Equation 3-5 as follows: Operating cash flow NOPAT Depreciation and amortization (3-5a) Using data from the income statement in Table 3-2, Allied's 2005 NOPAT was NOPAT $283.8(1 0.4) $283.8(0.6) $170.3 million Because depreciation was the only noncash charge, Allied's 2005 operating cash flow was Operating cash flow NOPAT $170.3 Depreciation and amortization $100 $270.3 million Free Cash Flow Earlier in the chapter we defined net cash flow as being equal to net income plus noncash adjustments, typically net income plus depreciation. Note, though, that cash flows cannot be maintained over time unless depreciating fixed assets are replaced, and new products must also be developed. Therefore, management is not completely free to use the available cash flow however it pleases. Therefore, we now define another term, free cash flow, which is the cash flow actually available for payments to investors (stockholders and debtholders) after the company has made the investments in fixed assets, new products, and working capital required to sustain ongoing operations. To be more specific, the value of a company's operations depends on its expected future free cash flows (FCF), defined as after-tax operating profit minus the investments in working capital and fixed assets necessary to sustain the business. Thus, free cash flow represents the cash that is actually available for payments to investors. Therefore, managers make their companies more valuable by increasing their free cash flow. Free Cash Flow The cash flow actually available for distribution to all investors (stockholders and debtholders) after the company has made all the investments in fixed assets, new products, and working capital necessary to sustain ongoing operations. 10 For large, complex firms complications can arise. For additional information see Tim Koller, Marc Goedhart, and David Wessels, Valuation: Measuring and Managing the Value of Companies, 4th edition (New York: John Wiley & Sons, 2005); and G. Bennett Stewart III, The Quest for Value, 2nd edition (New York: HarperCollins Publishers, 1999). Chapter 3 Financial Statements, Cash Flow, and Taxes 85 The following equation can be used to calculate free cash flow:11 FCF cEBIT(1 T) Depreciation d and amortization Capital expenditures Net operating working capital Operating cash flow Investment in operating capital In 2005 Allied's EBIT was $283.8 million, and its depreciation and amortization was $100 million. Its fixed assets increased by $130 million after $100 million of depreciation, so its capital expenditures must have been $230 million. Finally, its net operating working capital (current assets less spontaneous current liabilities) rose by $150 million. Therefore, its free cash flow was $109.7 million: FCF Operating cash flow [$283.8(1 $270.3 0.4) $380 Investment in operating capital ($230 $150) (3-6) $100] $109.7 million Even though Allied's operating cash flow was positive, its very high investment in operating capital resulted in a negative free cash flow. Because free cash flow is what is available for distribution to investors, not only was there nothing for investors, but investors actually had to put in more money to keep the business going. Investors provided most of the needed funds as debt. Is a negative free cash flow always bad? The answer is, Not necessarily; it depends on why the free cash flow was negative. If FCF was negative because NOPAT was negative, this is definitely bad, and it suggests that the company is experiencing operating problems. However, many high-growth companies have positive NOPAT but negative free cash flow because they must invest heavily in operating assets to support rapid growth. There is nothing wrong with a negative cash flow if it results from profitable growth. What is net operating working capital? What is total operating capital? What is NOPAT? What is free cash flow? Why is free cash flow the most important determinant of a firm's value? A company has NOPAT of $30 million, and its depreciation and amortization expense is $10 million. During the year the company's gross capital expenditures (total purchases of fixed assets) were $20 million and its net operating working capital increased by $10 million. What is the company's operating cash flow? ($40 million) What is its free cash flow? ($10 million) 11 In the finance literature, free cash flow is defined in two ways: (1) cash flow available to both stockholders and bondholders and (2) cash flow available to stockholders, that is, after interest payments. The first definition, which we prefer and incorporate into Equation 3-6, is the one most analysts use. FCF as found with Equation 3-6 can be discounted at the weighted average cost of capital (WACC) to find the value of the firm, whereas FCF after interest must be discounted at the cost of common stock to find the firm's value. This distinction is discussed at length in advanced finance courses, but the choice does not matter so long as the correct discount rate is used with each. 86 Part 2 Fundamental Concepts in Financial Management 3.10 MVA AND EVA Assets as reported on the financial statements reflect historical, in-the-past, values, not current market values, and there are often substantial differences between the two. Inflation results in differences, as do successful and unsuccessful operations. For example, it cost Microsoft very little to develop its first operating system, but that system turned out to be worth many billions that were not shown on its balance sheet. Of course, balance sheets must balance, so if the assets side of the statement totals to less than the market value of the firm's assets, then so will the liabilities and capital side. Debt values are fixed by contract, so it is the equity where the discrepancy between book and market values are concentrated. To illustrate, consider the following situation. The firm was started with $1 million of assets at book value (historical cost), $500,000 of which was provided by bondholders, and $500,000 by stockholders (50,000 shares purchased at $10 per share). However, the firm was very successful, and its assets now produce $2 million of free cash flow per year. Investors discount that free cash flow at a 10 percent rate, resulting in a value of $20 million for the firm. After deducting the $500,000 of debt, the market value of the equity is found to be $19.5 million versus the $500,000 stockholders invested in the firm. The stock price is $19,500,000/ 50,000 $390 per share, so the firm's managers have done a marvelous job for the stockholders. The accounting statements do not reflect market values, so they are not sufficient for purposes of evaluating managers' performance. To help fill this void, financial analysts have developed two additional performance measures, the first of which is MVA, or Market Value Added.12 MVA is simply the difference between the market value of a firm's equity and the book value as shown on the balance sheet, with market value found by multiplying the stock price by the number of shares outstanding. For our hypothetical firm, MVA is $19.5 million $0.5 million $19 million. For Allied, which has 50 million shares outstanding and a $23 price, the market value of the equity is $1,150 million versus a book value as shown on the balance sheet in Table 3-1 of $940 million. Therefore, Allied's MVA is $1,150 $940 $210 million. This $210 million represents the difference between the money Allied's stockholders have invested in the corporation since its founding-- including retained earnings--versus the cash they could get if they sold the business. The higher its MVA, the better the job management is doing for the firm's shareholders. Boards of directors often look at MVA when deciding on the compensation a firm's managers deserve. Note though, that just as all ships rise in a rising tide, most firms' stock prices rise in a rising stock market, so a positive MVA may not be entirely attributable to management. A related concept, Economic Value Added (EVA), sometimes called "economic profit," is closely related to MVA and is found as follows: Market Value Added (MVA) The excess of the market value of equity over its book value. Economic Value Added (EVA) Excess of NOPAT over capital costs. EVA Net operating profit after taxes 1NOPAT 2 EBIT 11 T2 Annual dollar cost of capital (3-7) Total investor-supplied operating capital After-tax percentage cost of capital 12 The concepts of EVA and MVA were developed by Joel Stern and Bennett Stewart, co-founders of the consulting firm Stern Stewart & Company. Stern Stewart copyrighted the terms "MVA" and "EVA," so other consulting firms have given other names to these values. Still, MVA and EVA are the terms most commonly used in practice. For more on MVA and EVA, see Stewart, The Quest for Value. Chapter 3 Financial Statements, Cash Flow, and Taxes 87 EVA is an estimate of a business's true economic profit for a given year, and it differs sharply from accounting net income primarily in that accounting income has no deduction for the cost of equity whereas this cost is deducted when calculating EVA. If EVA is positive, then after-tax operating income exceeds the cost of the capital needed to produce that income, and management's actions are adding value for stockholders. Positive EVA on a yearly basis will help ensure that MVA is also positive. Note that whereas MVA applies to the entire firm, EVA can be determined for divisions as well as for the company as a whole, so it is useful as a guide to "reasonable" compensation for divisional as well as top corporate managers. Define the terms "Market Value Added (MVA)" and "Economic Value Added (EVA)." How does EVA differ from accounting net income? 3.11 THE FEDERAL INCOME TAX SYSTEM Corporations must pay out a significant portion of their income as taxes, and individuals are also taxed on their income. We summarize some important points about the U.S. tax system here, based on 2004 provisions. A more detailed discussion is provided in Web Appendix 3A accessed through the ThomsonNOW Web site. Corporate Taxes Corporate income is generally taxed by the federal government at rates that begin at 15 percent and go up to 35 percent on taxable income of $10 million or more.13 Thus, the corporate tax structure is progressive in the sense that higher rates are imposed on companies with larger incomes. Most state governments also impose income taxes on corporations, with 5 percent being a typical rate. Therefore, larger companies generally pay a rate of about 40 percent on their income, and we typically use 40 percent in our examples. The tax system is incredibly complex, so we do not attempt to cover it in detail. However, as noted above, we do provide a bit more tax information on the ThomsonNOW Web site. Personal Taxes Individuals are taxed by the federal government at rates that begin at 10 percent and rise to 35 percent on incomes of $319,100 or more. Some states also impose a state income tax, with rates varying across states. Note that income on investments held in pension accounts is not taxed until the money is withdrawn, presumably after retirement. Thus, a person might be in the 35 percent tax bracket on his or her ordinary income, but the tax rate would be zero on income earned in a 401(k) or other retirement account (and certain college savings plans). A Web site of interest concerning federal tax law is http://www.taxsites.com/ federal.html. From this home page one can visit other sites that provide summaries of recent tax legislation or current information on corporate and individual tax rates. The official government Web site is http://www.irs.gov. Interest Paid Borrowers must pay interest on their debts. For a business, the interest payments are regarded as an expense, and they are deducted when calculating taxable income. Individuals also incur debts and pay interest, but generally individuals cannot deduct interest payments (the big exception is interest on home loans, which, within limits, is deductible). 13 Actually, the marginal corporate tax rate goes up to 38 percent for income between $15,000,000 and $18,333,333; however, it then declines to 35 percent for taxable income above $18,333,333. 88 Part 2 Fundamental Concepts in Financial Management Interest Earned Most interest earned, whether by businesses or individuals, is taxable. An important exception is that interest on most state and local government debt is exempt from federal taxes. State and local bonds are often called "munis," and they are generally purchased by individuals in high tax brackets. Dividends Paid Corporations pay dividends, and dividends paid are generally not a deductible expense. Thus, corporations can deduct interest paid but they cannot deduct dividends. Thus, if a company had a combined federal-plus-state tax rate of 40 percent and $10 million of pre-tax cash income, it could pay out all $10 million as interest but only $6 million of dividends because it would have to pay $4 million of taxes.14 Note that if one company uses a lot of debt financing, whereas another with similar operations uses only common stock financing, the stock-financed company will have no interest, hence no interest tax deductions, hence a higher income tax bill. The company that uses debt can thus pass more of its operating income on to investors (stockholders and debtholders). For this reason, our tax system encourages debt financing, as we discuss at length in the chapter on capital structure. Dividends Received Dividends received by an individual are taxed at the same tax rate as capital gains, 15 percent.15 Note that this creates a double tax on dividend income--the corporation that paid the dividend is first taxed, and then the individual who receives it is taxed again. For corporate recipients, the situation is somewhat different--the corporation that receives dividend income can exclude some of the dividends from its taxable income. This provision is in the Tax Code to minimize the amount of triple taxation that would otherwise occur--one corporation would pay dividends out of after-tax income, the second corporation would be taxed again on that income, and the person who received dividends from the second corporation would be taxed once more. Tax Loss Carry-Back and Carry-Forward Corporation income often fluctuates from year to year, so a firm might be taxed at a 40 percent rate one year and then have a large loss the following year, hence pay no taxes. The Tax Code allows firms to carry losses back to offset profits in prior years, and, if losses haven't been offset by past profits, to carry the remaining losses forward to offset future profits. The effect of this provision is to cause taxes to reflect average income over time. Capital Gains Capital gains are, generally speaking, defined as profits from the sale of assets that are not normally bought and sold in the course of business. For individuals, capital gains typically arise from the sale of stocks or bonds at a profit. Thus, if someone buys some Microsoft stock for $10,000 and later sells it for $15,000, then he or she will have a $5,000 capital gain. If the stock was held for less than a 14 This calculation is not exact, because the tax bill on $10 million of income would actually be somewhat lower ($3.4 million) because some of the income would be taxed at lower rates. 15 If an individual is in the 10 percent tax bracket, the applicable tax rate is only 5 percent. Chapter 3 Financial Statements, Cash Flow, and Taxes 89 year, the $5,000 gain is just added to ordinary income and taxed as such. If the stock had been held for more than a year, then the gain will be taxed at a lower rate. For someone in the top (35 percent) federal tax bracket, the long-term capital gains rate is generally 15 percent. Corporations face somewhat different rules, and individual tax rates also vary a bit. Depreciation When a business buys an asset with a life greater than one year, it depreciates the asset over the years in which it will be used. For stockholder reporting, the company generally estimates the actual likely years of use, divides the cost by the number of years, and charges the calculated value as a cost on the income statement each year. (This is called "straight-line depreciation.") However, for tax purposes Congress has specified different depreciation rates for different types of assets, and those rates generally result in higher depreciation charges than what the company uses for stockholder reporting. We discuss depreciation in greater detail in Chapter 12. Small Businesses If a business is a proprietorship or partnership, its income is allocated to its owners in proportion to their ownership interests. If the same business is operated as a corporation, there are two possibilities. First, if the firm meets certain requirements related to size and number of stockholders, then it can elect to be taxed as an S corporation. In this case, for tax purposes it is treated like a partnership. An S corporation can thus enjoy the advantages of the corporate form of organization yet still receive the tax advantages of a partnership. Most small business corporations are actually set up as S corporations. If the firm does not qualify for S corporation status, it is called a C corporation and is taxed at regular corporate tax rates. Explain the statement, "Our tax rates are progressive." What is a "muni" bond, and how are these bonds taxed? What are long-term capital gains? How does our tax system influence the use of debt financing by corporations? Differentiate between S and C corporations. Tying It All Together The primary purposes of this chapter were to describe the basic financial statements, to present some background information on cash flows, to differentiate between net cash flow and accounting income, and to provide an overview of the federal income tax system. In the next chapter, we build on this information to analyze a firm's financial statements. 90 Part 2 Fundamental Concepts in Financial Management SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) ST-1 Key terms Define each of the following terms: a. Annual report; balance sheet; income statement; statement of cash flows; statement of retained earnings b. Common stockholders' equity, or net worth; retained earnings; net working capital c. Depreciation; tangible assets; amortization; intangible assets; EBITDA d. Net cash flow; accounting profit e. Operating assets; nonoperating assets f. Total operating capital; net operating working capital g. Net operating profit after taxes (NOPAT); operating cash flow; free cash flow h. Market Value Added (MVA); Economic Value Added (EVA) i. Progressive tax j. Capital gain k. S corporation; C corporation Net income and cash flow Last year Rattner Robotics had $5 million in operating income (EBIT). Its depreciation expense was $1 million; its interest expense was $1 million; and its corporate tax rate was 40 percent. At year-end it had $14 million in current assets, $4 million in non-interest-bearing current liabilities, and $15 million in net plant and equipment. Assume that Rattner's only noncash item was depreciation. a. What was the company's net income? b. What was its net cash flow? c. What was its net operating profit after taxes (NOPAT)? d. What was its operating cash flow? e. What was its net operating working capital (NOWC)? f. If operating capital at the end of the previous year was $24 million, what was the company's free cash flow (FCF) for the year? g. If the firm had $4.5 million in retained earnings at the beginning of the year and paid out a total dividend of $1.2 million, what was its retained earnings at the end of the year? ST-2 QUESTIONS 3-1 3-2 3-3 3-4 3-5 What four financial statements are contained in most annual reports? What do the numbers on financial statements actually represent? Who are some of the basic users of financial statements, and how do they use them? If a "typical" firm reports $20 million of retained earnings on its balance sheet, could its directors declare a $20 million cash dividend without any qualms whatsoever? Explain the following statement: "While the balance sheet can be thought of as a snapshot of the firm's financial position at a point in time, the income statement reports on operations over a period of time." Financial statements are based on generally accepted accounting principles (GAAP) and audited by CPA firms, so do investors need to worry about the validity of those statements? Differentiate between accounting profit and net cash flow. Why do those two numbers differ? Differentiate between operating cash flow and net cash flow. Why might those two numbers differ? 3-6 3-7 3-8 Chapter 3 Financial Statements, Cash Flow, and Taxes 91 3-9 3-10 3-11 What's the difference between NOPAT and net income? How does debt affect the relationship between these two items? What is free cash flow? If you were an investor, why might you be more interested in free cash flow than net income? Would it be possible for a company to report negative free cash flow and still be highly valued by investors; that is, could a negative free cash flow ever be a good thing in the eyes of investors? What does double taxation of corporate income mean? Could income ever be subject to triple taxation? How does the deductibility of interest and dividends by the paying corporation affect the choice of financing (that is, the use of debt versus equity)? 3-12 3-13 PROBLEMS Easy Problems 14 3-1 Income statement Little Books Inc. recently reported $3 million of net income. Its EBIT was $6 million, and its tax rate was 40 percent. What was its interest expense? [Hint: Write out the headings for an income statement and then fill in the known values. Then divide $3 million of net income by (1 T) 0.6 to find the pre-tax income. The difference between EBIT and taxable income must be the interest expense. Use this same procedure to work some of the other problems.] Income statement Pearson Brothers recently reported an EBITDA of $7.5 million and net income of $1.8 million. It had $2.0 million of interest expense, and its corporate tax rate was 40 percent. What was its charge for depreciation and amortization? Net cash flow Kendall Corners Inc. recently reported net income of $3.1 million and depreciation of $500,000. What was its net cash flow? Assume it had no amortization expense. Statement of retained earnings In its most recent financial statements, Newhouse Inc. reported $50 million of net income and $810 million of retained earnings. The previous retained earnings were $780 million. How much dividends were paid to shareholders during the year? Balance sheet Which of the following actions are most likely to directly increase cash as shown on a firm's balance sheet? Explain, and state the assumptions that underlie your Register to View AnswerIt issues $2 million of new common stock. b. It buys new plant and equipment at a cost of $3 million. c. It reports a large loss for the year. d. It increases the dividends paid on its common stock. Statement of retained earnings Computer World Inc. paid out $22.5 million in total common dividends and reported $278.9 million of retained earnings at year-end. The prior year's retained earnings were $212.3 million. What was the net income? Statement of cash flows W.C. Cycling had $55,000 in cash at year-end 2004 and $25,000 in cash at year-end 2005. Cash flow from long-term investing activities totaled $250,000, and cash flow from financing activities totaled $170,000. a. What was the cash flow from operating activities? b. If accruals increased by $25,000, receivables and inventories increased by $100,000, and depreciation and amortization totaled $10,000, what was the firm's net income? Cash flow The Klaven Corporation had operating income (EBIT) of $750,000 and depreciation expense of $200,000. It is 100 percent equity financed (no debt), and its corporate tax rate is 40 percent. The firm had no amortization expense. What are net income, net cash flow, and operating cash flow? 3-2 3-3 3-4 Intermediate Problems 510 3-5 3-6 3-7 3-8 92 Part 2 Fundamental Concepts in Financial Management 3-9 MVA Henderson Industries has $500 million of common equity; its stock price is $60 per share; and its Market Value Added (MVA) is $130 million. How many common shares are currently outstanding? Cash flow Bailey Corporation's income statement (dollars are in thousands) is given here: Sales Operating costs excluding depreciation and amortization EBITDA Depreciation and amortization EBIT Interest EBT Taxes (40%) Net income $14,000,000 7,000,000 $ 7,000,000 3,000,000 $ 4,000,000 1,500,000 $ 2,500,000 1,000,000 $ 1,500,000 3-10 Its total operating capital is $20 billion, and its total after-tax dollar cost of operating capital is $2 billion. During the year, Bailey invested $1.3 billion in net operating capital. a. What is its NOPAT? b. What is its net cash flow? c. What is its operating cash flow? d. What is its free cash flow? Challenging Problems 1114 3-11 Income statement Hermann Industries is forecasting the following income statement: Sales Operating costs excluding depreciation and amortization EBITDA Depreciation and amortization EBIT Interest EBT Taxes (40%) Net income $8,000,000 4,400,000 $3,600,000 800,000 $2,800,000 600,000 $2,200,000 880,000 $1,320,000 The CEO would like to see higher sales and a forecasted net income of $2,500,000. Assume that operating costs (excluding depreciation and amortization) are 55 percent of sales, and depreciation and amortization and interest expenses will increase by 10 percent. The tax rate, which is 40 percent, will remain the same. What level of sales would generate $2,500,000 in net income? 3-12 Financial statements The Davidson Corporation's balance sheet and income statement are given here: Davidson Corporation: Balance Sheet as of December 31, 2005 (Millions of Dollars) Assets Cash and equivalents Accounts receivable Inventories Total current assets Net plant and equipment 15 515 880 $1,410 2,590 $ Liabilities and Equity Accounts payable Notes payable Accruals Total current liabilities Long-term bonds Total debt Common stock (100 million shares) Retained earnings Common equity Total liabilities and equity $ 120 220 280 $ 620 1,520 $2,140 260 1,600 $1,860 $4,000 Total assets $4,000 Chapter 3 Financial Statements, Cash Flow, and Taxes 93 Davidson Corporation: Income Statement for Year Ending December 31, 2005 (Millions of Dollars) Sales Operating costs excluding depreciation and amortization EBITDA Depreciation and amortization EBIT Interest EBT Taxes (40%) Net income Common dividends paid Earnings per share $6,250 5,230 $1,020 220 $ 800 180 $ 620 248 $ 372 $ 146 $ 3.72 a. b. c. d. e. All revenues were received in cash during the year and all costs except depreciation and amortization were paid in cash during the year. What was net cash flow? How was it different from reported accounting profit? Construct the statement of retained earnings for December 31, 2005. How much money has been reinvested in the firm over the years? At the present time, how large a check could be written without it bouncing? How much money must be paid to current creditors within the next year? 3-13 Free cash flow Financial information for Powell Panther Corporation is shown here: Powell Panther Corporation: Income Statements for Year Ending December 31 (Millions of Dollars) 2005 Sales Operating costs excluding depreciation and amortization EBITDA Depreciation and amortization Earnings before interest and taxes Interest Earnings before taxes Taxes (40%) Net income Common dividends Powell Panther Corporation: Balance Sheets as of December 31 (Millions of Dollars) 2005 Assets Cash and equivalents Accounts receivable Inventories Total current assets Net plant and equipment Total assets Liabilities and Equity Accounts payable Notes payable Accruals Total current liabilities Long-term bonds Total debt Common stock (50 million shares) Retained earnings Common equity Total liabilities and equity $ 12.0 180.0 180.0 $372.0 300.0 $672.0 $108.0 67.0 72.0 $247.0 150.0 $397.0 50.0 225.0 $275.0 $672.0 2004 $ 10.0 150.0 200.0 $360.0 250.0 $610.0 $ 90.0 51.5 60.0 $201.5 150.0 $351.5 50.0 208.5 $258.5 $610.0 $1,200.0 1,020.0 $ 180.0 30.0 $ 150.0 21.7 $ 128.3 51.3 $ 77.0 $ 60.5 2004 $1,000.0 850.0 $ 150.0 25.0 $ 125.0 20.2 $ 104.8 41.9 $ 62.9 $ 46.4 94 Part 2 Fundamental Concepts in Financial Management a. b. c. d. e. What was the 2005 NOPAT? What were the 2004 and 2005 net operating working capital? What were the 2004 and 2005 total operating capital? What was the 2005 free cash flow? How would you explain the large increase in 2005 dividends? 3-14 Income and cash flow analysis The Menendez Corporation expects to have sales of $12 million in 2006. Costs other than depreciation and amortization are expected to be 75 percent of sales, and depreciation and amortization expenses are expected to be $1.5 million. All sales revenues will be collected in cash, and costs other than depreciation and amortization must be paid for during the year. The corporate tax rate is 40 percent. a. Set up an income statement. What is the expected net cash flow? b. Suppose Congress changed the tax laws so that depreciation and amortization expenses doubled and there were no changes in operations. What would happen to reported profit and net cash flow? c. Now suppose that Congress reduced depreciation and amortization expenses by 50 percent. How would profit and net cash flow be affected? d. Would you prefer that Congress double or halve depreciation and amortization expenses? Why? e. Would a doubling of depreciation and amortization expenses possibly have an adverse effect on stock price and on the ability to borrow money? Explain. COMPREHENSIVE/SPREADSHEET PROBLEM 3-15 Financial statements, cash flow, and taxes Laiho Industries' 2004 and 2005 balance sheets (in thousands of dollars) are shown below: 2005 Cash Accounts receivable Inventories Total current assets Net fixed assets Total assets Accounts payable Accruals Notes payable Total current liabilities Long-term debt Total liabilities Common stock Retained earnings Total common equity Total liabilities and equity $102,850 103,365 38,444 $244,659 67,165 $311,824 $ 30,761 30,477 16,717 $ 77,955 76,264 $154,219 100,000 57,605 $157,605 $311,824 2004 $ 89,725 85,527 34,982 $210,234 42,436 $252,670 $ 23,109 22,656 14,217 $ 59,982 63,914 $123,896 90,000 38,774 $128,774 $252,670 a. b. c. Sales for 2005 were $455,150,000, and EBITDA was 15 percent of sales. Furthermore, depreciation was 11 percent of net fixed assets, interest was $8,575,000, the corporate tax rate was 40 percent, and Laiho pays 40 percent of its net income out in dividends. The firm has no amortization expense. Given this information, construct the 2005 income statement. Construct the statement of retained earnings for the year ending December 31, 2005, and the 2005 statement of cash flows. Calculate net working capital and net operating working capital. What are the differences in these two measures? Chapter 3 Financial Statements, Cash Flow, and Taxes 95 d. e. f. Calculate total operating capital, NOPAT, operating cash flow, and free cash flow for 2005. Calculate the 2005 MVA. There were 10 million shares outstanding and the year-end closing price was $17.25 per share. If Laiho increased its dividend payout ratio, what effect would this have on its corporate taxes paid? What effect would this have on the taxes paid by the company's shareholders? Integrated Case D'Leon Inc., Part I 3-16 Financial statements and taxes Donna Jamison, a 2000 graduate of the University of Florida with 4 years of banking experience, was recently brought in as assistant to the chairman of the board of D'Leon Inc., a small food producer that operates in north Florida and whose specialty is high-quality pecan and other nut products sold in the snack-foods market. D'Leon's president, Al Watkins, decided in 2004 to undertake a major expansion and to "go national" in competition with Frito-Lay, Eagle, and other major snack-food companies. Watkins felt that D'Leon's products were of a higher quality than the competition's; that this quality differential would enable it to charge a premium price; and that the end result would be greatly increased sales, profits, and stock price. The company doubled its plant capacity, opened new sales offices outside its home territory, and launched an expensive advertising campaign. D'Leon's results were not satisfactory, to put it mildly. Its board of directors, which consisted of its president and vice president plus its major stockholders (who were all local businesspeople), was most upset when directors learned how the expansion was going. Suppliers were being paid late and were unhappy, and the bank was complaining about the deteriorating situation and threatening to cut off credit. As a result, Watkins was informed that changes would have to be made, and quickly, or he would be fired. Also, at the board's insistence Donna Jamison was brought in and given the job of assistant to Fred Campo, a retired banker who was D'Leon's chairman and largest stockholder. Campo agreed to give up a few of his golfing days and to help nurse the company back to health, with Jamison's help. Jamison began by gathering the financial statements and other data given in Tables IC3-1, IC3-2, IC3-3, and IC3-4. Assume that you are Jamison's assistant, and you must help her answer the following questions for Campo. (Note: We will continue with this case in Chapter 4, and you will feel more comfortable with the analysis there, but answering these questions will help prepare you for Chapter 4. Provide clear explanations, not just yes or no answers!) a. What effect did the expansion have on sales, NOPAT, net operating working capital (NOWC), total operating capital, and net income? b. What effect did the company's expansion have on its net cash flow, operating cash flow, and free cash flow? c. Looking at D'Leon's stock price today, would you conclude that the expansion increased or decreased MVA? d. D'Leon purchases materials on 30-day terms, meaning that it is supposed to pay for purchases within 30 days of receipt. Judging from its 2005 balance sheet, do you think D'Leon pays suppliers on time? Explain. If not, what problems might this lead to? e. D'Leon spends money for labor, materials, and fixed assets (depreciation) to make products, and still more money to sell those products. Then, it makes sales that result in receivables, which eventually result in cash inflows. Does it appear that D'Leon's sales price exceeds its costs per unit sold? How does this affect the cash balance? f. Suppose D'Leon's sales manager told the sales staff to start offering 60-day credit terms rather than the 30day terms now being offered. D'Leon's competitors react by offering similar terms, so sales remain constant. What effect would this have on the cash account? How would the cash account be affected if sales doubled as a result of the credit policy change? g. Can you imagine a situation in which the sales price exceeds the cost of producing and selling a unit of output, yet a dramatic increase in sales volume causes the cash balance to decline? h. Did D'Leon finance its expansion program with internally generated funds (additions to retained earnings plus depreciation) or with external capital? How does the choice of financing affect the company's financial strength? 96 Part 2 Fundamental Concepts in Financial Management i. j. k. l. Refer to Tables IC3-2 and IC3-4. Suppose D'Leon broke even in 2005 in the sense that sales revenues equaled total operating costs plus interest charges. Would the asset expansion have caused the company to experience a cash shortage that required it to raise external capital? If D'Leon started depreciating fixed assets over 7 years rather than 10 years, would that affect (1) the physical stock of assets, (2) the balance sheet account for fixed assets, (3) the company's reported net income, and (4) its cash position? Assume the same depreciation method is used for stockholder reporting and for tax calculations, and the accounting change has no effect on assets' physical lives. Explain how earnings per share, dividends per share, and book value per share are calculated, and what they mean. Why does the market price per share not equal the book value per share? Explain briefly the tax treatment of (1) interest and dividends paid, (2) interest earned and dividends received, (3) capital gains, and (4) tax loss carry-back and carry-forward. How might each of these items affect D'Leon's taxes? TA B L E I C 3 - 1 Balance Sheets 2005 2004 Assets Cash Accounts receivable Inventories Total current assets Gross fixed assets Less accumulated depreciation Net fixed assets Total assets Liabilities and Equity Accounts payable Notes payable Accruals Total current liabilities Long-term debt Common stock (100,000 shares) Retained earnings Total equity Total liabilities and equity 7,282 632,160 1,287,360 $1,926,802 1,202,950 263,160 $ 939,790 $2,866,592 $ 524,160 636,808 489,600 $1,650,568 723,432 460,000 32,592 $ 492,592 $2,866,592 $ 57,600 351,200 715,200 $1,124,000 491,000 146,200 $ 344,800 $1,468,800 $ 145,600 200,000 136,000 $ 481,600 323,432 460,000 203,768 $ 663,768 $1,468,800 $ Chapter 3 Financial Statements, Cash Flow, and Taxes 97 TA B L E I C 3 - 2 Income Statements 2005 2004 $3,432,000 2,864,000 358,672 $3,222,672 $ 209,328 18,900 $ 190,428 43,828 $ 146,600 58,640 $ 87,960 $ $ $ $ 0.880 0.220 6.638 8.50 100,000 40.00% 40,000 0 Sales Cost of goods sold Other expenses Total operating costs excluding depreciation and amortization EBITDA Depreciation and amortization EBIT Interest expense EBT Taxes (40%) Net income EPS DPS Book value per share Stock price Shares outstanding Tax rate Lease payments Sinking fund payments $6,034,000 5,528,000 519,988 $6,047,988 ($ 13,988) 116,960 ($ 130,948) 136,012 ($ 266,960) (106,784)a ($ 160,176) ($ $ $ $ 1.602) 0.110 4.926 2.25 100,000 40.00% 40,000 0 Note: a The firm had sufficient taxable income in 2003 and 2004 to obtain its full tax refund in 2005. TA B L E I C 3 - 3 Statement of Retained Earnings, 2005 $203,768 (160,176) (11,000) $ 32,592 Balance of retained earnings, 12/31/04 Add: Net income, 2005 Less: Dividends paid Balance of retained earnings, 12/31/05 98 Part 2 Fundamental Concepts in Financial Management TA B L E I C 3 - 4 Statement of Cash Flows, 2005 OPERATING ACTIVITIES Net income Additions (Sources of Cash) Depreciation and amortization Increase in accounts payable Increase in accruals Subtractions (Uses of Cash) Increase in accounts receivable Increase in inventories Net cash provided by operating activities LONG-TERM INVESTING ACTIVITIES Cash used to acquire fixed assets FINANCING ACTIVITIES Increase in notes payable Increase in long-term debt Payment of cash dividends Net cash provided by financing activities Sum: net decrease in cash Plus: cash at beginning of year Cash at end of year ($160,176) 116,960 378,560 353,600 (280,960) (572,160) ($164,176) ($711,950) $436,808 400,000 (11,000) $825,808 ($ 50,318) 57,600 $ 7,282 Please go to the ThomsonNOW Web site to access the Cyberproblems. Chapter 3 Financial Statements, Cash Flow, and Taxes 99 Access the Thomson ONE problems though the ThomsonNOW Web site. Use the Thomson ONE--Business School Edition online database to work this chapter's questions. Exploring Starbucks' Financial Statements Over the past decade, Starbucks coffee shops have become an increasingly familiar part of the urban landscape. Currently, the company operates more than 6,000 coffee shops in all 50 states, the District of Columbia, and internationally, and in 2005 it had roughly 80,000 employees. Thomson ONE can access a wealth of financial information for companies such as Starbucks. To find some background information, begin by entering the company's ticker symbol, SBUX, and then selecting "GO." On the opening screen, you will see a lot of useful information, including a summary of what Starbucks does, a chart of its recent stock price, EPS estimates, some recent news stories, and a list of key financial data and ratios. In researching a company's operating performance, a good place to start is the recent stock price performance. At the top of the Stock Price Chart, click on the section labeled "Interactive Chart." From this point, we are able to obtain a chart of the company's stock price performance relative to the overall market, as measured by the S&P 500, between 1995 and 2005. To obtain a 10-year chart, go to "Time Frame," click on the down arrow, and select 10 years. Then, click on "Draw" and a 10-year price chart should appear. As you can see, Starbucks has had its ups and downs, but the company's overall performance has been quite strong, and it has beat the overall market handily. We can also find Starbucks' recent financial statements. Near the top of your screen, click on the "Financials" tab to find the company's balance sheet, income statement, and statement of cash flows for the past 5 years. Clicking on the Microsoft Excel icon downloads these statements directly to a spreadsheet. Discussion Questions 1. Looking at the most recent year available, what is the amount of total assets on Starbucks' balance sheet? What percentage is fixed assets, such as plant and equipment, and what percentage is current assets? How much has the company grown over the years that are shown? 2. Does Starbucks have a lot of long-term debt? What are the chief ways in which Starbucks has financed assets? 3. Looking at the statement of cash flows, what factors can explain the change in the company's cash position over the last couple of years? 4. Looking at the income statement, what are the company's most recent sales and net income? Over the past several years, what has been the sales growth rate? What has been the growth rate in net income? 5. Over the past few years, has there been a strong correlation between stock price performance and reported earnings? C H APTE R 4 ANALYSIS OF FINANCIAL STATEMENTS1 Lessons Learned from Enron and WorldCom In early 2001, Enron appeared to be on top of the world. The high-flying energy firm had a market capitalization of $60 billion, and its stock was trading at $80 a share. Wall Street analysts were touting its innovations and management success and strongly recommending the stock. Less than a year later, Enron had declared bankruptcy, its stock was basically worthless, and investors had lost billions of dollars. This dramatic and sudden collapse left many wondering how so much value could be destroyed in such a short period of time. While Enron's stock fell steadily throughout the first part of 2001, most analysts voiced no concerns. The general consensus was that it was simply caught up in a sell-off that was affecting the entire stock market and that its long-run prospects remained strong. However, a hint of trouble came when Enron's CEO, Jeffrey Skilling, unexpectedly resigned in August 2001; he was replaced by its chairman and previous CEO, Ken Lay. By the end of August, its stock had fallen to $35 a share. Two months later, Enron stunned the financial markets by announcing a $638 million loss, along with a $1.2 billion write-down in its book value equity. The write-down, which turned out to be grossly inadequate, stemmed primarily from losses realized on a series of partnerships set up by its CFO, Andrew Fastow. Shortly thereafter, it was revealed that Enron had Enron, WorldCom 1 AP PHOTO/RON EDMONDS We have covered this chapter both early in the course and toward the end. Early coverage gives students an overview of how financial decisions affect financial statements and results, and thus of what financial management is all about. If it is covered later, after coverage of bond and stock valuation, risk analysis, capital budgeting, capital structure, and working capital management, students can better understand the logic of the ratios and see how they are used for different purposes. Depending on students' backgrounds, instructors may want to cover the chapter early or late. Chapter 4 Analysis of Financial Statements 101 guaranteed the partnerships' debt, so its true liabilities were far higher than the financial statements indicated. These revelations destroyed Enron's credibility, caused its customers to flee, and led directly to its bankruptcy. Not surprisingly, Enron's investors and employees were enraged to learn that its senior executives had received $750 million in salaries, bonuses, and profits from stock options for good performance in the same year before the company went bankrupt. During that year, senior executives were bailing out of the stock as fast as they could, even as they put out misleading statements touting the stock to their employees and outside investors. Fastow has since pleaded guilty to fraud and is cooperating with authorities in the cases against his former bosses, Lay and Skilling, who have been indicted for their roles in Enron's collapse and await trial. After Enron declared bankruptcy, critics turned their attention to the company's auditor, Arthur Andersen, and to certain Wall Street analysts who had blindly recommended the stock over the years. Critics contended that the auditors and analysts neglected their responsibilities because of conflicts of interest. Andersen partners looked the other way because they didn't want to compromise their lucrative consulting contracts with Enron, and the analysts kept recommending the stock because they wanted to help the investment banking side of their firms get more Enron business. As if the Enron debacle was not enough, in June 2002 it was learned that WorldCom, an even larger company, had "cooked its books" and inflated its profits and cash flows by more than $11 billion. Shortly thereafter, WorldCom collapsed, with many more billions of investor losses and thousands unemployed. Enron had set up complicated partnerships to deceive investors, but WorldCom simply lied, reporting normal operating costs as capital expenditures and thus boosting its reported profits. Interestingly, Enron and WorldCom used the same auditing firm, Arthur Andersen, which was itself put out of business, causing about 70,000 employees to lose their jobs. It is also interesting to note that Citigroup's investment banking subsidiary, Salomon Smith Barney, earned many millions in fees from WorldCom, and that Salomon's lead telecom analyst, Jack Grubman, who helped bring in this business, did not downgrade WorldCom to a sell until the very day the fraud was announced. At that point the stock was selling for less than a dollar, down from a high of $64.50. The Enron and WorldCom collapses caused investors throughout the world to wonder if these companies' misdeeds were isolated situations or were symptomatic of undiscovered problems lurking in many other companies. Those fears led to a broad decline in stock prices, and President Bush expressed outrage at executives whose actions were imperiling our financial markets and economic system. In response to these and other abuses, Congress passed the Sarbanes-Oxley Act of 2002. One of its provisions requires the CEO and the CFO to sign a statement certifying that the "financial statements and disclosures fairly represent, in all material respects, the operations and financial condition" of the company. This will make it easier to haul off in handcuffs a CEO or CFO who has misled investors. Financial statements have undoubtedly improved in the last few years, and they now provide a wealth of good information that can be used by managers, investors, lenders, customers, suppliers, and regulators. As you will see in this chapter, a careful analysis of a company's statements can highlight its strengths and shortcomings. Also, as you will see, financial analysis can be used to predict how such strategic decisions as the sale of a division, a change in credit or inventory policy, or a plant expansion will affect a firm's future performance. 102 Part 2 Fundamental Concepts in Financial Management Putting Things In Perspective The primary goal of financial management is to maximize shareholders' wealth over the long run, not to maximize accounting measures such as net income or EPS. However, accounting data influence stock prices, and these data can be used to understand why a company is performing the way it is and to forecast where it is heading. Chapter 3 described the key financial statements and showed how they change as a firm's operations undergo change. Now, in Chapter 4, we show how the statements are used by managers to improve performance; by lenders to evaluate the likelihood of collecting on loans; and by stockholders to forecast earnings, dividends, and stock prices. If management is to maximize a firm's value, it must take advantage of the firm's strengths and correct its weaknesses. Financial analysis involves (1) comparing the firm's performance to other firms, especially those in the same industry, and (2) evaluating trends in the firm's financial position over time. These studies help management identify deficiencies and then take corrective actions. We focus here on how financial managers and investors evaluate firms' financial positions. Then, in later chapters, we examine the types of actions management can take to improve future performance and thus increase the firm's stock price. The most important ratio is the ROE, or return on equity, which is net income to common stockholders divided by total stockholders' equity. Stockholders obviously want to earn a high rate of return on their invested capital, and the ROE tells them the rate they are earning. If the ROE is high, then the stock price will also tend to be high, and actions that increase ROE are likely to increase the stock price. The other ratios provide information about how well such assets as inventory, accounts receivable, and fixed assets are managed, and about how the firm is financed. As we will see, these factors all affect the ROE, and management uses the other ratios primarily to help develop plans to improve the average ROE over the long run. 4.1 RATIO ANALYSIS Financial statements report both a firm's position at a point in time and its operations over some past period. However, their real value lies in the fact that they can be used to help predict future earnings and dividends. From an investor's standpoint, predicting the future is what financial statement analysis is all about, while from management's standpoint, financial statement analysis is useful both to help anticipate future conditions and, more important, as a starting point for planning actions that will improve future performance. Chapter 4 Analysis of Financial Statements 103 Financial ratios are designed to help one evaluate a financial statement. For example, Firm A might have debt of $5,248,760 and interest charges of $419,900, while Firm B might have debt of $52,647,980 and interest charges of $3,948,600. Which company is stronger? The burden of these debts, and the companies' ability to repay them, can best be evaluated (1) by comparing each firm's debt to its assets and (2) by comparing the interest it must pay to the income it has available for payment of interest. Such comparisons involve ratio analysis. In the paragraphs that follow, we will calculate Allied Food Products' financial ratios for 2005, using data from the balance sheets and income statements given in Tables 3-1 and 3-2. We will also evaluate the ratios relative to the industry averages.2 Note that the dollar amounts in the ratio calculations are generally in millions. 4.2 LIQUIDITY RATIOS A liquid asset is one that trades in an active market and hence can be quickly converted to cash at the going market price, and a firm's "liquidity position" deals with this question: Will the firm be able to pay off its debts as they come due in the coming year? As shown in Table 3-1 in Chapter 3, Allied has $310 million of debt that must be paid off within the coming year. Will it have trouble meeting those obligations? A full liquidity analysis requires the use of cash budgets, but by relating cash and other current assets to current liabilities, ratio analysis provides a quick, easy-to-use measure of liquidity. Two of the most commonly used liquidity ratios are discussed here. Liquid Asset An asset that can be converted to cash quickly without having to reduce the asset's price very much. Current Ratio The primary liquidity ratio is the current ratio, which is calculated by dividing current assets by current liabilities: Liquidity Ratios Ratios that show the relationship of a firm's cash and other current assets to its current liabilities. Current Ratio This ratio is calculated by dividing current assets by current liabilities. It indicates the extent to which current liabilities are covered by those assets expected to be converted to cash in the near future. Current ratio Current assets Current liabilities $1,000 $310 3.2 4.2 Industry average Current assets include cash, marketable securities, accounts receivable, and inventories. Allied's current liabilities consist of accounts payable, short-term notes payable, current maturities of long-term debt, accrued taxes, and accrued wages. If a company is getting into financial difficulty, it begins paying its bills (accounts payable) more slowly, borrowing from its bank, and so on, all of which increase current liabilities. If current liabilities are rising faster than current assets, the current ratio will fall, and this is a sign of possible trouble. Allied's current ratio of 3.2 is well below the industry average, 4.2, so its liquidity position is rather weak. Still, since its current assets are supposed to be converted to 2 In addition to the ratios discussed in this section, financial analysts sometimes employ a tool known as common size analysis. To form a common size balance sheet, simply divide each asset and liability item by total assets and then express the results as percentages. The resultant percentage statement can be compared with statements of larger or smaller firms, or with those of the same firm over time. To form a common size income statement, divide each income statement item by sales. With a spreadsheet, which most analysts use, this is trivially easy. 104 Part 2 Fundamental Concepts in Financial Management cash within a year, it is likely that they could be liquidated at close to their stated value. With a current ratio of 3.2, Allied could liquidate current assets at only 31 percent of book value and still pay off current creditors in full.3 Although industry average figures are discussed later in some detail, note that an industry average is not a magic number that all firms should strive to maintain--in fact, some very well-managed firms may be above the average while other good firms are below it. However, if a firm's ratios are far removed from the averages for its industry, an analyst should be concerned about why this variance occurs. Thus, a deviation from the industry average should signal the analyst (or management) to check further. Quick, or Acid Test, Ratio Quick (Acid Test) Ratio This ratio is calculated by deducting inventories from current assets and then dividing the remainder by current liabilities. The second most used liquidity ratio is the quick, or acid test, ratio, which is calculated by deducting inventories from current assets and then dividing the remainder by current liabilities: Quick, or acid test, ratio Current assets Inventories Current liabilities $385 $310 1.2 2.2 Industry average Inventories are typically the least liquid of a firm's current assets, hence they are the assets on which losses are most likely to occur in the event of liquidation. Therefore, this measure of a firm's ability to pay off short-term obligations without relying on the sale of inventories is important. The industry average quick ratio is 2.2, so Allied's 1.2 ratio is quite low in comparison with other firms in its industry. Still, if the accounts receivable can be collected, the company can pay off its current liabilities without having to liquidate its inventories. What are some characteristics of a liquid asset? Give some examples. What two ratios are used to analyze a firm's liquidity position? Write out their equations. Why is the current ratio the most commonly used measure of shortterm solvency? Which current asset is typically the least liquid? A company has current liabilities of $500 million, and its current ratio is 2.0. What is its level of current assets? ($1,000 million) If this firm's quick ratio is 1.6, how much inventory does it have? ($200 million) Asset Management Ratios A set of ratios that measure how effectively a firm is managing its assets. 4.3 ASSET MANAGEMENT RATIOS A second group of ratios, the asset management ratios, measures how effectively the firm is managing its assets. These ratios answer this question: Does the amount of each type of asset seem reasonable, too high, or too low in view of 3 1/3.2 0.31, or 31%. Note also that 0.31($1,000) $310, the current liabilities balance. Chapter 4 Analysis of Financial Statements 105 current and projected sales? When they acquire assets, Allied and other companies must obtain capital from banks or other sources. If a firm has too many assets, its cost of capital will be too high and its profits will be depressed. On the other hand, if assets are too low, profitable sales will be lost. The asset management ratios described in this section are important. Inventory Turnover Ratio "Turnover ratios" are ratios where sales are divided by some asset, and as the name implies, they show how many times the item is "turned over" during the year. Thus, the inventory turnover ratio is defined as sales divided by inventories: Inventory Turnover Ratio This ratio is calculated by dividing sales by inventories. Inventory turnover ratio Sales Inventories $3,000 $615 4.9 10.9 Industry average As a rough approximation, each item of Allied's inventory is sold out and restocked, or "turned over," 4.9 times per year. "Turnover" is a term that originated many years ago with the old Yankee peddler, who would load up his wagon with goods, then go off on his route to peddle his wares. The merchandise was called "working capital" because it was what he actually sold, or "turned over," to produce his profits, whereas his "turnover" was the number of trips he took each year. Annual sales divided by inventory equaled turnover, or trips per year. If he made 10 trips per year, stocked 100 pans, and made a gross profit of $5 per pan, his annual gross profit would be (100)($5)(10) $5,000. If he went faster and made 20 trips per year, his gross profit would double, other things held constant. So, his turnover directly affected his profits. Allied's turnover of 4.9 is much lower than the industry average of 10.9. This suggests that it is holding too much inventory. Excess inventory is, of course, unproductive and represents an investment with a low or zero rate of return. Allied's low inventory turnover ratio also makes us question the current ratio. With such a low turnover, the firm may be holding obsolete goods not worth their stated value.4 Note that sales occur over the entire year, whereas the inventory figure is for one point in time. For this reason, it might be better to use an average inventory measure.5 If the business is highly seasonal, or if there has been a strong upward or downward sales trend during the year, it is especially useful to make an adjustment. To maintain comparability with industry averages, however, we did not use the average inventory figure. 4 A problem arises when calculating and analyzing the inventory turnover ratio. Sales are stated at market prices, so if inventories are carried at cost, as they generally are, the calculated turnover overstates the true turnover ratio. Therefore, it might be more appropriate to use cost of goods sold in place of sales in the formula's numerator. However, some established compilers of financial ratio statistics such as Dun & Bradstreet use the ratio of sales to inventories carried at cost. To have a figure that can be compared with those published by Dun & Bradstreet and similar organizations, it is necessary to measure inventory turnover with sales in the numerator, as we do here. 5 Preferably, the average inventory value should be calculated by summing the monthly figures during the year and dividing by 12. If monthly data are not available, the beginning and ending figures can be added and then divided by 2. Both methods adjust for growth but not for seasonal effects. 106 Part 2 Fundamental Concepts in Financial Management Days Sales Outstanding Days Sales Outstanding (DSO) This ratio is calculated by dividing accounts receivable by average sales per day; it indicates the average length of time the firm must wait after making a sale before it receives cash. Days sales outstanding (DSO), also called the "average collection period" (ACP), is used to appraise accounts receivable, and it is calculated by dividing accounts receivable by average daily sales to find how many days' sales are tied up in receivables. Thus, the DSO represents the average length of time that the firm must wait after making a sale before receiving cash. Allied has 46 days sales outstanding, well above the 36-day industry average: DSO Days sales outstanding Receivables Average sales per day $375 $3,000>365 $375 $8.2192 Receivables Annual sales>365 45.625 days 46 days 36 days Industry average Note that in this calculation we used a 365-day year. Some analysts use a 360day year; on this basis Allied's DSO would have been slightly lower, 45 days.6 The DSO can also be evaluated by comparing it with the terms on which the firm sells its goods. For example, Allied's sales terms call for payment within 30 days, so the fact that 46 days' sales, not 30 days', are outstanding indicates that customers, on the average, are not paying their bills on time. This deprives the company of funds that could be used to reduce bank loans or some other type of costly capital. Moreover, with a high average DSO, it is likely that a number of customers are paying very late, and those customers may well be in financial trouble, in which case Allied may never be able to collect the receivable.7 Therefore, if the trend in DSO over the past few years has been rising, but the credit policy has not been changed, this would be strong evidence that steps should be taken to expedite the collection of accounts receivable. Fixed Assets Turnover Ratio Fixed Assets Turnover Ratio The ratio of sales to net fixed assets. The fixed assets turnover ratio measures how effectively the firm uses its plant and equipment. It is the ratio of sales to net fixed assets: Fixed assets turnover ratio Sales Net fixed assets 3.0 2.8 $3,000 $1,000 Industry average 6 It would be somewhat better to use average receivables, either an average of the monthly figures or (Beginning receivables Ending receivables)/2 ($315 $375)/2 $345 in the formula. Had average annual receivables been used, Allied's DSO on a 365-day basis would have been $345/$8.2192 41.975 days, or approximately 42 days. The 42-day figure is a more accurate one, but our interest is in comparisons, and because the industry average was based on year-end receivables, the 46-day number is better for our purposes. The DSO is discussed further in Part 6. 7 For example, if further analysis along the lines suggested in Part 6 indicated that 85 percent of the customers pay in 30 days, then for the DSO to average 46 days, the remaining 15 percent must be paying on average in 136.67 days. Paying that late suggests financial difficulties. In Part 6 we also discuss refinements into this analysis, but a DSO of 46 days would alert a good analyst of the need to dig deeper. Chapter 4 Analysis of Financial Statements 107 Allied's ratio of 3.0 times is slightly above the 2.8 industry average, indicating that it is using its fixed assets at least as intensively as other firms in the industry. Therefore, Allied seems to have about the right amount of fixed assets relative to its sales. Potential problems may arise when interpreting the fixed assets turnover ratio. Recall that fixed assets are shown on the balance sheet at their historical costs, less depreciation. Inflation has caused the value of many assets that were purchased in the past to be seriously understated. Therefore, if we compared an old firm that had acquired many of its fixed assets years ago at low prices with a new company with similar operations that had acquired its fixed assets only recently, we would probably find that the old firm had the higher fixed assets turnover ratio. However, this would be more reflective of when the assets were acquired than of inefficiency on the part of the new firm. The accounting profession is trying to develop procedures for making financial statements reflect current values rather than historical values, which would help us make better comparisons. However, at the moment the problem still exists, so financial analysts must recognize that a problem exists and deal with it judgmentally. In Allied's case, the issue is not serious because all firms in the industry have been expanding at about the same rate, hence the balance sheets of the comparison firms are reasonably comparable.8 Total Assets Turnover Ratio The final asset management ratio, the total assets turnover ratio, measures the turnover of all the firm's assets, and it is calculated by dividing sales by total assets: Total Assets Turnover Ratio This ratio is calculated by dividing sales by total assets. Total assets turnover ratio Sales Total assets $3,000 $2,000 1.5 1.8 Industry average Allied's ratio is somewhat below the industry average, indicating that it is not generating enough sales given its total assets. Sales should be increased, some assets should be disposed of, or a combination of these steps should be taken. Identify four ratios that are used to measure how effectively a firm manages its assets, and write out their equations. If one firm is growing rapidly and another is not, how might this distort a comparison of their inventory turnover ratios? If you wanted to evaluate a firm's DSO, with what would you compare it? What potential problem might arise when comparing different firms' fixed assets turnover ratios? A firm has annual sales of $100 million, $20 million of inventory, and $30 million of accounts receivable. What is its inventory turnover ratio? (5 ) What is its DSO based on a 365-day year? (109.5 days) 8 See FASB #89, Financial Reporting and Changing Prices (December 1986), for a discussion of the effects of inflation on financial statements. The report's age indicates how difficult the problem is. 108 Part 2 Fundamental Concepts in Financial Management 4.4 DEBT MANAGEMENT RATIOS Financial Leverage The use of debt financing. The extent to which a firm uses debt financing, or financial leverage, has three important implications: (1) By raising funds through debt, stockholders can control a firm with a limited amount of equity investment. (2) Creditors look to the equity, or owner-supplied funds, to provide a margin of safety, so the higher the proportion of the total capital provided by stockholders, the less the risk faced by creditors. (3) If the firm earns more on its assets than the interest rate it pays on debt, then using debt "leverages," or magnifies, the return on equity, ROE. Table 4-1 illustrates both the potential benefits and risks resulting from the use of debt.9 Here we analyze two companies that are identical except for how they are financed. Firm U (for "Unleveraged") has no debt and thus 100 percent common equity, whereas Firm L (for "Leveraged") is financed with half debt at a 10 percent interest rate and half equity. Both companies have $100 of assets. Their sales will range from $150 down to $75, depending on business conditions, with an expected level of $100. Some of their operating costs (rent, the president's salary, and so on) are fixed and will be there regardless of the level of sales, while other costs (some labor costs, materials, and so forth) will vary with sales.10 When we deduct total operating costs from sales revenues, we are left with operating income, or earnings before interest and taxes (EBIT). Notice in the table that everything is the same for the leveraged and unleveraged firms down through operating income--thus, they have the same EBIT under the three states of the economy. However, things then begin to differ. Firm U has no debt so it pays no interest, and its taxable income is the same as its operating income, and it then pays a 40 percent state and federal tax to get to its net income, which is $27 under good conditions and $0 under bad conditions. When net income is divided by common equity, we get the ROE, which ranges from 27 percent to 0 percent for Firm U. Firm L has the same EBIT under each condition, but it uses $50 of debt with a 10 percent interest rate, so it has $5 of interest charges regardless of business conditions. This amount is deducted from EBIT to get to taxable income, taxes are then taken out, and the result is net income, which ranges from $24 to $5, depending on conditions.11 At first blush it looks like Firm U is better off under all conditions, but this is not correct--we need to consider how much the two firms' stockholders have invested. Firm L's stockholders have put up only $50, so when that investment is divided into net income, we see that their ROE under good conditions is a whopping 48 percent (versus 27 percent for U) and is 12 percent (versus 9 percent for U) under expected conditions. However, L's ROE falls to 10 percent under bad conditions, which means that it would go bankrupt if those conditions last for several years. There are two reasons for the leveraging effect: (1) Because interest is deductible, the use of debt lowers the tax bill and leaves more of the firm's operating income available to its investors. (2) If operating income as a percentage of 9 We discuss ROE in more depth later in the chapter, and we examine the effects of leverage in detail in the chapter on capital structure. 10 The financial statements do not show the breakdown between fixed and variable operating costs, but companies can and do make this breakdown for internal purposes. Of course, the distinction is not always clear, because what's a fixed cost in the very short run can become a variable cost over a longer time horizon. It's interesting to note that companies are moving toward making more of their costs variable, using such techniques as increasing bonuses rather than base salaries, switching to profit-sharing plans rather than fixed-pension plans, and outsourcing various parts and materials. 11 As we discussed in the last chapter, firms can carry losses back or forward for several years. Therefore, if Firm L had profits and thus paid taxes in recent prior years, it could carry its loss under bad conditions back and receive a credit (a check from the government). In Table 4-1 we assume that the firm cannot use the carry-back/carry-forward provision. Chapter 4 Analysis of Financial Statements 109 TA B L E 4 - 1 Effects of Financial Leverage on Stockholder Returns FIRM U [UNLEVERAGED (NO DEBT)] Current assets Fixed assets Total assets $ 50 50 $100 Debt Common equity Total liabilities and equity BUSINESS CONDITIONS Good Expected $100.0 45.0 40.0 85.0 $ 15.0 0.0 $ 15.0 6.0 $ 9.0 9.0% $ 0 100 $100 Bad $75.0 45.0 30.0 75.0 $ 0.0 0.0 $ 0.0 0.0 $ 0.0 0.0% Sales revenues Operating costs Fixed Variable Total operating costs Operating income (EBIT) Interest (Rate = 10%) Earnings before taxes (EBT) Taxes (Rate = 40%) Net income (NI) ROEU $150.0 45.0 60.0 105.0 $ 45.0 0.0 $ 45.0 18.0 $ 27.0 27.0% FIRM L [LEVERAGED (SOME DEBT)] Current assets Fixed assets Total assets $ 50 50 $100 Debt Common equity Total liabilities and equity BUSINESS CONDITIONS Good Expected $100.0 45.0 40.0 85.0 $ 15.0 5.0 $ 10.0 4.0 $ 6.0 12.0% $ 50 50 $100 Bad $75.0 45.0 30.0 75.0 $ 0.0 5.0 $ 5.0 0.0 $ 5.0 10.0% Sales revenues Operating costs Fixed Variable Total operating costs Operating income (EBIT) Interest (Rate = 10%) Earnings before taxes (EBT) Taxes (Rate = 40%) Net income (NI) ROEL $150.0 45.0 60.0 105.0 $ 45.0 5.0 $ 40.0 16.0 $ 24.0 48.0% assets exceeds the interest rate on debt, as it generally is expected to do, then a company can use debt to acquire assets, pay the interest on the debt, and have something left over as a "bonus" for its stockholders. Under the expected conditions, our hypothetical firms expect to earn 15 percent on assets versus a 10 percent cost of debt, and this, combined with the tax benefit of debt, pushes Firm L's expected rate of return on equity up far above that of Firm U. We see, then, that firms with relatively high debt ratios have higher expected returns when the economy is normal, but they are exposed to risk of loss when the economy enters a recession. Therefore, decisions about the use of debt require firms to balance higher expected returns against increased risk. Determining the optimal amount of debt is a complicated process, and we defer a discussion of 110 Part 2 Fundamental Concepts in Financial Management that subject to a later chapter on capital structure. For now, we simply look at two procedures analysts use to examine the firm's debt: (1) They check the balance sheet to determine the proportion of total funds represented by debt, and (2) they review the income statement to see the extent to which fixed charges are covered by operating profits. Total Debt to Total Assets Debt Ratio The ratio of total debt to total assets. The ratio of total debt to total assets, generally called the debt ratio, measures the percentage of funds provided by creditors: Debt ratio Total debt Total assets $1,060 $310 $750 $2,000 $2,000 Industry average 53.0% 40.0% Total debt includes all current liabilities and long-term debt. Creditors prefer low debt ratios because the lower the ratio, the greater the cushion against creditors' losses in the event of liquidation. Stockholders, on the other hand, may want more leverage because it can magnify expected earnings. Allied's debt ratio is 53.0 percent, which means that its creditors have supplied more than half the total financing. As we will discuss in the capital structure chapter, a number of factors affect a company's optimal debt ratio. Nevertheless, the fact that Allied's debt ratio exceeds the industry average raises a red flag, and this will make it relatively costly for Allied to borrow additional funds without first raising more equity. Creditors will be reluctant to lend the firm more money, and management would probably be subjecting the firm to the risk of bankruptcy if it sought to borrow a substantial amount of additional funds.12 Times-Interest-Earned Ratio Times-Interest-Earned (TIE) Ratio The ratio of earnings before interest and taxes (EBIT) to interest charges; a measure of the firm's ability to meet its annual interest payments. The times-interest-earned (TIE) ratio is determined by dividing earnings before interest and taxes (EBIT in Table 3-2) by the interest charges: Times-interest-earned (TIE) ratio EBIT Interest charges 3.2 6.0 $283.8 $88 Industry average The TIE ratio measures the extent to which operating income can decline before the firm is unable to meet its annual interest costs. Failure to pay interest will bring legal action by the firm's creditors and probably result in bankruptcy. Note that earnings before interest and taxes, rather than net income, is used in the numerator. Because interest is paid with pre-tax dollars, the firm's ability to pay current interest is not affected by taxes. 12 The ratio of debt to equity is also used in financial analysis. The debt-to-assets (D/A) and debt-toequity (D/E) ratios are simply transformations of each other: D>A D>E D/E = and D/A = 1 D>A 1 D>E Chapter 4 Analysis of Financial Statements 111 Allied's interest is covered 3.2 times. The industry average is 6 times, so Allied is covering its interest charges by a relatively low margin of safety. Thus, the TIE ratio reinforces the primary conclusion from our analysis of the debt ratio, namely, that Allied would face difficulties if it attempted to borrow additional funds. EBITDA Coverage Ratio The TIE ratio is useful for assessing the ability to meet interest charges on debt, but it has two shortcomings: (1) Interest is not the only fixed financial charge-- companies must also retire debt on a fixed schedule, and many firms also lease assets and thus must make lease payments. If they fail to repay debt or meet lease payments, they can be forced into bankruptcy. (2) EBIT does not represent all the cash flow available to service debt, especially if a firm has high depreciation and/or amortization charges. To account for these deficiencies, bankers and others also use the EBITDA coverage ratio, which shows all of the cash flow available for payments in the numerator and all of the required financial payments in the denominator. This ratio is defined as follows:13 EBITDA coverage ratio EBITDA Interest $383.8 $28 $88 $20 $28 Lease payments Lease payments 3.0 4.3 $411.8 $136 Principal payments EBITDA Coverage Ratio A ratio whose numerator includes all cash flows available to meet fixed financial charges and whose denominator includes all fixed financial charges. Industry average Regarding the numerator, Allied had EBITDA of $383.8 million, consisting of $283.8 million of operating income (EBIT) and $100 million of depreciation. However, $28 million of lease payments were deducted when we calculated EBITDA, yet that $28 million was available to meet financial charges. Therefore, we must add it back to EBITDA, giving a total of $411.8 million that is available for fixed financial charges.14 Fixed financial charges consisted of $88 million of interest, $20 million of sinking fund payments, and $28 million of lease payments, for a total of $136 million.15 Therefore, Allied covered its fixed financial charges by 3.0 times. However, if operating income declines, the coverage will fall, and operating income certainly can decline. As Allied's ratio is well below the industry average, we again see that the company has a relatively high level of debt. 13 Different analysts define the EBITDA coverage ratio in different ways. For example, some would omit the lease payment information, and others would "gross up" principal payments by dividing them by (1 T) because these payments are not tax deductions, hence must be made with after-tax cash flows. We included lease payments because, for many firms, they are quite important, and failing to make them can lead to bankruptcy just as surely as can failure to make payments on "regular" debt. We did not gross up principal payments because, if a company is in financial difficulty, its tax rate will probably be zero, hence the gross up is not necessary whenever the ratio is really important. 14 Lease payments are included in the numerator because, unlike interest, they were deducted when EBITDA was calculated. We want to find all the funds that were available to service fixed charges, so lease payments must be added to the EBIT and DA to find the funds that could be used to service debt and meet lease payments. 15 A sinking fund is a required annual payment designed to reduce the balance of a bond or preferred stock issue. A sinking fund payment is like the principal repayment portion of the payment on an amortized loan, but sinking funds are used for publicly traded bond issues, whereas amortization payments are used for bank loans and other private loans. 112 Part 2 Fundamental Concepts in Financial Management The EBITDA coverage ratio is most useful for relatively short-term lenders such as banks, which rarely make loans (except real estatebacked loans) for longer than about five years. Over a relatively short period, depreciationgenerated funds can be used to service debt. Over a longer time, those funds must be reinvested to maintain the plant and equipment or else the company cannot remain in business. Therefore, banks and other relatively short-term lenders focus on the EBITDA coverage ratio, whereas long-term bondholders focus on the TIE ratio. What are three important implications of financial leverage? How does the use of financial leverage affect stockholders' control position? How does the U.S. tax structure influence a firm's willingness to finance with debt? How does the decision to use debt involve a risk-versus-return trade-off? Explain the following statement: "Analysts look at both balance sheet and income statement ratios when appraising a firm's financial condition." Name three ratios that are used to measure financial leverage, and write out their equations. A company has EBITDA of $500 million, interest payments of $50 million, lease payments of $40 million, and required principal payments (due this year) of $30 million. What is its EBITDA coverage ratio? (4.5 ) 4.5 PROFITABILITY RATIOS Accounting statements reflect things that happened in the past, but they also give us clues about what's really important--what's likely to happen in the future. The liquidity, asset management, and debt ratios covered thus far tell us something about the firm's policies and operations. Now we turn to the profitability ratios, which reflect the net result of all of the financing policies and operating decisions. Profitability Ratios A group of ratios that show the combined effects of liquidity, asset management, and debt on operating results. Profit Margin on Sales This ratio measures net income per dollar of sales; it is calculated by dividing net income by sales. Profit Margin on Sales The profit margin on sales, calculated by dividing net income by sales, gives the profit per dollar of sales: Profit margin on sales Net income Sales $117.5 $3,000 3.9% 5.0% Industry average Allied's profit margin is below the industry average of 5 percent. This sub-par result occurs because costs are too high. High costs, in turn, generally occur because of inefficient operations. However, Allied's low profit margin is also a Chapter 4 Analysis of Financial Statements 113 G L O B A L P E R S P E C T I V E S Global Accounting Standards: Can One Size Fit All? These days you must be a good financial detective to analyze financial statements, especially if the company operates overseas. Despite attempts to standardize accounting practices, there are still many differences in financial reporting in different countries that create headaches for investors making cross-border company comparisons. However, as businesses become more global and more foreign companies list on U.S. stock exchanges, accountants and regulators are realizing the need for a global convergence of accounting standards. As a result, the writing is on the wall regarding accounting standards, and differences are disappearing. The effort to internationalize accounting standards began in 1973 with the formation of the International Accounting Standards Committee. However, in 1998 it became apparent that a full-time rule-making body with global representation was necessary, so the International Accounting Standards Board (IASB), with members representing nine major countries, was established. The IASB was charged with the responsibility for creating a set of International Financial Reporting Standards (IFRS) for European Union (EU) companies by January 1, 2005, when more than 7,000 publicly listed European companies were supposed to conform to these standards. In contrast, only 350 European companies were using international standards as of 2003. A number of other countries, including Australia and other Pacific Rim countries, South Africa, Canada, Russia, Japan, and China are interested in adopting IFRS. A survey of senior executives from 85 financial institutions worldwide found that 92 percent of those responding favored a single set of international standards but only 55 percent thought universal adoption was achievable. Obviously, the globalization of accounting standards is a huge endeavor--one that will involve compromises between the IASB and FASB. Part of the problem is that U.S. GAAP takes a rulesbased approach, while the IASB insists on using a principles-based approach. With a rules-based system, companies can tell whether or not they are in compliance, but they can also develop ways to get around a rule and thus subvert its intent. With a principles-based system, there is greater uncertainty about whether certain border-line procedures will be allowed, but such a system makes it easier to prosecute on the basis of intent. A global accounting structure would enable investors and practitioners around the world to read and understand financial reports produced anywhere in the world. In addition, it would enhance all companies' access to all capital markets, which would improve investor diversification, reduce risk, and lower the cost of capital. However, it remains to be seen whether the IASB's lofty goal can be achieved. Sources: "All Accountants Soon May Speak the Same Language," The Wall Street Journal, August 29, 1995, p. A15; Jim Cole, "Global Standards Loom for Accounting," East Bay Business Times, November 12, 2001; "Accountants Struggle to Reconcile Rules," BestWire, April 28, 2003; "For and Against; Standards Need Time to Work," Accountancy Age, June 5, 2003, p. 16; Larry Schlesinger, "Overview; Bringing about a New Dawn," Accountancy Age, September 4, 2003, p. 18; Cassell Bryan-Low, "Deals & Deal Makers: Accounting Changes Are in Store," The Wall Street Journal, September 10, 2003, p. C4; and Fay Hansen, "Get Ready for New Global Accounting Standards," January 2004, www.BusinessFinanceMag.com. result of its heavy use of debt. Recall that net income is income after interest. Therefore, if two firms have identical operations in the sense that their sales, operating costs, and EBIT are the same, but if one firm uses more debt than the other, it will have higher interest charges. Those interest charges will pull net income down, and as sales are constant, the result will be a relatively low profit margin. In this situation, the low profit margin would indicate a difference in financing strategies, not an operating problem. Thus, the firm with the low profit margin might end up with a higher rate of return on its stockholders' investment due to its use of financial leverage. Note too that while a high return on sales is good, other things held constant, other things may not be held constant--we must also be concerned with turnover. If a firm sets a very high price on its products, it may get a high return on each sale but not make many sales. That might result in a high profit margin but still not be optimal because total sales are low. 114 Part 2 Fundamental Concepts in Financial Management We will see exactly how profit margins, the use of debt, and turnover interact to affect overall stockholder returns shortly, when we examine the Du Pont equation. Return on Total Assets Return on Total Assets (ROA) The ratio of the net income to total assets. The ratio of net income to total assets measures the return on total assets (ROA) after interest and taxes: Return on total assets ROA Net income Total assets $117.5 $2,000 5.9% 9.0% Industry average Allied's 5.9 percent return is well below the 9 percent industry average. This is not good, but a low return on assets is not necessarily bad--it could result from a conscious decision to use a lot of debt, in which case high interest expenses will cause net income to be relatively low. Debt is part of the reason for Allied's low ROA. Never forget--you must look at a number of ratios, see what each suggests, and then look at the overall situation when you judge the performance of a company and try to figure out what it should do to improve. Basic Earning Power (BEP) Ratio Basic Earning Power (BEP) Ratio This ratio indicates the ability of the firm's assets to generate operating income; calculated by dividing EBIT by total assets. The basic earning power (BEP) ratio is calculated by dividing earnings before interest and taxes (EBIT) by total assets: Basic earning power (BEP) ratio EBIT Total assets $283.8 $2,000 14.2% 18.0% Industry average This ratio shows the raw earning power of the firm's assets, before the influence of taxes and leverage, and it is useful when comparing firms with different degrees of financial leverage and tax situations. Because of its low turnover ratios and poor profit margin on sales, Allied is not earning as high a return on assets as the average food-processing company.16 16 A related ratio is the return on investors' capital, defined as follows: Return on investors' capital Net income Interest Debt Equity The numerator shows the dollar returns to investors, the denominator shows the money investors have put up, and the ratio itself shows the rate of return on all investors' capital. This ratio is especially important in regulated industries such as electric utilities, where regulators are concerned about companies' using their monopoly power to earn excessive returns on investors' capital. In fact, regulators try to set electric rates at levels that will force the return on investors' capital to equal a company's cost of capital as defined in Chapter 10. Chapter 4 Analysis of Financial Statements 115 Return on Common Equity The "bottom-line" accounting ratio is the return on common equity (ROE), found as follows: Return on Common Equity (ROE) The ratio of net income to common equity; measures the rate of return on common stockholders' investment. Return on common equity ROE Net income Common equity $117.5 $940 12.5% 15.0% Industry average Stockholders expect to earn a return on their money, and this ratio tells how well they are doing in an accounting sense. Allied's 12.5 percent return is below the 15 percent industry average, but not as far below as the return on total assets. This somewhat better ROE is due to the company's greater use of debt, a point that we discussed earlier in the chapter. Identify four profitability ratios, and write out their equations. Why is the basic earning power ratio useful? Why does the use of debt lower the ROA? What does ROE measure? Since interest expense lowers profits and thus the ROA, does using debt necessarily lower the ROE? Explain. A company has $20 billion of sales and $1 billion of net income. Its total assets are $10 billion, financed half by debt and half by common equity. What is its profit margin? (5%) What is its ROA? (10%) What is its ROE? (20%) Would ROA increase if the firm used less leverage? (yes) Would ROE increase? (no) 4.6 MARKET VALUE RATIOS The ROE reflects the effects of all the other ratios and is the best single measure of performance in an accounting sense. Investors obviously like to see a high ROE, and high ROEs are generally positively correlated with high stock prices. However, other things come into play. As we saw earlier, financial leverage generally increases the ROE but leverage also increases the firm's risk, which investors dislike. So, if a high ROE is achieved by the use of a very large amount of debt, the stock price might well be lower than it would be with less debt and a lower ROE. Similarly, investors are interested in growth, and if the current ROE was achieved by holding back on research and development costs, which will constrain future growth, this will not be regarded favorably. This takes us to a final group of ratios, the market value ratios, which relate the firm's stock price to its earnings, cash flow, and book value per share. These ratios give management an indication of what investors think of the company's risk and future prospects. If the liquidity, asset management, debt management, and profitability ratios all look good, and if these conditions have been stable over time, then the market value ratios will be high, the stock price will probably be as high as can be expected, and management has been doing a good job and should be rewarded. Otherwise, changes might be needed. Market Value Ratios A set of ratios that relate the firm's stock price to its earnings, cash flow, and book value per share. 116 Part 2 Fundamental Concepts in Financial Management Price/Earnings Ratio Price/Earnings (P/E) Ratio The ratio of the price per share to earnings per share; shows the dollar amount investors will pay for $1 of current earnings. The price/earnings (P/E) ratio shows how much investors are willing to pay per dollar of reported profits. Allied's stock sells for $23, so with an EPS of $2.35 its P/E ratio is 9.8: Price>earnings 1P>E2 ratio Price per share Earnings per share $23.00 $2.35 9.8 11.3 Industry average As we will see in Chapter 9, P/E ratios are higher for firms with strong growth prospects and relatively little risk. Allied's P/E ratio is below the average for other food processors, so this suggests that the company is regarded as being somewhat riskier than most, as having poor growth prospects, or both. Price/Cash Flow Ratio Price/Cash Flow Ratio The ratio of price per share divided by cash flow per share; shows the dollar amount investors will pay for $1 of cash flow. In some industries, stock price is tied more closely to cash flow rather than net income. Consequently, investors often look at the price/cash flow ratio: Price>cash flow Price per share Cash flow per share $23.00 $4.35 5.3 5.4 Industry average The calculation for cash flow per share was discussed in Chapter 3, but to refresh your memory, it is equal to net income plus depreciation and amortization divided by common shares outstanding. Allied's price/cash flow ratio is slightly below the industry average, once again suggesting that its growth prospects are below average, its risk is above average, or both. Note that for some purposes analysts look at multiples beyond just the price/earnings and the price/cash flow ratios. For example, depending on the industry, analysts may look at price/sales, price/customers, or price/(EBITDA per share). Ultimately, though, value depends on earnings and cash flows, so if these "exotic" ratios do not forecast future levels of EPS and cash flow, they may turn out to be misleading.17 Market/Book Ratio The ratio of a stock's market price to its book value gives another indication of how investors regard the company. Companies that are well regarded by investors--which means companies with safe and growing earnings and cash 17 During the "Internet bubble" of the late 1990s and early 2000s, some Internet companies were valued by multiplying the number of "hits" to a Web site times some sort of multiple. If those hits translated to sales and profits, this procedure would have made sense, but generally they did not, and the result was a vast overvaluation of stocks and a subsequent huge crash. Keep your eye on earnings and cash flows. Chapter 4 Analysis of Financial Statements 117 flows--sell at higher multiples of book value than those with low returns. First, we find Allied's book value per share: Book value per share Common equity Shares outstanding $940 50 $18.80 Then we divide the market price per share by the book value per share to get the market/book (M/B) ratio, which for Allied is 1.2 times: Market>book ratio M>B Market price per share Book value per share $23.00 $18.80 1.2 1.7 Market/Book (M/B) Ratio The ratio of a stock's market price to its book value. Industry average Investors are willing to pay less for a dollar of Allied's book value than for one of an average food-processing company. This is consistent with our other findings. In today's market (September 2005), the average Standard & Poor's (S&P) 500 company had a market/book ratio of about 2.87.18 Because M/B ratios typically exceed 1.0, this means that investors are willing to pay more for stocks than their accounting book values. This situation occurs primarily because asset values, as reported by accountants on corporate balance sheets, do not reflect either inflation or "goodwill." Thus, assets purchased years ago at preinflation prices are carried at their original costs, even though inflation might have caused their actual values to rise substantially, and successful going concerns have a value greater than their historical costs. If a company earns a low rate of return on its assets, then its M/B ratio will be relatively low versus an average company. Some airlines, which have not fared well in recent years, sell at M/B ratios well below 1.0, while very successful firms such as Microsoft achieve high rates of return on their assets, resulting in market values far in excess of their book values. In September 2005 Microsoft's book value per share was about $4.49 versus a market price of $26.28, so its market/book ratio was $26.28/$4.49 5.9 times. Describe three ratios that relate a firm's stock price to its earnings, cash flow, and book value per share, and write out their equations. How do these market value ratios reflect investor's opinions about a stock's risk and expected future growth? What does the price/earnings (P/E) ratio show? If one firm's P/E ratio is lower than that of another, what are some factors that might explain the difference? How is book value per share calculated? Explain how inflation and "goodwill" built up over time could cause book values to deviate from market values. 18 This was obtained from the key ratios section shown in http://moneycentral.msn.com. 118 Part 2 Fundamental Concepts in Financial Management 4.7 TREND ANALYSIS Trend Analysis An analysis of a firm's financial ratios over time; used to estimate the likelihood of improvement or deterioration in its financial condition. It is important to analyze trends in ratios as well as their absolute levels, for trends give clues as to whether a firm's financial condition is likely to improve or to deteriorate. To do a trend analysis, simply plot a ratio over time, as shown in Figure 4-1. This graph shows that Allied's rate of return on common equity has been declining since 2002, even though the industry average has been relatively stable. All the other ratios could be analyzed similarly. How is a trend analysis done? What important information does a trend analysis provide? 4.8 TYING THE RATIOS TOGETHER: THE DU PONT EQUATIONS Basic Du Pont Equation A formula that shows that the rate of return on assets can be found as the product of the profit margin times the total assets turnover. Table 4-2 summarizes Allied's ratios. The profit margin times the total assets turnover is called the basic Du Pont equation, and it gives the rate of return on assets (ROA): ROA Profit margin Net income Sales 3.9% 1.5 Total assets turnover Sales Total assets 5.9% (4-1) Allied made 3.9 percent, or 3.9 cents, on each dollar of sales, and assets were "turned over" 1.5 times during the year. Therefore, the company earned a return of 5.9 percent on its assets. FIGURE 4-1 Rate of Return on Common Equity, 20012005 ROE (%) 16 14 12 10 Industry Allied 2001 2002 2003 2004 2005 Chapter 4 Analysis of Financial Statements 119 TA B L E 4 - 2 Allied Food Products: Summary of Financial Ratios (Millions of Dollars) Formula Calculation Ratio Industry Average Comment Ratio Liquidity Current Current assets Current liabilities Current assets Inventories Current liabilities $1,000 $310 $385 $310 3.2 4.2 Poor Quick 1.2 2.2 Poor Asset Management Inventory turnover Sales Inventories Receivables Annual sales>365 Sales Net fixed assets Sales Total assets $3,000 $615 $375 $8.2192 $3,000 $1,000 $3,000 $2,000 4.9 10.9 Poor Days sales outstanding (DSO) 46 days 36 days Poor Fixed assets turnover 3.0 2.8 OK Total assets turnover Debt Management Total debt to total assets Times-interestearned 1TIE2 EBITDA coverage 1.5 1.8 Somewhat low Earnings before interest and taxes 1EBIT 2 Interest charges EBITDA Interest Lease payments Lease payments Total debt Total assets $1,060 $2,000 $283.8 $88 $411.8 $136 53.0% 3.2 40.0% 6.0 High (risky) Low (risky) Principal payments 3.0 4.3 Low (risky) Profitability Profit margin on sales Return on total assets 1ROA 2 Basic earning power 1BEP2 Return on common equity 1ROE2 Market Value Price/earnings (P/E) Price per share Earnings per share Price per share Cash flow per share Market price per share Book value per share $23.00 $2.35 $23.00 $4.35 $23.00 $18.80 9.8 11.3 Low Net income Sales Net income Total assets Earnings before interest and taxes 1EBIT2 Total assets Net income Common equity $117.5 $3,000 $117.5 $2,000 $283.8 $2,000 $117.5 $940 3.9% 5.0% Poor 5.9% 9.0% Poor 14.2% 18.0% Poor 12.5% 15.0% Poor Price/cash flow 5.3 5.4 Low Market/book (M/B) 1.2 1.7 Low 120 Part 2 Fundamental Concepts in Financial Management If the company were financed only with common equity, the rate of return on assets (ROA) and the return on equity (ROE) would be the same because total assets would equal common equity: ROA Net income Total assets Net income Common equity ROE This equality holds if and only if the company uses no debt. Allied does use debt, so its common equity is less than its total assets. Therefore, the return to the common stockholders (ROE) must be greater than the ROA of 5.9 percent. Specifically, to go from the rate of return on assets (ROA) to the return on equity (ROE) we multiply by the equity multiplier, which is the ratio of total assets to common equity: Equity multiplier Total assets Common equity Firms that use large amounts of debt (more leverage) will necessarily have a high equity multiplier--the greater the debt, the less the equity, hence the higher the equity multiplier. For example, if a firm has $1,000 of assets and finances with $800, or 80 percent debt, then its equity will be $200 and its equity multiplier will be $1,000/$200 5. Had it used only $200 of debt, its equity would have been $800, and its equity multiplier would have been only $1,000/$800 1.25.19 Allied's return on equity (ROE) depends on its ROA and its use of leverage:20 ROE ROA Equity multiplier Total assets Common equity (4-2) Net income Total assets 5.9% 5.9% 12.5% 2.13 $2,000/$940 When they are combined, Equations 4-1 and 4-2 form the extended Du Pont equation, which shows how the profit margin, the total assets turnover ratio, and the equity multiplier combine to determine the ROE: ROE (Profit margin)(Total assets turnover)(Equity multiplier) Net income Sales Sales Total assets Total assets Common equity (4-3) 19 Expressed algebraically, Debt ratio D A A A E A A E A 1 1 Equity multiplier Here D is debt, E is equity, A is total assets, and A/E is the equity multiplier. This equation ignores preferred stock. 20 Note that we could also find the ROE by "grossing up" the ROA, that is, by dividing the ROA by the common equity fraction: ROE ROA/Equity fraction 5.9%/0.47 12.5%. The two procedures are algebraically equivalent. Chapter 4 Analysis of Financial Statements 121 For Allied, we have ROE (3.9%)(1.5)(2.13) 12.5% The 12.5 percent rate of return could, of course, be calculated directly: both Sales and Total assets cancel, leaving Net income/Common equity $117.5/$940 12.5%. However, the extended Du Pont equation shows how the profit margin, total assets turnover, and use of debt combine to determine the return on equity. Allied's management can use the extended Du Pont equation to analyze ways of improving performance. Focusing on the profit margin, marketing people can study the effects of raising sales prices (or lowering them to increase volume), of moving into new products or markets with higher margins, and so on. Cost accountants can study various expense items and, working with engineers, purchasing agents, and other operating personnel, seek ways to hold down costs. Regarding the "turnover" term, the financial staff, working with both production and marketing people, can investigate ways to reduce the investment in various types of assets. Finance people can also analyze the effects of alternative financing strategies, seeking ways to hold down interest expense and the risk associated with debt while still using leverage to increase the return on equity. As a result of such an analysis, Ellen Jackson, Allied's president, recently announced a series of moves that are expected to cut operating costs by more than 20 percent per year. Jackson and Allied's other executives have a strong incentive for improving its financial performance because their compensation is based to a large extent on how well the company does. Its executives receive a salary that is sufficient to cover their living costs, but their compensation package also includes stock options that will be awarded if and only if Allied meets or exceeds target levels for earnings and the stock price. These target levels are based on its performance relative to other food companies. So, if it does well, then Jackson and the other executives--and the stockholders--will also do well. But if things deteriorate, Jackson could be looking for a new job. Write out the equation for the basic Du Pont equation. What is the equity multiplier? How can management use the extended Du Pont equation to analyze ways of improving the firm's performance? 4.9 COMPARATIVE RATIOS AND "BENCHMARKING" Ratio analysis almost always involves comparisons--a company's ratios are compared with industry average figures. However, like most firms, Allied's managers go one step further--they also compare their ratios with those of leading food companies. This technique is called benchmarking, and the companies used for the comparison are called benchmark companies. Allied's management benchmarks against Campbell Soup, a leading manufacturer of canned soups; Dean Foods, a processor of canned and frozen vegetables; Del Monte Foods, a processor of fruits and vegetables; H. J. Heinz, which makes ketchup and other products; Flowers Industries, a producer of bakery and snack-food goods; Sara Lee, a manufacturer of baked goods; and Hershey Foods Corp., a producer of A good site for comparative ratios is http:// moneycentral.msn.com. Here you can find stock quotes, detailed company reports, company ratios, and comparative ratios. Benchmarking The process of comparing a particular company with a group of "benchmark" companies. 122 Part 2 Fundamental Concepts in Financial Management chocolates, nonchocolate confectionary products, and pasta. Ratios are calculated for each company, then listed in descending order as shown below for the profit margin (the firms' latest 12 months' results reported by Yahoo!Finance as of September 15, 2005): Company Hershey Foods Campbell Soup H. J. Heinz Allied Food Products Del Monte Foods Sara Lee Flowers Industries Dean Foods Profit Margin 11.9% 9.4 7.9 3.9 3.9 3.7 3.6 2.6 TA B L E 4 - 3 Key Financial Ratios for Selected Industriesa Current Ratio 1.1 2.5 1.8 1.0 1.4 2.6 2.0 1.2 1.1 1.5 1.0 1.6 1.1 1.3 0.8 0.9 1.7 2.6 2.0 1.7 2.2 2.1 1.1 Inventory Turnoverb 9.3 4.4 8.2 7.8 59.4 4.7 4.6 16.1 11.0 27.5 49.4 4.8 10.9 6.1 13.2 30.3 3.6 3.2 3.6 5.2 7.7 3.9 3.4 Total Assets Turnover 0.9 1.6 0.6 0.8 1.1 0.7 1.1 3.6 2.4 1.6 0.7 0.6 0.5 0.7 0.4 1.1 1.3 0.8 1.1 1.0 0.7 1.1 0.8 Debt Ratioc 70.8% 44.2 85.3 65.0 40.8 39.4 52.6 64.1 73.9 57.2 56.8 58.3 53.4 69.0 64.8 55.1 65.5 41.1 51.9 61.9 50.0 51.6 77.6 Days Sales Profit Outstandingd Margin 49.3 12.7 202.8 39.7 38.4 70.2 36.1 18.1 9.1 47.4 35.1 42.9 57.0 71.6 29.2 11.2 32.6 76.0 53.7 46.2 86.9 49.3 32.3 2.8% 5.0 2.6 10.6 9.8 5.7 4.4 2.0 0.5 4.3 6.0 8.4 9.9 2.7 8.7 5.7 3.8 5.4 3.4 3.9 0.2 2.8 6.2 Return on Assets 2.6% 8.2 1.6 8.5 10.0 4.0 4.6 7.1 1.2 6.5 4.1 5.0 5.4 1.8 3.1 6.2 4.8 4.3 3.8 3.7 0.2 3.1 5.0 Return on Equity 8.9% 14.7 10.9 24.3 16.9 6.6 9.7 19.8 4.6 15.2 9.5 12.0 11.6 5.8 8.8 13.8 13.9 7.3 7.9 9.7 0.4 6.4 22.3 Industry Name Aerospace/defense Apparel stores Auto manufacturing--major Beverage (soft drink) Education and training services Electronics--diversified Food processing Food wholesalers Grocery stores Health services--specialized Lodging Metals and minerals--industrial Newspapers Paper and paper products Railroad Restaurant Retail--department stores Scientific and technical instruments Sporting goods Steel and iron Telecommunications equipment Textile manufacturing Tobacco (cigarettes) Notes: The ratios presented are averages for each industry. Ratios for the individual companies are also available. b The inventory turnover ratio in this table is calculated as the company's latest 12 months of cost of sales divided by the average of its inventory for the last quarter and the comparable year earlier quarter. c The debt ratio in this table is calculated as 1 (ROA/ROE). d The days sales outstanding ratio in this table was calculated as 365/Receivable turnover. The receivable turnover is calculated as the company's latest 12 months of sales divided by the average of its receivables for the last quarter and the comparable year earlier quarter. Source: Data obtained from the Key Ratios section, http://moneycentral.msn.com, February 25, 2005. a Chapter 4 Analysis of Financial Statements 123 Looking for Warning Signs within the Financial Statements Enron's decline spurred a renewed interest in financial accounting, and analysts now scour companies' financial statements to see if trouble is lurking. This renewed interest has led to a list of "red flags" to consider when reviewing a company's financial statements. For example, after conferring with New York University Accounting Professor Baruch Lev, Fortune magazine's Shawn Tully identified the following warning signs: Year after year, a company reports restructuring charges and/or write-downs. This practice raises concerns because companies can use writedowns to mask operating expenses and thus results in overstated earnings. A company's earnings have been propped up through a series of acquisitions. Acquisitions can increase earnings if the acquiring company has a higher P/E than the acquired firm, but such "growth" cannot be sustained over the long run. A company depreciates its assets more slowly than the industry average. Lower depreciation boosts current earnings, but again, this cannot be sustained because eventually depreciation must be recognized. A company routinely has high earnings but low cash flow. As Tully points out, this warning sign would have exposed Enron's problems. In the second quarter of 2001 (a few months before its problems began to unfold), Enron reported earnings of $423 million versus a cash flow of minus $527 million. Along similar lines, after consulting with various professionals, Ellen Simon of the Newark Star Ledger came up with her list of "red flags": You wouldn't buy the stock at today's price. You don't really understand the company's financial statements. The company is in a business that lends itself to "creative accounting." The company keeps taking nonrecurring charges. Accounts receivable and inventory are increasing faster than sales revenue. The company's insiders are selling their stock. The company is making aggressive acquisitions, especially in unrelated fields. There is some overlap between these two lists. Also, none of these items automatically means there is something wrong with the company--instead, the items should be viewed as warning signs that cause you to take a closer look at the company's performance before making an investment. The benchmarking setup makes it easy for Allied's management to see exactly where it stands relative to the competition. As the data show, Allied is in the middle of its benchmark group relative to its profit margin, so it has lots of room for improvement. Other ratios are analyzed similarly. Comparative ratios are available from a number of sources, including the MSN Money Web site, http://moneycentral.msn.com. Table 4-3 presents a list of key ratios for a variety of industries covered by this site. Useful ratios are also compiled by Value Line Investment Survey, Dun and Bradstreet (D&B), and Robert Morris Associates, which is the national association of bank loan officers. Also, financial statement data for thousands of publicly owned corporations are available on other Internet sites, and as brokerage houses, banks, and other financial institutions have access to these data, security analysts can and do generate comparative ratios tailored to their specific needs. Each of the data-supplying organizations uses a somewhat different set of ratios designed for its own purposes. For example, D&B deals mainly with small firms, many of which are proprietorships, and it sells its services primarily to banks and other lenders. Therefore, D&B is concerned largely with the creditor's viewpoint, and its ratios emphasize current assets and liabilities, not market 124 Part 2 Fundamental Concepts in Financial Management value ratios. So, when you select a comparative data source, you should be sure that your emphasis is similar to that of the agency whose ratios you plan to use. Additionally, there are often definitional differences in the ratios presented by different sources, so before using a source, be sure to verify the exact definitions of the ratios to ensure consistency with your own work. Why is it useful to do comparative ratio analyses? Differentiate between trend and comparative analyses. What is benchmarking? 4.10 USES AND LIMITATIONS OF RATIO ANALYSIS As noted earlier, ratio analysis is used by three main groups: (1) managers, who employ ratios to help analyze, control, and thus improve their firms' operations; (2) credit analysts, including bank loan officers and bond rating analysts, who analyze ratios to help judge a company's ability to pay its debts; and (3) stock analysts, who are interested in a company's efficiency, risk, and growth prospects. In later chapters we will look more closely at the basic factors that underlie each ratio, which will give you a better idea about how to interpret and use ratios. Note, though, that while ratio analysis can provide useful information concerning a company's operations and financial condition, it does have limitations that necessitate care and judgment. Some potential problems are listed here: 1. Many large firms operate different divisions in different industries, and for such companies it is difficult to develop a meaningful set of industry averages. Therefore, ratio analysis is more useful for small, narrowly focused firms than for large, multidivisional ones. 2. Most firms want to be better than average, so merely attaining average performance is not necessarily good. As a target for high-level performance, it is best to focus on the industry leaders' ratios. Benchmarking helps in this regard. 3. Inflation has badly distorted many firms' balance sheets--recorded values are often substantially different from "true" values. Further, because inflation affects both depreciation charges and inventory costs, profits are also affected. Thus, a ratio analysis for one firm over time, or a comparative analysis of firms of different ages, must be interpreted with judgment. 4. Seasonal factors can also distort a ratio analysis. For example, the inventory turnover ratio for a food processor will be radically different if the balance sheet figure used for inventory is the one just before versus just after the close of the canning season. This problem can be minimized by using monthly averages for inventory (and receivables) when calculating turnover ratios. 5. Firms can employ "window dressing" techniques to make their financial statements look stronger. To illustrate, a Chicago builder borrowed on a twoyear basis on December 27, 2005, held the proceeds of the loan as cash for a few days, and then paid off the loan ahead of time on January 2, 2006. This improved his current and quick ratios, and made his year-end 2005 balance sheet look good. However, the improvement was strictly window dressing; a week later the balance sheet was back at the old level. 6. Different accounting practices can distort comparisons. As noted earlier, inventory valuation and depreciation methods can affect financial statements To find quick information about a company, link to http://www.investor .reuters.com. Here you can find company profiles and snapshots, stock price quotes and share information, key ratios, and comparative ratios. "Window Dressing" Techniques Techniques employed by firms to make their financial statements look better than they really are. Chapter 4 Analysis of Financial Statements 125 and thus distort comparisons among firms. Also, if one firm leases a substantial amount of its productive equipment, then its assets may appear low relative to sales because leased assets often do not appear on the balance sheet. At the same time, the liability associated with the lease obligation may not appear as debt. Therefore, leasing can artificially improve both the turnover and the debt ratios. However, the accounting profession has taken steps to reduce this problem. 7. It is difficult to generalize about whether a particular ratio is "good" or "bad." For example, a high current ratio may indicate a strong liquidity position, which is good, or excessive cash, which is bad (because excess cash in the bank is a nonearning asset). Similarly, a high fixed assets turnover ratio may indicate either that the firm uses its assets efficiently or that it is short of cash and cannot afford to make needed investments. 8. A firm may have some ratios that look "good" and others that look "bad," making it difficult to tell whether the company is, on balance, strong or weak. However, statistical procedures can be used to analyze the net effects of a set of ratios. Many banks and other lending organizations use such procedures to analyze firms' financial ratios, and then to classify them according to their probability of getting into financial trouble.21 Ratio analysis is useful, but analysts should be aware of these problems and make adjustments as necessary. Ratio analysis conducted in a mechanical, unthinking manner is dangerous, but used intelligently and with good judgment, it can provide useful insights into a firm's operations. Your judgment in interpreting a set of ratios is bound to be weak at this point, but it will improve as you read the remaining chapters of this book. List three types of users of ratio analysis. Would the different users emphasize the same or different types of ratios? Explain. List several potential problems with ratio analysis. 4.11 PROBLEMS WITH ROE In Chapter 1 we said that managers should strive to maximize shareholder wealth. If a firm takes steps to improve its ROE, does it mean that shareholder wealth will also increase? Not necessarily, for despite its widespread use and the fact that ROE and shareholder wealth are often highly correlated, serious problems can arise if a firm uses ROE as its sole performance measure. First, ROE does not consider risk. While shareholders clearly care about returns, they also care about risk. To illustrate this point, consider two divisions within the same firm. Division S has stable cash flows and a predictable 15 percent ROE. Division R, on the other hand, has a 16 percent expected ROE, but its cash flows are quite risky, so the expected ROE may not materialize. If managers were compensated solely on the basis of ROE, and if the expected ROEs were actually achieved, then Division R's manager would receive a higher bonus than S's, even though S might actually be creating more value for shareholders as a result of its lower risk. Also, as we discussed earlier, financial leverage can increase expected ROE but at the cost of higher risk, so raising ROE through greater use of leverage may not be good. 21 The technique used is discriminant analysis. The seminal work on this subject was by Edward I. Altman, "Financial Ratios, Discriminant Analysis, and the Prediction of Corporate Bankruptcy," Journal of Finance, September 1968, pp. 589609. 126 Part 2 Fundamental Concepts in Financial Management EVA and ROE To better understand the idea behind EVA and how it is connected to ROE, let's look at Keller Electronics. Keller has $100,000 in investor-supplied operating capital, which, in turn, consists of $50,000 of long-term debt and $50,000 of common equity. The company has no preferred stock or notes payable. The long-term debt has a 10 percent interest rate. However, since the company is in the 40 percent tax bracket and interest expense is tax deductible, the after-tax cost of debt is only 6 percent. On the basis of their assessment of the company's risk, shareholders require a 14 percent return. This 14 percent return is what shareholders could expect to earn if they were to take their money elsewhere and invest in stocks that have the same risk as Keller. Keller's overall cost of capital is a weighted average of the cost of debt and equity, and it is 10 percent, found as 0.50(6%) 0.50(14%) 10%. The total dollar cost of capital per year is 0.10($100,000) $10,000. Now let's look at Keller's income statement. Its operating income, EBIT, is $20,000, and its interest expense is 0.10($50,000) $5,000. Therefore, its taxable income is $20,000 $5,000 $15,000. Taxes equal 40 percent of taxable income, or 0.4($15,000) $6,000, so the firm's net income is $9,000, and its return on equity, ROE, is $9,000/$50,000 18%. Now what is Keller's EVA? The basic formula for EVA is EVA EBIT (1 Corporate tax rate) (Total investor-supplied operating capital) (After-tax percentage cost of capital) $20,000(1 $2,000 This $2,000 EVA indicates that Keller provided its shareholders with $2,000 more than they could have earned elsewhere by investing in other stocks with the same risk as Keller's stock. To see where this $2,000 comes from, let's trace what happens to the money: The firm generates $20,000 in operating income. $6,000 goes to the government to pay taxes, leaving $14,000. $5,000 goes to the bondholders in the form of interest payments, thus leaving $9,000. $7,000 is what Keller's shareholders expected to earn: (0.14)($50,000) $7,000. Note that this $7,000 payment is not a requirement to stay in business--companies can stay in business as long as they pay their bills and their taxes. However, this $7,000 is what shareholders expected to earn, and it is the amount the firm must earn if it is to avoid reducing shareholder wealth. 0.40) ($100,000)(0.10) Second, ROE does not consider the amount of invested capital. To illustrate, consider a large company that has $100 invested in Project A, which has an ROE of 50 percent, and $1,000,000 invested in Project B, which has a 40 percent ROE. The projects are equally risky, and the two returns are both well above the company's cost of the capital invested in the projects. In this example, Project A has a higher ROE, but because it is so small, it does little to enhance shareholder wealth. Project B, on the other hand, has the lower ROE, but it adds much more to shareholder value. Consider one last problem with ROE. Assume that you manage a division of a large firm. The firm uses ROE as the sole performance measure, and it determines bonuses on the basis of ROE. Toward the end of the year, your division's ROE is an impressive 45 percent. Now you have an opportunity to invest in a large, low-risk project that has an estimated ROE of 35 percent, which is well above the firm's cost of capital. Even though this project is profitable, you might be reluctant to make the investment because it would reduce your division's average ROE, and therefore reduce the size of your year-end bonus. These three examples suggest that a project's return must be combined with its risk and size to determine its effect on shareholder value: Chapter 4 Analysis of Financial Statements 127 What's left over, the $2,000, is EVA. In this case, Keller's management created wealth because it provided shareholders with a return greater than what they presumably would have earned on alternative investments with the same risk as Keller's stock. equity. Indeed, using the simple example above, we could also express EVA as net income minus the dollar cost of equity: EVA Net Income [(Equity capital) (Cost of equity capital)] $9,000 $2,000 Note that this is the same number we calculated before when we used the other formula for calculating EVA. Note also that the expression above could be rewritten as follows: EVA (Equity capital)[Net income/Equity capital Cost of equity capital] [($50,000)(0.14)] Some Additional Points In practice, it is often necessary to make several adjustments in order to arrive at a "better" measure of EVA. The adjustments deal with leased assets, depreciation, and other accounting details. Shareholders may not immediately receive the $9,000 that Keller made for them this year (the $7,000 that shareholders expected plus the $2,000 of EVA). Keller can either pay its earnings out as dividends or keep them in the firm as retained earnings. In either event, the $9,000 is shareholders' money. The factors influencing the dividend payout decision are discussed in the chapter on dividend policy. or simply as EVA (Equity capital)(ROE Cost of equity capital) The Connection between ROE and EVA EVA is different from the traditional accounting measure of profit because EVA explicitly considers not just the interest cost of debt but also the cost of This last expression implies that EVA depends on three factors: rate of return, as reflected in ROE; risk, which affects the cost of equity; and size, which is measured by the equity employed. Recall that earlier in this chapter we said that shareholder value depends on risk, return, and capital invested. This final equation illustrates this point. Value f(ROE, Risk, Size) ROE is only one dimension of the value equation, and because actions that increase expected ROE may also affect the other two factors, steps designed to increase expected ROE may in some cases be inconsistent with increasing shareholder wealth. Note that we say "expected ROE," not simply ROE. All management decisions are designed to do something in the future, hence to affect future outcomes. With all this in mind, academics, practitioners, and consultants have developed alternative measures that attempt to overcome ROE's potential problems when it is used to gauge performance. One such measure is Economic Value Added (EVA), which was mentioned in Chapter 3 where we calculated EVA. For a discussion of the connection between ROE and EVA, see the accompanying box, "EVA and ROE." If a firm takes steps that increase its expected future ROE, does this mean that shareholder wealth will also increase? Explain. 128 Part 2 Fundamental Concepts in Financial Management 4.12 LOOKING BEYOND THE NUMBERS Hopefully, working through this chapter has increased your ability to understand and interpret financial statements. This is critically important for anyone making business decisions, evaluating performance, or forecasting likely future developments. Moreover, sound financial analysis involves more than just calculating numbers--good analysis requires that certain qualitative factors be considered when evaluating a company. These factors, as summarized by the American Association of Individual Investors (AAII), include the following: 1. Are the company's revenues tied to one key customer? If so, the company's performance may decline dramatically if the customer goes elsewhere. On the other hand, if the relationship is firmly entrenched, this might actually stabilize sales. 2. To what extent are the company's revenues tied to one key product? Companies that focus on a single product may be more efficient, but this lack of diversification also increases risk. If revenues come from several different products, the overall bottom line will be less affected by an event that leads to a drop in the demand for one of the products. 3. To what extent does the company rely on a single supplier? Depending on a single supplier may lead to unanticipated shortages, which investors and potential creditors should consider. 4. What percentage of the company's business is generated overseas? Companies with a large percentage of overseas business are often able to realize higher growth and larger profit margins. However, firms with large overseas operations may be exposed to regional stability problems, and cash flows from their various operations also depend on the values of different currencies. 5. Competition. Increases in competition tend to lower prices and profit margins. In forecasting future performance, it is important to assess both the likely actions of the current competitors and the entry by new competitors. 6. Future products. Is it necessary for the company to invest heavily in research and development? If so, its future prospects will depend critically on the success of new products in the pipeline. For example, the market's assessment of Boeing's and Airbus's future profits depends on how their next generations of planes are shaping up. Likewise, investors in pharmaceutical companies are interested in knowing whether the company has a strong pipeline of potential blockbuster drugs, and that those products are doing well in the required tests. 7. Legal and regulatory environment. Changes in laws and regulations have important implications for many industries. For example, when forecasting the future of tobacco companies, it is crucial to factor in the effects of proposed regulations and pending or likely lawsuits. Likewise, when assessing banks, telecommunications firms, and electric utilities, analysts need to forecast both the extent to which these industries will be regulated in the future and the ability of individual firms to respond to changes in regulation. Students might want to refer to AAII's educational Web site at http://www .aaii.com. The site provides information on investing basics, financial planning, portfolio management, and the like, so individuals can manage their own assets more effectively. What are some qualitative factors analysts should consider when evaluating a company's likely future financial performance? Chapter 4 Analysis of Financial Statements 129 Tying It All Together The primary purpose of this chapter was to discuss techniques investors and managers use to analyze financial statements. The five main categories of ratios were discussed using data for Allied Foods, and we explained how trend analysis and benchmarking are used. It is important to realize ratio analysis is useful, but it must be done intelligently and with good judgment if it is to provide useful insights into firms' operations. SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) ST-1 Key terms Define each of the following terms: a. Liquidity ratios: current ratio; quick ratio b. Asset management ratios: inventory turnover ratio; days sales outstanding (DSO); fixed assets turnover ratio; total assets turnover ratio c. Financial leverage: debt ratio; times-interest-earned (TIE) ratio; EBITDA coverage ratio d. Profitability ratios: profit margin on sales; basic earning power (BEP) ratio; return on total assets (ROA); return on common equity (ROE) e. Market value ratios: price/earnings (P/E) ratio; price/cash flow ratio; market/ book (M/B) ratio f. Trend analysis; comparative ratio analysis; benchmarking g. Basic and extended Du Pont equations; book value per share h. "Window dressing"; seasonal effects on ratios Debt ratio Last year, K. Billingsworth & Co. had earnings per share of $4 and dividends per share of $2. Total retained earnings increased by $12 million during the year, while book value per share at year-end was $40. Billingsworth has no preferred stock, and no new common stock was issued during the year. If its year-end total debt was $120 million, what was the company's year-end debt/assets ratio? Ratio analysis The following data apply to A.L. Kaiser & Company (millions of dollars): Cash and equivalents Fixed assets Sales Net income Current liabilities Current ratio DSOa ROE a ST-2 ST-3 $100.00 $283.50 $1,000.00 $50.00 $105.50 3.0 40.55 days 12% This calculation is based on a 365-day year. Kaiser has no preferred stock--only common equity, current liabilities, and long-term debt. a. Find Kaiser's (1) accounts receivable, (2) current assets, (3) total assets, (4) ROA, (5) common equity, (6) quick ratio, and (7) long-term debt. 130 Part 2 Fundamental Concepts in Financial Management b. In part a, you should have found Kaiser's accounts receivable (A/R) $111.1 million. If Kaiser could reduce its DSO from 40.55 days to 30.4 days while holding other things constant, how much cash would it generate? If this cash were used to buy back common stock (at book value), thus reducing common equity, how would this affect (1) the ROE, (2) the ROA, and (3) the total debt/total assets ratio? QUESTIONS 4-1 Financial ratio analysis is conducted by four groups of analysts: short-term lenders, longterm lenders, stockholders, and managers. What is the primary emphasis of each group, and how would that affect the ratios they focus on? Why would the inventory turnover ratio be more important for someone analyzing a grocery store chain than an insurance company? Over the past year, M. D. Ryngaert & Co. had an increase in its current ratio and a decline in its total assets turnover ratio. However, the company's sales, cash and equivalents, DSO, and its fixed assets turnover ratio remained constant. What balance sheet accounts must have changed to produce the indicated changes? Profit margins and turnover ratios vary from one industry to another. What differences would you expect to find between the turnover ratios, profit margins, and Du Pont equations for a grocery chain and a steel company? How does inflation distort ratio analysis comparisons, both for one company over time (trend analysis) and when different companies are being compared? Are only balance sheet items or both balance sheet and income statement items affected? If a firm's ROE is low and management wants to improve it, explain how using more debt might help. Give some examples that illustrate how (a) seasonal factors and (b) different growth rates might distort a comparative ratio analysis. How might these problems be alleviated? Why is it sometimes misleading to compare a company's financial ratios with those of other firms that operate in the same industry? Suppose you were comparing a discount merchandiser with a high-end merchandiser. Suppose further that both companies had identical ROEs. If you applied the extended Du Pont equation to both firms, would you expect the three components to be the same for each company? If not, explain what balance sheet and income statement items might lead to the component differences. Indicate the effects of the transactions listed in the following table on total current assets, current ratio, and net income. Use ( ) to indicate an increase, ( ) to indicate a decrease, and (0) to indicate either no effect or an indeterminate effect. Be prepared to state any necessary assumptions, and assume an initial current ratio of more than 1.0. (Note: A good accounting background is necessary to answer some of these questions; if yours is not strong, just answer the questions you can handle.) Total Current Current Assets Ratio a. b. c. d. e. f. g. h. Cash is acquired through issuance of additional common stock. Merchandise is sold for cash. Federal income tax due for the previous year is paid. A fixed asset is sold for less than book value. A fixed asset is sold for more than book value. Merchandise is sold on credit. Payment is made to trade creditors for previous purchases. A cash dividend is declared and paid. Effect on Net Income 4-2 4-3 4-4 4-5 4-6 4-7 4-8 4-9 4-10 _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ Chapter 4 Analysis of Financial Statements 131 Total Current Current Assets Ratio i. j. k. l. m. n. o. p. q. r. s. t. Cash is obtained through short-term bank loans. Short-term notes receivable are sold at a discount. Marketable securities are sold below cost. Advances are made to employees. Current operating expenses are paid. Short-term promissory notes are issued to trade creditors in exchange for past due accounts payable. Ten-year notes are issued to pay off accounts payable. A fully depreciated asset is retired. Accounts receivable are collected. Equipment is purchased with short-term notes. Merchandise is purchased on credit. The estimated taxes payable are increased. _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ Effect on Net Income _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ PROBLEMS Easy Problems 16 4-1 4-2 4-3 Days sales outstanding Baker Brothers has a DSO of 40 days, and its annual sales are $7,300,000. What is its accounts receivable balance? Assume it uses a 365-day year. Debt ratio Bartley Barstools has an equity multiplier of 2.4, and its assets are financed with some combination of long-term debt and common equity. What is its debt ratio? Du Pont analysis Doublewide Dealers has an ROA of 10 percent, a 2 percent profit margin, and an ROE of 15 percent. What is its total assets turnover? What is its equity multiplier? Market/book ratio Jaster Jets has $10 billion in total assets. Its balance sheet shows $1 billion in current liabilities, $3 billion in long-term debt, and $6 billion in common equity. It has 800 million shares of common stock outstanding, and its stock price is $32 per share. What is Jaster's market/book ratio? Price/earnings ratio A company has an EPS of $2.00, a cash flow per share of $3.00, and a price/cash flow ratio of 8.0 . What is its P/E ratio? Du Pont and ROE A firm has a profit margin of 2 percent and an equity multiplier of 2.0. Its sales are $100 million and it has total assets of $50 million. What is its ROE? Du Pont and net income Ebersoll Mining has $6 million in sales; its ROE is 12 percent; and its total assets turnover is 3.2 . The company is 50 percent equity financed. What is its net income? Basic earning power Duval Manufacturing recently reported the following information: Net income ROA Interest expense $600,000 8% $225,000 4-4 4-5 4-6 Intermediate Problems 719 4-7 4-8 Its tax rate is 35 percent. What is its basic earning power (BEP)? 4-9 M/B and share price You are given the following information: Stockholders' equity $3.75 billion; price/earnings ratio 3.5; common shares outstanding 50 million; and market/book ratio 1.9. Calculate the price of a share of the company's common stock. Ratio calculations Assume you are given the following relationships for the Brauer Corp.: Sales/total assets Return on assets (ROA) Return on equity (ROE) 1.5 3% 5% 4-10 Calculate Brauer's profit margin and debt ratio. 4-11 EBITDA coverage ratio Willis Publishing has $30 billion in total assets. Its basic earning power (BEP) ratio is 20 percent, and its times-interest-earned ratio is 8.0. Willis' depreciation and amortization expense totals $3.2 billion. It has $2 billion in lease payments, and 132 Part 2 Fundamental Concepts in Financial Management $1 billion must go toward principal payments on outstanding loans and long-term debt. What is Willis's EBITDA coverage ratio? 4-12 Ratio calculations Graser Trucking has $12 billion in assets, and its tax rate is 40 percent. Its basic earning power (BEP) ratio is 15 percent, and its return on assets (ROA) is 5 percent. What is its times-interest-earned (TIE) ratio? Times-interest-earned ratio The H.R. Pickett Corp. has $500,000 of debt outstanding, and it pays an annual interest rate of 10 percent. Its annual sales are $2 million, its average tax rate is 30 percent, and its net profit margin on sales is 5 percent. What is its TIE ratio? Return on equity Midwest Packaging's ROE last year was only 3 percent, but its management has developed a new operating plan that calls for a total debt ratio of 60 percent, which will result in annual interest charges of $300,000. Management projects an EBIT of $1,000,000 on sales of $10,000,000, and it expects to have a total assets turnover ratio of 2.0. Under these conditions, the tax rate will be 34 percent. If the changes are made, what will be its return on equity? Return on equity and quick ratio Lloyd Inc. has sales of $200,000, a net income of $15,000, and the following balance sheet: Cash Receivables Inventories Net fixed assets Total assets $ 10,000 50,000 150,000 90,000 $300,000 Accounts payable Other current liabilities Long-term debt Common equity Total liabilities and equity $ 30,000 20,000 50,000 200,000 $300,000 4-13 4-14 4-15 The new owner thinks that inventories are excessive and can be lowered to the point where the current ratio is equal to the industry average, 2.5 , without affecting either sales or net income. If inventories are sold off and not replaced thus reducing the current ratio to 2.5 , if the funds generated are used to reduce common equity (stock can be repurchased at book value), and if no other changes occur, by how much will the ROE change? What will be the firm's new quick ratio? 4-16 Return on equity Central City Construction (CCC) needs $1 million of assets to get started, and it expects to have a basic earning power ratio of 20 percent. CCC will own no securities, so all of its income will be operating income. If it chooses to, CCC can finance up to 50 percent of its assets with debt, which will have an 8 percent interest rate. Assuming a 40 percent tax rate on all taxable income, what is the difference between its expected ROE if CCC finances with 50 percent debt versus its expected ROE if it finances entirely with common stock? Conceptual: Return on equity Which of the following statements is most correct? (Hint: Work Problem 4-16 before answering 4-17, and consider the solution setup for 4-16, as you think about 4-17.) a. If a firm's expected basic earning power (BEP) is constant for all of its assets and exceeds the interest rate on its debt, then adding assets and financing them with debt will raise the firm's expected return on common equity (ROE). b. The higher its tax rate, the lower a firm's BEP ratio will be, other things held constant. c. The higher the interest rate on its debt, the lower a firm's BEP ratio will be, other things held constant. d. The higher its debt ratio, the lower a firm's BEP ratio will be, other things held constant. e. Statement a is false, but statements b, c, and d are all true. TIE ratio AEI Incorporated has $5 billion in assets, and its tax rate is 40 percent. Its basic earning power (BEP) ratio is 10 percent, and its return on assets (ROA) is 5 percent. What is AEI's times-interest-earned (TIE) ratio? Current ratio The Petry Company has $1,312,500 in current assets and $525,000 in current liabilities. Its initial inventory level is $375,000, and it will raise funds as additional notes payable and use them to increase inventory. How much can its short-term debt (notes payable) increase without pushing its current ratio below 2.0? DSO and accounts receivable Harrelson Inc. currently has $750,000 in accounts receivable, and its days sales outstanding (DSO) is 55 days. It wants to reduce its DSO to 35 days by pressuring more of its customers to pay their bills on time. If this policy is adopted the company's average sales will fall by 15 percent. What will be the level of accounts receivable following the change? Assume a 365-day year. 4-17 4-18 4-19 Challenging Problems 2024 4-20 Chapter 4 Analysis of Financial Statements 133 4-21 P/E and stock price Fontaine Inc. recently reported net income of $2 million. It has 500,000 shares of common stock, which currently trades at $40 a share. Fontaine continues to expand and anticipates that 1 year from now its net income will be $3.25 million. Over the next year it also anticipates issuing an additional 150,000 shares of stock, so that 1 year from now it will have 650,000 shares of common stock. Assuming its price/earnings ratio remains at its current level, what will be its stock price 1 year from now? Balance sheet analysis Complete the balance sheet and sales information that follows using the following financial data: Debt ratio: 50% Current ratio: 1.8 Total assets turnover: 1.5 Days sales outstanding: 36.5 daysa Gross profit margin on sales: (Sales Inventory turnover ratio: 5 a 4-22 Cost of goods sold)/Sales 25% Calculation is based on a 365-day year. Accounts payable Long-term debt Common stock Retained earnings Total liabilities and equity Cost of goods sold Balance Sheet Cash Accounts receivable Inventories Fixed assets Total assets Sales 60,000 97,500 $300,000 4-23 Ratio analysis Data for Barry Computer Co. and its industry averages follow. a. Calculate the indicated ratios for Barry. b. Construct the extended Du Pont equation for both Barry and the industry. c. Outline Barry's strengths and weaknesses as revealed by your analysis. d. Suppose Barry had doubled its sales as well as its inventories, accounts receivable, and common equity during 2005. How would that information affect the validity of your ratio analysis? (Hint: Think about averages and the effects of rapid growth on ratios if averages are not used. No calculations are needed.) Barry Computer Company: Balance Sheet as of December 31, 2005 (In Thousands) Cash Receivables Inventories Total current assets Net fixed assets Total assets $ 77,500 336,000 241,500 $655,000 292,500 $947,500 Accounts payable Notes payable Other current liabilities Total current liabilities Long-term debt Common equity Total liabilities and equity $129,000 84,000 117,000 $330,000 256,500 361,000 $947,500 Barry Computer Company: Income Statement for Year Ended December 31, 2005 (In Thousands) Sales Cost of goods sold Materials Labor Heat, light, and power Indirect labor Depreciation Gross profit Selling expenses General and administrative expenses Earnings before interest and taxes (EBIT) Interest expense Earnings before taxes (EBT) Federal and state income taxes (40 percent) Net income $1,607,500 $717,000 453,000 68,000 113,000 41,500 1,392,500 $ 215,000 115,000 30,000 $ $ $ 70,000 24,500 45,500 18,200 27,300 134 Part 2 Fundamental Concepts in Financial Management Ratio Current Quick Days sales outstandinga Inventory turnover Total assets turnover Net profit margin ROA ROE Total debt/total assets a Barry _____ _____ _____ _____ _____ _____ _____ _____ _____ Industry Average 2.0 1.3 35 days 6.7 3.0 1.2% 3.6% 9.0% 60.0% Calculation is based on a 365-day year. 4-24 Du Pont analysis A firm has been experiencing low profitability in recent years. Perform an analysis of the firm's financial position using the extended Du Pont equation. The firm has no lease payments, but has a $2 million sinking fund payment on its debt. The most recent industry average ratios and the firm's financial statements are as follows: Industry Average Ratios Current ratio Debt/total assets Times interest earned EBITDA coverage Inventory turnover Days sales outstandinga a 2 30% 7 9 10 24 days Fixed assets turnover Total assets turnover Profit margin on sales Return on total assets Return on common equity 6 3 3% 9% 12.9% Calculation is based on a 365-day year. Balance Sheet as of December 31, 2005 (Millions of Dollars) Cash and equivalents Net receivables Inventories Total current assets $ 78 66 159 $303 Accounts payable Notes payable Other current liabilities Total current liabilities Long-term debt Total liabilities Gross fixed assets Less depreciation Net fixed assets Total assets 225 78 $147 $450 Common stock Retained earnings Total stockholders' equity Total liabilities and equity $ 45 45 21 $ 111 24 $ 135 114 201 $ 315 $ 450 Income Statement for Year Ended December 31, 2005 (Millions of Dollars) Net sales Cost of goods sold Gross profit Selling expenses EBITDA Depreciation expense Earnings before interest and taxes (EBIT) Interest expense Earnings before taxes (EBT) Taxes (40%) Net income $795.0 660.0 $135.0 73.5 $ 61.5 12.0 $ 49.5 4.5 $ 45.0 18.0 $ 27.0 Chapter 4 Analysis of Financial Statements 135 a. b. c. d. e. Calculate those ratios that you think would be useful in this analysis. Construct an extended Du Pont equation, and compare the company's ratios to the industry average ratios. Do the balance sheet accounts or the income statement figures seem to be primarily responsible for the low profits? Which specific accounts seem to be most out of line relative to other firms in the industry? If the firm had a pronounced seasonal sales pattern, or if it grew rapidly during the year, how might that affect the validity of your ratio analysis? How might you correct for such potential problems? COMPREHENSIVE/SPREADSHEET PROBLEM 4-25 Ratio analysis The Corrigan Corporation's 2004 and 2005 financial statements follow, along with some industry average ratios. a. Assess Corrigan's liquidity position, and determine how it compares with peers and how the liquidity position has changed over time. b. Assess Corrigan's asset management position, and determine how it compares with peers and how its asset management efficiency has changed over time. c. Assess Corrigan's debt management position, and determine how it compares with peers and how its debt management has changed over time. d. Assess Corrigan's profitability ratios, and determine how they compare with peers and how the profitability position has changed over time. e. Assess Corrigan's market value ratios, and determine how their valuation compares with peers and how it has changed over time. f. Calculate Corrigan's ROE, as well as the industry average ROE, using the extended Du Pont equation. From this analysis, how does Corrigan's financial position compare with the industry average numbers? g. What do you think would happen to its ratios if the company initiated cost-cutting measures that allowed it to hold lower levels of inventory and substantially decreased the cost of goods sold? No calculations are necessary. Think about which ratios would be affected by changes in these two accounts. Corrigan Corporation: Balance Sheets as of December 31 2005 Cash Accounts receivable Inventories Total current assets Land and building Machinery Other fixed assets Total assets Accounts and notes payable Accrued liabilities Total current liabilities Long-term debt Common stock Retained earnings Total liabilities and equity $ 72,000 439,000 894,000 $ 2004 65,000 328,000 813,000 $1,405,000 238,000 132,000 61,000 $1,836,000 $ 432,000 170,000 $ 602,000 404,290 575,000 254,710 $1,836,000 $1,206,000 271,000 133,000 57,000 $1,667,000 $ 409,500 162,000 $ 571,500 258,898 575,000 261,602 $1,667,000 136 Part 2 Fundamental Concepts in Financial Management Corrigan Corporation: Income Statements for Years Ending December 31 2005 Sales Cost of goods sold Gross operating profit General administrative and selling expenses Depreciation Miscellaneous Earnings before taxes (EBT) Taxes (40%) Net income Per-Share Data 2005 EPS Cash dividends Market price (average) P/E ratio Number of shares outstanding Industry Financial Ratiosa Current ratio Inventory turnoverb Days sales outstandingc Fixed assets turnoverb Total assets turnoverb Return on assets Return on equity Debt ratio Profit margin on sales P/E ratio Price/cash flow ratio a b 2004 $3,635,000 2,980,000 $ 655,000 213,550 154,500 127,000 $ 159,950 63,980 $ 95,970 2004 $4.17 $0.95 $23.57 5.65 23,000 $4,240,000 3,680,000 $ 560,000 236,320 159,000 134,000 $ $ 30,680 12,272 18,408 $0.80 $1.10 $12.34 15.4 23,000 2.7 7.0 32 days 13.0 2.6 9.1% 18.2% 50.0% 3.5% 6.0 3.5 Industry average ratios have been constant for the past 4 years. Based on year-end balance sheet figures. c Calculation is based on a 365-day year. Integrated Case D'Leon Inc., Part II 4-26 Financial statement analysis Part I of this case, presented in Chapter 3, discussed the situation that D'Leon Inc., a regional snack-foods producer, was in after an expansion program. D'Leon had increased plant capacity and undertaken a major marketing campaign in an attempt to "go national." Thus far, sales have not been up to the forecasted level, costs have been higher than were projected, and a large loss occurred in 2005 rather than the expected profit. As a result, its managers, directors, and investors are concerned about the firm's survival. Donna Jamison was brought in as assistant to Fred Campo, D'Leon's chairman, who had the task of getting the company back into a sound financial position. D'Leon's 2004 and 2005 balance sheets and income statements, together with projections for 2006, are given in Tables IC4-1 and IC4-2. In addition, Table IC4-3 gives the company's 2004 and 2005 financial ratios, together with industry average data. The 2006 projected financial statement data represent Jamison's and Campo's best guess for 2006 results, assuming that some new financing is arranged to get the company "over the hump." Chapter 4 Analysis of Financial Statements 137 Jamison examined monthly data for 2005 (not given in the case), and she detected an improving pattern during the year. Monthly sales were rising, costs were falling, and large losses in the early months had turned to a small profit by December. Thus, the annual data look somewhat worse than final monthly data. Also, it appears to be taking longer for the advertising program to get the message across, for the new sales offices to generate sales, and for the new manufacturing facilities to operate efficiently. In other words, the lags between spending money and deriving benefits were longer than D'Leon's managers had anticipated. For these reasons, Jamison and Campo see hope for the company--provided it can survive in the short run. Jamison must prepare an analysis of where the company is now, what it must do to regain its financial health, and what actions should be taken. Your assignment is to help her answer the following questions. Provide clear explanations, not yes or no answers. a. Why are ratios useful? What are the five major categories of ratios? b. Calculate D'Leon's 2006 current and quick ratios based on the projected balance sheet and income statement data. What can you say about the company's liquidity positions in 2004, 2005, and as projected for 2006? We often think of ratios as being useful (1) to managers to help run the business, (2) to bankers for credit analysis, and (3) to stockholders for stock valuation. Would these different types of analysts have an equal interest in these liquidity ratios? c. Calculate the 2006 inventory turnover, days sales outstanding (DSO), fixed assets turnover, and total assets turnover. How does D'Leon's utilization of assets stack up against other firms in its industry? d. Calculate the 2006 debt, times-interest-earned, and EBITDA coverage ratios. How does D'Leon compare with the industry with respect to financial leverage? What can you conclude from these ratios? e. Calculate the 2006 profit margin, basic earning power (BEP), return on assets (ROA), and return on equity (ROE). What can you say about these ratios? f. Calculate the 2006 price/earnings ratio, price/cash flow ratio, and market/book ratio. Do these ratios indicate that investors are expected to have a high or low opinion of the company? g. Use the extended Du Pont equation to provide a summary and overview of D'Leon's financial condition as projected for 2006. What are the firm's major strengths and weaknesses? h. Use the following simplified 2006 balance sheet to show, in general terms, how an improvement in the DSO would tend to affect the stock price. For example, if the company could improve its collection procedures and thereby lower its DSO from 45.6 days to the 32-day industry average without affecting sales, how would that change "ripple through" the financial statements (shown in thousands below) and influence the stock price? Accounts receivable Other current assets Net fixed assets Total assets $ 878 1,802 817 $3,497 Debt Equity Liabilities plus equity $1,545 1,952 $3,497 i. Does it appear that inventories could be adjusted, and, if so, how should that adjustment affect D'Leon's profitability and stock price? j. In 2005, the company paid its suppliers much later than the due dates, and it was not maintaining financial ratios at levels called for in its bank loan agreements. Therefore, suppliers could cut the company off, and its bank could refuse to renew the loan when it comes due in 90 days. On the basis of data provided, would you, as a credit manager, continue to sell to D'Leon on credit? (You could demand cash on delivery--that is, sell on terms of COD--but that might cause D'Leon to stop buying from your company.) Similarly, if you were the bank loan officer, would you recommend renewing the loan or demand its repayment? Would your actions be influenced if, in early 2006, D'Leon showed you its 2006 projections plus proof that it was going to raise more than $1.2 million of new equity? k. In hindsight, what should D'Leon have done back in 2004? l. What are some potential problems and limitations of financial ratio analysis? m. What are some qualitative factors analysts should consider when evaluating a company's likely future financial performance? 138 Part 2 Fundamental Concepts in Financial Management TA B L E I C 4 - 1 Balance Sheets 2006E 2005 2004 Assets Cash Accounts receivable Inventories Total current assets Gross fixed assets Less accumulated depreciation Net fixed assets Total assets Liabilities and Equity Accounts payable Notes payable Accruals Total current liabilities Long-term debt Common stock Retained earnings Total equity Total liabilities and equity $ 85,632 878,000 1,716,480 $ 7,282 632,160 1,287,360 $ 57,600 351,200 715,200 $2,680,112 1,197,160 380,120 $ 817,040 $3,497,152 $ 436,800 300,000 408,000 $1,144,800 400,000 1,721,176 231,176 $1,952,352 $3,497,152 $1,926,802 1,202,950 263,160 $ 939,790 $2,866,592 $ 524,160 636,808 489,600 $1,650,568 723,432 460,000 32,592 $ 492,592 $2,866,592 $1,124,000 491,000 146,200 $ 344,800 $1,468,800 $ 145,600 200,000 136,000 $ 481,600 323,432 460,000 203,768 $ 663,768 $1,468,800 Note: "E" indicates estimated. The 2006 data are forecasts. TA B L E I C 4 - 2 Income Statements 2006E 2005 $6,034,000 5,528,000 519,988 $6,047,988 ($ 13,988) 116,960 ($ 130,948) 136,012 ($ 266,960) ( 106,784)a ($ 160,176) ($1.602) $0.110 $4.926 $2.25 100,000 40.00% 40,000 0 2004 $3,432,000 2,864,000 358,672 $3,222,672 $ 209,328 18,900 $ 190,428 43,828 $ 146,600 58,640 $ 87,960 $0.880 $0.220 $6.638 $8.50 100,000 40.00% 40,000 0 Sales Cost of goods sold Other expenses Total operating costs excluding depreciation EBITDA Depreciation EBIT Interest expense EBT Taxes (40%) Net income EPS DPS Book value per share Stock price Shares outstanding Tax rate Lease payments Sinking fund payments $7,035,600 5,875,992 550,000 $6,425,992 $ 609,608 116,960 $ 492,648 70,008 $ 422,640 169,056 $ 253,584 $1.014 $0.220 $7.809 $12.17 250,000 40.00% 40,000 0 a Note: "E" indicates estimated. The 2006 data are forecasts. The firm had sufficient taxable income in 2003 and 2004 to obtain its full tax refund in 2005. Chapter 4 Analysis of Financial Statements 139 TA B L E I C 4 - 3 Ratio Analysis 2006E 2005 1.2 0.4 4.7 38.2 6.4 2.1 82.8% 1.0 0.1 2.7% 4.6% 5.6% 32.5% 1.4 5.2 0.5 $4.93 2004 2.3 0.8 4.8 37.4 10.0 2.3 54.8% 4.3 3.0 2.6% 13.0% 6.0% 13.3% 9.7 8.0 1.3 $6.64 Industry Average 2.7 1.0 6.1 32.0 7.0 2.6 50.0% 6.2 8.0 3.5% 19.1% 9.1% 18.2% 14.2 11.0 2.4 n.a. Current Quick Inventory turnover Days sales outstanding (DSO)a Fixed assets turnover Total assets turnover Debt ratio TIE EBITDA coverage Profit margin Basic earning power ROA ROE Price/earnings Price/cash flow Market/book Book value per share Note: "E" indicates estimated. The 2006 data are forecasts. Calculation is based on a 365-day year. a Please go to the ThomsonNOW Web site to access the Cyberproblems. 140 Part 2 Fundamental Concepts in Financial Management Access the Thomson ONE problems though the ThomsonNOW Web site. Use the Thomson ONE--Business School Edition online database to work this chapter's questions. Conducting a Financial Ratio Analysis on Ford Motor Company In Chapter 3, we took a look at Starbucks' financial statements. Now we use Thomson One to analyze Ford Motor Company. Enter Ford's ticker symbol (F) and select "GO." If we select the tab at the top labeled "Financials," we can find Ford's key financial statements for the past several years. At the "Financials" screen on the second line of tabs, select the "Fundamental Ratios" tab. If you then select the SEC Database Ratios from the pull-down menu, you can select either annual or quarterly ratios. Under annual ratios, there is an in-depth summary of Ford's various ratios over the past 3 years. This information enables you to evaluate Ford's performance over time for each of the ratio categories that we mention in the text (liquidity, asset management, debt management, profitability, and market-based ratios). The text mentions that financial statement analysis has two major components: a trend analysis, where we evaluate changes in the key ratios over time, and a peer analysis, where we compare financial ratios with firms that are in the same industry and/or line of business. We have already used Thomson One to conduct a trend analysis--next we use this tool to conduct a peer analysis. If we click on the "Peers" tab (on the first line of tabs) near the top of the screen, some summary financial information for Ford and a few of its peers will be presented. If you click on the "Peer Sets" tab (second line of tabs), you can modify the list of peer firms. The default setup is "Peers set by SIC Code." To obtain a comparison of many of the key ratios presented in the text, just click on "Financials" (second line of tabs) and select "Key Financial Ratios" from the drop-down menu. Discussion Questions 1. What has happened to Ford's liquidity position over the past 3 years? How does Ford's liquidity compare with its peers? (Hint: You may use both the peer key financial ratios and liquidity comparison to answer this question.) 2. Take a look at Ford's inventory turnover ratio. How does this ratio compare with its peers? Have there been any interesting changes over time in this measure? Do you consider Ford's inventory management to be a strength or a weakness? 3. Construct a simple Du Pont analysis for Ford and its peers. What are Ford's strengths and weaknesses relative to its competitors? C H APTE R 5 FINANCIAL MARKETS AND INSTITUTIONS A Strong Financial System Is Necessary for a Growing and Prosperous Economy Financial managers and investors don't operate in a vacuum--they make decisions within a large and complex financial environment. This environment includes financial markets and institutions, tax and regulatory policies, and the state of the economy. The environment both determines the available financial alternatives and affects the outcomes of various decisions. Thus, it is crucial that investors and financial managers have a good understanding of the environment in which they operate. History shows that a strong financial system is a necessary ingredient for a growing and prosperous economy. Companies raising capital to finance capital expenditures as well as investors saving to accumulate funds for future use require well-functioning financial markets and institutions. Over the past few decades, changing technology and improving communications have increased cross-border transactions and expanded the scope and efficiency of the global financial system. Companies routinely raise funds throughout the world to finance projects all around the globe. Likewise, with the click of a mouse an individual investor in Nebraska can deposit funds in a European bank or purchase a mutual fund that invests in Chinese securities. It is important to recognize that at the most fundamental level well-functioning markets and institutions are based heavily on trust. An investor who deposits money in a bank, buys stock through an online brokerage account, or contacts her broker to buy a mutual fund places her money and trust in the hands of the financial institutions that provide her with advice and transaction services. Similarly, when businesses approach commercial or investment banks to raise capital, they are relying on these institutions to provide them with funds under the best possible terms, and with sound, objective advice. While changing technology and globalization have made it possible for more and more types of financial transactions to take place, a series of scandals in recent years have rocked the financial industry and have led many to JOHN GRESS/REUTERS/CORBIS 142 Part 2 Fundamental Concepts in Financial Management question whether some of our institutions are serving their own or their clients' interests. Many of these questionable practices have come to light because of the efforts of a single man: the Attorney General of New York, Eliot Spitzer. In 2001, Spitzer exposed conflicts of interest within investment banking firms regarding dealings between their underwriters, who help companies issue new securities, and their analysts, who make recommendations to individual investors to purchase these securities. Allegations were made that to attract the business of firms planning to issue new securities, investment banks leaned on their analysts to write glowing, overly optimistic research reports on these firms. While such practices helped produce large underwriting fees for the investment banks, they compromised their ability to provide the objective, independent research on which their clients depended. A few years later, Spitzer turned his attention to the mutual fund industry, where he exposed unethical fee structures and trading practices of some of the leading funds. More recently, Spitzer has questioned whether some insurance brokers have compromised their clients' interests in order to steer business toward insurers, who provide the broker with rebates of different types.1 While some have criticized Spitzer for being overly zealous and politically ambitious, his efforts have appropriately brought to light many questionable practices. Hopefully, this spotlight will put pressure on the institutions to establish practices that will restore the public's trust and lead to a better financial system in the long run. Putting Things In Perspective In earlier chapters, we discussed financial statements and showed how financial managers and others analyze them to evaluate a firm's operations and financial position--past, current, and future. To make good decisions, financial managers must understand the environment and markets within which businesses operate. Therefore, in this chapter we describe the markets where capital is raised, securities are traded, and stock prices are established, as well as the institutions that operate in these markets. Because the overall objective of financial managers is to maximize shareholder value, we also take a closer look at how the stock market operates, and we discuss the concept of market efficiency. 1 For example, some insurance companies allowed brokers to keep premiums for as much as a year before remitting them to the insurance companies. The brokers invested these premiums and earned interest on them, and this gave them an incentive to steer business to these companies rather than to insurance companies whose policies might be better for the brokers' clients. Chapter 5 Financial Markets and Institutions 143 5.1 AN OVERVIEW OF THE CAPITAL ALLOCATION PROCESS Businesses, individuals, and governments often need to raise capital. For example, suppose Carolina Power & Light (CP&L) forecasts an increase in the demand for electricity in North Carolina, and the company decides to build a new power plant. Because CP&L almost certainly will not have the $1 billion or so necessary to pay for the plant, the company will have to raise this capital in the financial markets. Or suppose Mr. Fong, the proprietor of a San Francisco hardware store, decides to expand into appliances. Where will he get the money to buy the initial inventory of TV sets, washers, and freezers? Similarly, if the Johnson family wants to buy a home that costs $200,000, but they have only $40,000 in savings, how can they raise the additional $160,000? And if the city of New York wants to borrow $200 million to finance a new sewer plant, or the federal government needs money to meet its needs, they too need access to the capital markets. On the other hand, some individuals and firms have incomes that are greater than their current expenditures, so they have funds available to invest. For example, Carol Hawk has an income of $36,000, but her expenses are only $30,000, and as of December 31, 2004, Ford Motor Company had accumulated roughly $23.5 billion of cash and equivalents, which it has available for future investments. People and organizations with surplus funds are saving today in order to accumulate funds for future use. A household might save to pay for future expenses such as their children's education or their retirement, while a business might save to fund future investments. Those with surplus funds expect to earn a positive return on their investments. People and organizations who need money today borrow to fund their current expenditures. They understand that there is a cost to this capital, and this cost is essentially the return that the investors with surplus funds expect to earn on those funds. In a well-functioning economy, capital will flow efficiently from those who supply capital to those who demand it. This transfer of capital can take place in the three different ways described in Figure 5-1: 1. Direct transfers of money and securities, as shown in the top section, occur when a business sells its stocks or bonds directly to savers, without going through any type of financial institution. The business delivers its securities to savers, who in turn give the firm the money it needs. 2. As shown in the middle section, transfers may also go through an investment banking house such as Merrill Lynch, which underwrites the issue. An underwriter serves as a middleman and facilitates the issuance of securities. The company sells its stocks or bonds to the investment bank, which in turn sells these same securities to savers. The businesses' securities and the savers' money merely "pass through" the investment banking house. However, the investment bank does buy and hold the securities for a period of time, so it is taking a risk--it may not be able to resell them to savers for as much as it paid. Because new securities are involved and the corporation receives the proceeds of the sale, this is called a primary market transaction. 3. Transfers can also be made through a financial intermediary such as a bank or mutual fund. Here the intermediary obtains funds from savers in exchange for its own securities. The intermediary uses this money to buy and hold businesses' securities. For example, a saver might deposit dollars in a bank, receiving from it a certificate of deposit, and then the bank might lend the money to a small business as a mortgage loan. Thus, intermediaries literally create new forms of capital--in this case, certificates of deposit, which are both safer and more liquid than mortgages and thus are better for most 144 Part 2 Fundamental Concepts in Financial Management FIGURE 5-1 1. Direct Transfers Diagram of the Capital Formation Process Securities (Stocks or Bonds) Business Dollars Savers 2. Indirect Transfers through Investment Bankers Securities Business Dollars 3. Indirect Transfers through a Financial Intermediary Business's Securities Business Dollars Financial Intermediary Investment Banking Houses Securities Savers Dollars Intermediary's Securities Dollars Savers savers to hold. The existence of intermediaries greatly increases the efficiency of money and capital markets. Often the entity needing capital is a business, and specifically a corporation, but it is easy to visualize the demander of capital being a home purchaser, a small business, a government unit, and so on. For example, if your uncle lends you money to help fund a new business after you graduate, this would be a direct transfer of funds. Alternatively, if your family borrows money to purchase a home, you will probably raise the funds through a financial intermediary such as your local commercial bank or mortgage banker, which in turn may acquire its funds from a national institution, such as Fannie Mae. In a global context, economic development is highly correlated with the level and efficiency of financial markets and institutions.2 It is difficult, if not impossible, for an economy to reach its full potential if it doesn't have access to a well-functioning financial system. For this reason, policy makers often promote the globalization of financial markets. In a well-developed economy like that of the United States, an extensive set of markets and institutions has evolved over time to facilitate the efficient allocation of capital. To raise capital efficiently, managers must understand how these markets and institutions work. Identify three different ways capital is transferred between savers and borrowers. Why do policy makers promote the globalization of financial markets? 2 For a detailed review of the evidence linking financial development to economic growth, see Ross Levine, "Finance and Growth: Theory and Evidence," NBER Working Paper no. w10766, September 2004. Chapter 5 Financial Markets and Institutions 145 5.2 FINANCIAL MARKETS People and organizations wanting to borrow money are brought together with those having surplus funds in the financial markets. Note that "markets" is plural; there are a great many different financial markets in a developed economy such as ours. We briefly describe the different types of financial markets and some recent trends in these markets. Types of Markets Different financial markets serve different types of customers or different parts of the country. Financial markets also vary depending on the maturity of the securities being traded and the types of assets used to back the securities. For these reasons it is often useful to classify markets along the following dimensions: 1. Physical asset versus financial asset markets. Physical asset markets (also called "tangible" or "real" asset markets) are those for products such as wheat, autos, real estate, computers, and machinery. Financial asset markets, on the other hand, deal with stocks, bonds, notes, mortgages, and other claims on real assets, as well as with derivative securities whose values are derived from changes in the prices of other assets. A share of Ford stock is a "pure financial asset," while an option to buy Ford shares is a derivative security whose value depends on the price of Ford stock. 2. Spot versus futures markets. Spot markets are markets in which assets are bought or sold for "on-the-spot" delivery (literally, within a few days). Futures markets are markets in which participants agree today to buy or sell an asset at some future date. For example, a farmer may enter into a futures contract in which he agrees today to sell 5,000 bushels of soybeans six months from now at a price of $5 a bushel. On the other side, an international food producer looking to buy soybeans in the future may enter into a futures contract in which it agrees to buy soybeans six months from now. 3. Money versus capital markets. Money markets are the markets for short-term, highly liquid debt securities. The New York, London, and Tokyo money markets are among the world's largest. Capital markets are the markets for intermediate- or long-term debt and corporate stocks. The New York Stock Exchange, where the stocks of the largest U.S. corporations are traded, is a prime example of a capital market. There is no hard and fast rule on this, but when describing debt markets, "short term" generally means less than 1 year, "intermediate term" means 1 to 10 years, and "long term" means more than 10 years. 4. Primary versus secondary markets. Primary markets are the markets in which corporations raise new capital. If GE were to sell a new issue of common stock to raise capital, this would be a primary market transaction. The corporation selling the newly created stock receives the proceeds from the sale in a primary market transaction. Secondary markets are markets in which existing, already outstanding, securities are traded among investors. Thus, if Jane Doe decided to buy 1,000 shares of GE stock, the purchase would occur in the secondary market. The New York Stock Exchange is a secondary market because it deals in outstanding, as opposed to newly issued, stocks and bonds. Secondary markets also exist for mortgages, various other types of loans, and other financial assets. The corporation whose securities are being traded is not involved in a secondary market transaction and, thus, does not receive any funds from such a sale. Spot Markets The markets in which assets are bought or sold for "on-the-spot" delivery. Futures Markets The markets in which participants agree today to buy or sell an asset at some future date. Money Markets The financial markets in which funds are borrowed or loaned for short periods (less than one year). Capital Markets The financial markets for stocks and for intermediate- or longterm debt (one year or longer). Primary Markets Markets in which corporations raise capital by issuing new securities. Secondary Markets Markets in which securities and other financial assets are traded among investors after they have been issued by corporations. 146 Part 2 Fundamental Concepts in Financial Management Private Markets Markets in which transactions are worked out directly between two parties. Public Markets Markets in which standardized contracts are traded on organized exchanges. 5. Private versus public markets. Private markets, where transactions are negotiated directly between two parties, are differentiated from public markets, where standardized contracts are traded on organized exchanges. Bank loans and private debt placements with insurance companies are examples of private market transactions. Because these transactions are private, they may be structured in any manner that appeals to the two parties. By contrast, securities that are issued in public markets (for example, common stock and corporate bonds) are ultimately held by a large number of individuals. Public securities must have fairly standardized contractual features, both to appeal to a broad range of investors and also because public investors do not generally have the time and expertise to study unique, nonstandardized contracts. Their wide ownership also ensures that public securities are relatively liquid. Private market securities are, therefore, more tailor-made but less liquid, whereas publicly traded securities are more liquid but subject to greater standardization. Other classifications could be made, but this breakdown is sufficient to show that there are many types of financial markets. Also, note that the distinctions among markets are often blurred and unimportant except as a general point of reference. For example, it makes little difference if a firm borrows for 11, 12, or 13 months, hence, whether we have a "money" or "capital" market transaction. You should be aware of the important differences among types of markets, but don't get hung up trying to distinguish them at the boundaries. A healthy economy is dependent on efficient funds transfers from people who are net savers to firms and individuals who need capital. Without efficient transfers, the economy simply could not function: Carolina Power & Light could not raise capital, so Raleigh's citizens would have no electricity; the Johnson family would not have adequate housing; Carol Hawk would have no place to invest her savings; and so on. Obviously, the level of employment and productivity, hence our standard of living, would be much lower. Therefore, it is absolutely essential that our financial markets function efficiently--not only quickly, but also at a low cost.3 Table 5-1 (on pages 148149) gives a listing of the most important instruments traded in the various financial markets. The instruments are arranged from top to bottom in ascending order of typical length of maturity. As we go through the book, we will look in more detail at many of the instruments listed in Table 5-1. For example, we will see that there are many varieties of corporate bonds, ranging from "plain vanilla" bonds to bonds that are convertible into common stocks to bonds whose interest payments vary depending on the inflation rate. Still, the table gives an idea of the characteristics and costs of the instruments traded in the major financial markets. Recent Trends Financial markets have experienced many changes during the last two decades. Technological advances in computers and telecommunications, along with the globalization of banking and commerce, have led to deregulation, and this has increased competition throughout the world. The result is a much more effi- 3 As the countries of the former Soviet Union and other Eastern European nations move toward capitalism, just as much attention must be paid to the establishment of cost-efficient financial markets as to electrical power, transportation, communications, and other infrastructure systems. Economic efficiency is simply impossible without a good system for allocating capital within the economy. Chapter 5 Financial Markets and Institutions 147 cient, internationally linked market, but one that is far more complex than existed a few years ago. While these developments have been largely positive, they have also created problems for policy makers. At one conference, Federal Reserve Board Chairman Alan Greenspan stated that modern financial markets "expose national economies to shocks from new and unexpected sources and with little if any lag." He went on to say that central banks must develop new ways to evaluate and limit risks to the financial system. Large amounts of capital move quickly around the world in response to changes in interest and exchange rates, and these movements can disrupt local institutions and economies. Globalization has exposed the need for greater cooperation among regulators at the international level. Various committees are currently working to improve coordination, but the task is not easy. Factors that complicate coordination include (1) the differing structures among nations' banking and securities industries, (2) the trend in Europe toward financial services conglomerates, and (3) reluctance on the part of individual countries to give up control over their national monetary policies. Still, regulators are unanimous about the need to close the gaps in the supervision of worldwide markets. Another important trend in recent years has been the increased use of derivatives. A derivative is any security whose value is derived from the price of some other "underlying" asset. An option to buy IBM stock is a derivative, as is a contract to buy Japanese yen six months from now. The value of the IBM option depends on the price of IBM's stock, and the value of the Japanese yen "future" depends on the exchange rate between yen and dollars. The market for derivatives has grown faster than any other market in recent years, providing corporations with new opportunities but also exposing them to new risks. Derivatives can be used either to reduce risks or to speculate. Suppose an importer's costs rise and its net income falls when the dollar falls relative to the yen. That company could reduce its risk by purchasing derivatives whose values increase when the dollar declines. This is a hedging operation, and its purpose is to reduce risk exposure. Speculation, on the other hand, is done in the hope of high returns, but it raises risk exposure. For example, several years ago Procter & Gamble disclosed that it lost $150 million on derivative investments, and Orange County (California) went bankrupt as a result of its treasurer's speculation in derivatives. The size and complexity of derivatives transactions concern regulators, academics, and members of Congress. Fed Chairman Greenspan noted that, in theory, derivatives should allow companies to manage risk better, but that it is not clear whether recent innovations have "increased or decreased the inherent stability of the financial system." Derivative Any financial asset whose value is derived from the value of some other "underlying" asset. Distinguish between physical asset and financial asset markets. What's the difference between spot and futures markets? Distinguish between money and capital markets. What's the difference between primary and secondary markets? Differentiate between private and public markets. Why are financial markets essential for a healthy economy and economic growth? What is a derivative, and how is its value related to that of an "underlying asset"? 148 Part 2 Fundamental Concepts in Financial Management TA B L E 5 - 1 Summary of Major Market Instruments, Market Participants, and Security Characteristics SECURITY CHARACTERISTICS Instrument (1) U.S. Treasury bills Market (2) Money Major Participants (3) Sold by U.S. Treasury to finance federal expenditures A firm's promise to pay, guaranteed by a bank Issued by financially secure firms to large investors Issued by major moneycenter commercial banks to large investors Invest in Treasury bills, CDs, and commercial paper; held by individuals and businesses Issued by banks outside U.S. Riskiness (4) Default-free Original Maturity (5) 91 days to 1 year Up to 180 days Interest Rate on 2/1/05a (6) 2.48% Bankers' acceptances Money Low degree of risk if guaranteed by a strong bank Low default risk 2.68 Dealer commercial paper Negotiable certificates of deposit (CDs) Money Up to 270 days Up to 1 year 2.67 Money Default risk depends on the strength of the issuing bank Low degree of risk 2.70 Money market mutual funds Money No specific maturity (instant liquidity) Up to 1 year 1.69 Eurodollar market time deposits Money Default risk depends on the strength of the issuing bank Risk is variable 2.70 Consumer credit, including credit card debt U.S. Treasury notes and bonds Money Issued by banks/ credit unions/finance companies to individuals Issued by U.S. government Variable Variable, but goes up to 20% or more 4.65 Capital No default risk, but price will decline if interest rates rise 2 to 30 years a The yields reported (except for corporate and municipal bonds) are from The Wall Street Journal. Money market rates assume a 3-month maturity. Corporate and municipal bond rates are for 30-year AAA-rated bonds; quotes are from Federal Reserve Statistical Release. 5.3 FINANCIAL INSTITUTIONS Direct funds transfers are more common among individuals and small businesses, and in economies where financial markets and institutions are less developed. While businesses in more developed economies do occasionally rely on direct transfers, they generally find it more efficient to enlist the services of one or more financial institutions when it comes time to raise capital. In the United States and other developed nations, a set of highly efficient financial intermediaries has evolved. Their original roles were generally quite specific, but many of them have diversified to the point where they serve Chapter 5 Financial Markets and Institutions 149 TA B L E 5 - 1 (Continued) SECURITY CHARACTERISTICS Instrument (1) Mortgages Market (2) Capital Major Participants (3) Borrowings from commercial banks and S&Ls by individuals and businesses Issued by state and local governments to individuals and institutional investors Issued by corporations to individuals and institutional investors Riskiness (4) Risk is variable Original Maturity (5) Up to 30 years Interest Rate on 2/1/05a (6) 5.20 State and local government bonds Capital Riskier than U.S. government securities, but exempt from most taxes Riskier than U.S. government securities, but less risky than preferred and common stocks; varying degree of risk within bonds depending on strength of issuer Risk similar to corporate bonds Up to 30 years 4.40 Corporate bonds Capital Up to 40 yearsb 5.22 Leases Capital Similar to debt in that firms can lease assets rather than borrow and then buy the assets Issued by corporations to individuals and institutional investors Issued by corporations to individuals and institutional investors Generally 3 to 20 years Similar to bond yields Preferred stocks Capital Riskier than corporate bonds, but less risky than common stock Risky Unlimited 6 to 8% Common stocksc Capital Unlimited NA b c Just recently, a few corporations have issued 100-year bonds; however, the majority have issued bonds with maturities less than 40 years. While common stocks do not pay interest, they are expected to provide a "return" in the form of dividends and capital gains. As you will see in Chapter 8, historical stock returns have averaged between 10 and 15 percent a year. Of course, if you buy a stock, your actual return may be considerably higher or lower than these historical averages. many different markets. As a result, the differences between institutions have tended to become blurred. Still, there remains a degree of institutional identity, and therefore it is useful to describe the major categories of financial institutions here: 1. Investment banking houses such as Merrill Lynch, Morgan Stanley, Goldman Sachs, or Credit Suisse Group provide a number of services to both investors and companies planning to raise capital. Such organizations (a) help Investment Banking House An organization that underwrites and distributes new investment securities and helps businesses obtain financing. 150 Part 2 Fundamental Concepts in Financial Management Commercial Bank Traditional department store of finance serving a variety of savers and borrowers. 2. Financial Services Corporation A firm that offers a wide range of financial services, including investment banking, brokerage operations, insurance, and commercial banking. 3. 4. 5. 6. 7. 8. Mutual Funds Organizations that pool investor funds to purchase financial instruments and thus reduce risks through diversification. 9. corporations design securities with features that are currently attractive to investors, (b) then buy these securities from the corporation, and (c) resell them to savers. Although the securities are sold twice, this process is really one primary market transaction, with the investment banker acting as a facilitator to help transfer capital from savers to businesses. Commercial banks, such as Bank of America, Wells Fargo, Wachovia, and J. P. Morgan Chase, are the traditional "department stores of finance" because they serve a variety of savers and borrowers. Historically, commercial banks were the major institutions that handled checking accounts and through which the Federal Reserve System expanded or contracted the money supply. Today, however, several other institutions also provide checking services and significantly influence the money supply. Conversely, commercial banks are providing an ever-widening range of services, including stock brokerage services and insurance. Financial services corporations are large conglomerates that combine many different financial institutions within a single corporation. Examples of financial services corporations, most of which started in one area but have now diversified to cover most of the financial spectrum, include Citigroup, American Express, Fidelity, and Prudential. Savings and loan associations (S&Ls) traditionally served individual savers and residential and commercial mortgage borrowers, taking the funds of many small savers and then lending this money to home buyers and other types of borrowers. In the 1980s, the S&L industry experienced severe problems when (a) short-term interest rates paid on savings accounts rose well above the returns earned on the existing mortgages held by S&Ls and (b) commercial real estate suffered a severe slump, resulting in high mortgage default rates. Together, these events forced many S&Ls to merge with stronger institutions or close their doors. Mutual savings banks, which are similar to S&Ls, operate primarily in the northeastern states, accepting savings primarily from individuals, and lending mainly on a long-term basis to home buyers and consumers. Credit unions are cooperative associations whose members are supposed to have a common bond, such as being employees of the same firm. Members' savings are loaned only to other members, generally for auto purchases, home improvement loans, and home mortgages. Credit unions are often the cheapest source of funds available to individual borrowers. Pension funds are retirement plans funded by corporations or government agencies for their workers and administered primarily by the trust departments of commercial banks or by life insurance companies. Pension funds invest primarily in bonds, stocks, mortgages, and real estate. Life insurance companies take savings in the form of annual premiums; invest these funds in stocks, bonds, real estate, and mortgages; and finally make payments to the beneficiaries of the insured parties. In recent years, life insurance companies have also offered a variety of tax-deferred savings plans designed to provide benefits to the participants when they retire. Mutual funds are corporations that accept money from savers and then use these funds to buy stocks, long-term bonds, or short-term debt instruments issued by businesses or government units. These organizations pool funds and thus reduce risks by diversification. They also achieve economies of scale in analyzing securities, managing portfolios, and buying and selling securities. Different funds are designed to meet the objectives of different types of savers. Hence, there are bond funds for those who desire safety, stock funds for savers who are willing to accept significant risks in the hope of higher returns, and still other funds that are used as interest-bearing Chapter 5 Financial Markets and Institutions 151 checking accounts (money market funds). There are literally thousands of different mutual funds with dozens of different goals and purposes. Mutual funds have grown more rapidly than most other institutions in recent years, in large part because of a change in the way corporations provide for employees' retirement. Before the 1980s, most corporations said, in effect, "Come work for us, and when you retire, we will give you a retirement income based on the salary you were earning during the last five years before you retired." The company was then responsible for setting aside funds each year to make sure it had the money available to pay the agreed-upon retirement benefits. That situation is changing rapidly. Today, new employees are likely to be told, "Come work for us, and we will give you some money each payday that you can invest for your future retirement. You can't get the money until you retire (without paying a huge tax penalty), but if you invest wisely, you can retire in comfort." Most workers recognize that they don't know enough to invest wisely, so they turn their retirement funds over to a mutual fund. Hence, mutual funds are growing rapidly. Excellent information on the objectives and past performances of the various funds are provided in publications such as Value Line Investment Survey and Morningstar Mutual Funds, which are available in most libraries and on the Internet. 10. Hedge funds are similar to mutual funds because they accept money from savers and use the funds to buy various securities, but there are some important differences. While mutual funds are registered and regulated by the Securities and Exchange Commission (SEC), hedge funds are largely unregulated. This difference in regulation stems from the fact that mutual funds typically target small investors, whereas hedge funds typically have large minimum investments (often exceeding $1 million) that are effectively marketed to institutions and individuals with high net worths. Different hedge fund managers follow different strategies. For example, a hedge fund manager who believes that the spreads between corporate and Treasury bond yields are too large might simultaneously buy a portfolio of corporate bonds and sell a portfolio of Treasury bonds. In this case, the portfolio is "hedged" against overall movements in interest rates, but it will do well if the spread between these securities narrows. Likewise, hedge fund managers may take advantage of perceived incorrect valuations in the stock market, that is, where a stock's market and intrinsic values differ. Hedge funds generally charge large fees, often a fixed amount plus 15 to 20 percent of the fund's capital gains. The average hedge fund has done quite well in recent years. In a recent report, Citigroup estimates that the average hedge fund has produced an annual return of 11.9 percent since 1990. Over the same time period, the average annual returns of the overall stock market were 10.5 percent, and the returns on mutual funds were even lower, 9.2 percent. Given the stock market's relatively lackluster performance in recent years, an increasing number of investors have flocked to hedge funds. Between 1999 and 2004, the money managed by them more than quadrupled to roughly $800 billion. However, the same article in BusinessWeek that highlighted the strong growth and relative performance of these funds also suggested that their returns are showing signs of weakness and emphasized that they are certainly not without risk.4 Indeed, some hedge funds take on risks that are considerably higher than that of an average individual stock or mutual fund. Moreover, in recent years, some have also produced spectacular losses. For example, many 4 Money Market Funds Mutual funds that invest in short-term, low-risk securities and allow investors to write checks against their accounts. See Anne Tergesen, "Time to Hedge on Hedge Funds? New Research Shows that Returns Are Sliding, and Some Don't Help You Diversify," BusinessWeek, September 13, 2004, p. 104. 152 Part 2 Fundamental Concepts in Financial Management hedge fund investors suffered large losses in 1998 when the Russian economy collapsed. That same year, the Federal Reserve had to step in to help rescue Long Term Capital Management, a high-profile hedge fund whose managers included several well-respected practitioners as well as two Nobel Prizewinning professors who were experts in investment theory.5 As hedge funds have become more popular, many have begun to lower their minimum investment requirements. Perhaps not surprisingly, their rapid growth and shift toward smaller investors have also led to a call for more regulation. With the notable exception of hedge funds, financial institutions have been heavily regulated to ensure the safety of these institutions and thus to protect investors. Historically, many of these regulations--which have included a prohibition on nationwide branch banking, restrictions on the types of assets the institutions could buy, ceilings on the interest rates they could pay, and limitations on the types of services they could provide--tended to impede the free flow of capital and thus hurt the efficiency of our capital markets. Recognizing this fact, policy makers took several steps during the 1980s and 1990s to deregulate financial services companies. For example, the barriers that restricted banks from expanding nationwide were eliminated. Likewise, regulations that once forced a strict separation of commercial and investment banking have been relaxed. The result of the ongoing regulatory changes has been a blurring of the distinctions between the different types of institutions. Indeed, the trend in the United States today is toward huge financial services corporations, which own banks, S&Ls, investment banking houses, insurance companies, pension plan operations, and mutual funds, and which have branches across the country and around the world. For example, Citigroup combines one of the world's largest commercial banks (Citibank), a huge insurance company (Travelers), and a major investment bank (Smith Barney), along with numerous other subsidiaries that operate throughout the world. Citigroup's structure is similar to that of major institutions in Europe, Japan, and elsewhere around the globe. Panel A of Table 5-2 lists the 10 largest U.S. bank and thrift holding companies, while Panel B shows the leading world banking companies. Among the world's 10 largest, only one (Citigroup) is based in the United States. While U.S. banks have grown dramatically as a result of recent mergers, they are still small by global standards. Panel C of the table lists the 10 leading underwriters in terms of dollar volume of new debt and equity issues. Six of the top underwriters are also major commercial banks or are part of bank holding companies, which confirms the continued blurring of distinctions among different types of financial institutions. What is the difference between a pure commercial bank and a pure investment bank? List the major types of financial institutions, and briefly describe the primary function of each. What are some important differences between mutual and hedge funds? How are they similar? 5 See Franklin Edwards, "Hedge Funds and the Collapse of Long Term Capital Management," Journal of Economic Perspectives, Vol. 13, no. 2 (Spring 1999), pp. 189210, for a thoughtful review of the implications of Long Term Capital Management's collapse. Chapter 5 Financial Markets and Institutions 153 TA B L E 5 - 2 10 Largest U.S. Bank and Thrift Holding Companies and World Banking Companies and Top 10 Leading Underwriters Panel B World Banking Companiesb Mizuho Financial Group (Tokyo) Citigroup Inc. (New York) Allianz AG (Munich) UBS AG (Zurich) HSBC Holdings PLC (London) Deutsche Bank AG (Frankfurt) Credit Agricole (Paris) BNP Paribas (Paris) ING Group NV (Amsterdam) Sumitomo Mitsui Financial Group (Tokyo) Panel C Leading Global Underwritersc Citigroup Inc. Morgan Stanley J. P. Morgan Merrill Lynch Lehman Brothers Credit Suisse First Boston Deutsche Bank AG UBS AG Goldman Sachs Banc of America Securities Panel A U.S. Bank and Thrift Holding Companiesa Citigroup Inc. Bank of America Corp. J. P. Morgan Chase & Co. Wells Fargo & Co. Wachovia Corp. MetLife Inc. Bank One Washington Mutual Inc. U.S. Bancorp SunTrust Banks Inc. Notes: Ranked by total assets as of June 30, 2004. Source: "Top 150 Bank and Thrift Holding Companies with the Most Assets," AmericanBanker.com, October 19, 2004. b Ranked by total assets as of December 31, 2003. Source: "World's Largest Banking Companies by Assets," AmericanBanker.com, November 12, 2004. c Ranked by dollar amount raised through new issues (stocks and bonds) in 2004. For this ranking, the lead underwriter (manager) is given credit for the entire issue. Source: Adapted from The Wall Street Journal, January 3, 2005, p. R17. a 5.4 THE STOCK MARKET As noted earlier, secondary markets are those in which outstanding, previously issued securities are traded. By far the most active secondary market, and the most important one to financial managers, is the stock market, where the prices of firms' stocks are established. Because the primary goal of financial managers is to maximize their firms' stock prices, knowledge of the stock market is important to anyone involved in managing a business. While the two leading stock markets today are the New York Stock Exchange and the Nasdaq stock market, stocks are actually traded using a variety of market procedures. However, there are just two basic types of stock markets: (1) physical location exchanges, which include the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), and several regional stock exchanges, and (2) electronic dealer-based markets that include the Nasdaq stock market, the less formal over-the-counter market, and the recently developed electronic communications networks (ECNs). (See the box entitled, "The NYSE and Nasdaq Combine Forces with the Leading Online Trading Systems.") Because the physical location exchanges are easier to describe and understand, we consider them first. 154 Part 2 Fundamental Concepts in Financial Management Citigroup Built to Compete in a Changing Environment The financial environment has been undergoing tremendous changes, including breakthroughs in technology, increased globalization, and shifts in the regulatory environment. All of these factors have presented financial managers and investors with opportunities, but those opportunities are accompanied by substantial risks. Consider the case of Citigroup Inc., which was created in 1998 when Citicorp and Travelers Group (which included the investment firm Salomon Smith Barney) merged. Citigroup today operates in more than 100 countries, has roughly 200 million customers and 275,000 employees, and holds more than $1.4 trillion (that's over a thousand billion!) worth of assets. Citigroup resulted from three important trends: 1. A regulatory change made it possible for U.S. corporations to engage in commercial banking, investment banking, and insurance. 2. Increased globalization made it desirable for financial institutions to follow their clients and operate in many countries. Changing technology led to increased economies of scale and scope, both of which increase the relative efficiency of huge, diversified companies such as Citigroup. 3. The same forces that are transforming the financial services industry have affected other industries. In particular, the growth of the Internet has provided many companies with increased opportunities, but it has also created additional competition and risk. For example, it has altered the way millions of consumers purchase airline tickets, hotel rooms, books, and automobiles. Consequently, financial managers must understand today's technological environment and be ready to change operations as the environment evolves. The Physical Location Stock Exchanges Physical Location Exchanges Formal organizations having tangible physical locations that conduct auction markets in designated ("listed") securities. The physical location exchanges are tangible physical entities. Each of the larger ones occupies its own building, has a limited number of members, and has an elected governing body--its board of governors. Members are said to have "seats" on the exchange, although everybody stands up. These seats, which are bought and sold, give the holder the right to trade on the exchange. There are currently 1,366 seats on the New York Stock Exchange (this number has remained constant since 1953). In early 2005, a seat on the NYSE sold for $1.0 million, which was considerably lower than the record high of $2.65 million. Seat prices are at multiyear lows due to low trading volume, declines in commissions earned, and recent scandals that have rocked the NYSE. Most of the larger investment banking houses operate brokerage departments, and they own seats on the exchanges and designate one or more of their officers as members. The exchanges are open on all normal working days, with the members meeting in a large room equipped with telephones and other electronic equipment that enable each member to communicate with his or her firm's offices throughout the country. Like other markets, security exchanges facilitate communication between buyers and sellers. For example, Merrill Lynch (the fourth largest brokerage firm) might receive an order in its Atlanta office from a customer who wants to buy shares of GE stock. Simultaneously, the Denver office of Morgan Stanley (the second largest brokerage firm) might receive an order from a customer wishing to sell shares of GE. Each broker communicates electronically with the firm's representative on the NYSE. Other brokers throughout the country are Chapter 5 Financial Markets and Institutions 155 The NYSE and Nasdaq Combine Forces with the Leading Online Trading Systems The forces that spurred consolidation in the financial services industry have also promoted online trading systems that bypass the traditional exchanges. These systems, which are known as electronic communications networks (ECNs), use electronic technology to bring buyers and sellers together. As of early 2005, the majority of these transactions were conducted by two firms: Instinet Group and Archipelago. The rise of ECNs has accelerated the move toward 24-hour trading. Large clients who want to trade after other markets have closed may utilize an ECN, thus bypassing the NYSE and Nasdaq. The move toward faster, cheaper, and continuous trading obviously benefits investors, but it does present regulators, who try to ensure that all investors have access to a "level playing field," with a number of headaches. Recognizing the new threat, the two leading exchanges have not been content to stand idly by. In April 2005, the NYSE announced plans to acquire Archipelago and to turn itself into a public company. If the deal goes through, the new company will be called NYSE Group Inc., and 70 percent of the combined company will be owned by those who currently hold seats on the NYSE. Archipelago shareholders will own the remaining 30 percent. Two days after this stunning announcement, Nasdaq announced its own plans to purchase Instinet. These announced mergers confirm the growing importance of electronic trading and have led many to conclude that the floor traders who buy and sell stock on the NYSE may soon become a thing of the past as an increasing number of transactions take place electronically. Others contend that there will remain a role for these floor traders for at least the foreseeable future. In any event, what is clear is that the financial landscape of stock trading will continue to undergo dramatic changes in the upcoming years. Sources: Katrina Brooker, "Online Investing: It's Not Just for Geeks Anymore," Fortune, December 21, 1998, pp. 8998; "Fidelity, Schwab Part of Deal to Create Nasdaq Challenger," The Milwaukee Journal Sentinel, July 22, 1999, p. 1; Aaron Lucchetti, Susanne Craig, and Dennis K. Berman, "NYSE to Acquire Electronic Trader and Go Public," The Wall Street Journal, April 21, 2005, p. A1; and "Nasdaq Agrees to Buy Instinet for $1.88 Billion," www.wsj.com, Wall Street Online, April 22, 2005. also communicating with their own exchange members. The exchange members with sell orders offer the shares for sale, and they are bid for by the members with buy orders. Thus, the exchanges operate as auction markets.6 6 The NYSE is actually a modified auction market, wherein people (through their brokers) bid for stocks. Originally--about 200 years ago--brokers would literally shout, "I have 100 shares of Erie for sale; how much am I offered?" and then sell to the highest bidder. If a broker had a buy order, he or she would shout, "I want to buy 100 shares of Erie; who'll sell at the best price?" The same general situation still exists, although the exchanges now have members known as specialists who facilitate the trading process by keeping an inventory of shares of the stocks in which they specialize. If a buy order comes in at a time when no sell order arrives, the specialist will sell off some inventory. Similarly, if a sell order comes in, the specialist will buy and add to inventory. The specialist sets a bid price (the price the specialist will pay for the stock) and an asked price (the price at which shares will be sold out of inventory). The bid and asked prices are set at levels designed to keep the inventory in balance. If many buy orders start coming in because of favorable developments or sell orders come in because of unfavorable events, the specialist will raise or lower prices to keep supply and demand in balance. Bid prices are somewhat lower than asked prices, with the difference, or spread, representing the specialist's profit margin. Special facilities are available to help institutional investors such as mutual or pension funds sell large blocks of stock without depressing their prices. In essence, brokerage houses that cater to institutional clients will purchase blocks (defined as 10,000 or more shares) and then resell the stock to other institutions or individuals. Also, when a firm has a major announcement that is likely to cause its stock price to change sharply, it will ask the exchanges to halt trading in its stock until the announcement has been made and digested by investors. 156 Part 2 Fundamental Concepts in Financial Management The Over-the-Counter and the Nasdaq Stock Markets While the stocks of most large companies trade on the NYSE, a larger number of stocks trade off the exchange in what has traditionally been referred to as the over-the-counter (OTC) market. An explanation of the term "over-the-counter" will help clarify how this term arose. As noted earlier, the exchanges operate as auction markets--buy and sell orders come in more or less simultaneously, and exchange members match these orders. If a stock is traded infrequently, perhaps because the firm is new or small, few buy and sell orders come in, and matching them within a reasonable amount of time would be difficult. To avoid this problem, some brokerage firms maintain an inventory of such stocks and stand prepared to make a market for these stocks. These "dealers" buy when individual investors want to sell, and then sell part of their inventory when investors want to buy. At one time, the inventory of securities was kept in a safe, and the stocks, when bought and sold, were literally passed over the counter. Today, these markets are often referred to as dealer markets. A dealer market includes all facilities that are needed to conduct security transactions, but they are not made on the physical location exchanges. These facilities include (1) the relatively few dealers who hold inventories of these securities and who are said to "make a market" in these securities; (2) the thousands of brokers who act as agents in bringing the dealers together with investors; and (3) the computers, terminals, and electronic networks that provide a communication link between dealers and brokers. The dealers who make a market in a particular stock quote the price at which they will pay for the stock (the bid price) and the price at which they will sell shares (the ask price). Each dealer's prices, which are adjusted as supply and demand conditions change, can be read off computer screens all across the world. The bid-ask spread, which is the difference between bid and asked prices, represents the dealer's markup, or profit. The dealer's risk increases if the stock is more volatile, or if the stock trades infrequently. Generally, we would expect volatile, infrequently traded stocks to have wider spreads in order to compensate the dealers for assuming the risk of holding them in inventory. Brokers and dealers who participate in the over-the-counter market are members of a self-regulatory body known as the National Association of Securities Dealers (NASD), which licenses brokers and oversees trading practices. The computerized network used by the NASD is known as the NASD Automated Quotation System (Nasdaq). Nasdaq started as just a quotation system, but it has grown to become an organized securities market with its own listing requirements. Over the past decade the competition between the NYSE and Nasdaq has become increasingly fierce. In an effort to become more competitive with the NYSE and with international markets, the Nasdaq and the AMEX merged in 1998 to form the NasdaqAmex Market Group. The merger turned out to be less than successful, and in early 2005 the AMEX members agreed to buy the exchange back from the NASD. Since most of the larger companies trade on the NYSE, the market capitalization of NYSE-traded stocks is much higher than for stocks traded on Nasdaq ($12.6 trillion compared with $3.7 trillion at year-end 2004). However, reported volume (number of shares traded) is often larger on Nasdaq, and more companies are listed on Nasdaq.7 Interestingly, many high-tech companies such as Microsoft and Intel have remained on Nasdaq even though they easily meet the listing requirements of the NYSE. At the same time, however, other high-tech companies such as Gateway, America Online, and Iomega have left Nasdaq for the NYSE. Despite these defec7 Over-the-Counter (OTC) Market A large collection of brokers and dealers, connected electronically by telephones and computers, that provides for trading in unlisted securities. Dealer Market Includes all facilities that are needed to conduct security transactions not conducted on the physical location exchanges. One transaction on Nasdaq generally shows up as two separate trades (the buy and the sell). This "double counting" makes it difficult to compare the volume between stock markets. Chapter 5 Financial Markets and Institutions 157 tions, Nasdaq's growth over the past decade has been impressive. In the years ahead, competition between Nasdaq and the NYSE will no doubt remain fierce. What are the differences between the physical location exchanges and the Nasdaq stock market? What is the bid-ask spread? 5.5 THE MARKET FOR COMMON STOCK Some companies are so small that their common stocks are not actively traded; they are owned by only a few people, usually the companies' managers. These firms are said to be privately owned, or closely held, corporations, and their stock is called closely held stock. In contrast, the stocks of most larger companies are owned by thousands of investors, most of whom are not active in management. These companies are called publicly owned corporations, and their stock is called publicly held stock. A recent study found that institutional investors owned about 46 percent of all publicly held common stocks. Included are pension plans (26 percent), mutual funds (10 percent), foreign investors (6 percent), insurance companies (3 percent), and brokerage firms (1 percent). These institutions buy and sell relatively actively, however, so they account for about 75 percent of all transactions. Thus, institutional investors have a significant influence on the prices of individual stocks. Closely Held Corporation A corporation that is owned by a few individuals who are typically associated with the firm's management. Publicly Owned Corporation A corporation that is owned by a relatively large number of individuals who are not actively involved in its management. Types of Stock Market Transactions We can classify stock market transactions into three distinct categories: 1. Trading in the outstanding shares of established, publicly owned companies: the secondary market. Allied Food Products, the company we analyzed in Chapters 3 and 4, has 50 million shares of stock outstanding. If the owner of 100 shares sells his or her stock, the trade is said to have occurred in the secondary market. Thus, the market for outstanding shares, or used shares, is the secondary market. The company receives no new money when sales occur in this market. 2. Additional shares sold by established, publicly owned companies: the primary market. If Allied decides to sell (or issue) an additional 1 million shares to raise new equity capital, this transaction is said to occur in the primary market.8 3. Initial public offerings by privately held firms: the IPO market. In the summer of 2004 Google sold shares to the public for the first time at $85 per share. By September 2005, the stock was selling for $303, so it had more than tripled. Several years ago, the Coors Brewing Company, which was owned by the Coors family at the time, decided to sell some stock to raise capital needed for a major expansion program.9 These types of transactions are called Allied has 60 million shares authorized but only 50 million outstanding; thus, it has 10 million authorized but unissued shares. If it had no authorized but unissued shares, management could increase the authorized shares by obtaining stockholders' approval, which would generally be granted without any arguments. 9 The stock Coors offered to the public was designated Class B, and it was nonvoting. The Coors family retained the founders' shares, called Class A stock, which carried full voting privileges. The company was large enough to obtain an NYSE listing, but at that time the Exchange had a requirement that listed common stocks must have full voting rights, which precluded Coors from obtaining an NYSE listing. 8 158 Part 2 Fundamental Concepts in Financial Management Going Public The act of selling stock to the public at large by a closely held corporation or its principal stockholders. Initial Public Offering (IPO) Market The market for stocks of companies that are in the process of going public. going public--whenever stock in a closely held corporation is offered to the public for the first time, the company is said to be going public. The market for stock that is just being offered to the public is called the initial public offering (IPO) market. IPOs have received a lot of attention in recent years, primarily because a number of "hot" issues have realized spectacular gains--often in the first few minutes of trading. Consider the 1999 IPO of Red Hat Inc., the open-source provider of software products and services. The company's underwriters set an offering price of $14 per share. However, because of intense demand for the issue, the stock's price rose more than 270 percent the first day of trading. With the recent stock market decline, we have also seen a decline in the number of new IPOs. Table 5-3 lists the largest, the best performing, and the worst performing IPOs of 2004, and it shows how they performed from their offering dates through year-end 2004. As the table shows, not all IPOs are as well received as Red Hat's. Moreover, even if you are able to identify a "hot" issue, it is often difficult to purchase shares in the initial offering. These deals are generally oversubscribed, which means that the demand for shares at the offering price exceeds the number of shares issued. In such instances, investment bankers favor large institutional investors (who are their best customers), and small investors find it hard, if not impossible, to get in on the ground floor. They can buy the stock in the after-market, but evidence suggests that if you do not get in on the ground floor the average IPO underperforms the overall market over the long run.10 Indeed, the subsequent performance of Red Hat illustrates the risks that arise when investing in new issues. Figure 5-2 plots Red Hat's stock price from the time of its IPO in 1999 to early February 2005. After its dramatic first day run-up, Red Hat's stock closed just above $54 per share. Demand for the stock continued to surge, and the price reached a high of just over $300 in December 1999. Soon afterward, the company announced a two-for-one stock split. (Note that Figure 5-2 considers the stock split.) The split effectively cut the stock's price in half, but it doubled the number of shares held by each shareholder. After adjusting for the split, the stock's price stood at $132 per share in early January 2000. Soon thereafter, Red Hat's price tumbled--indeed, by mid-year 2001 its price was $3.50 per share, which was equivalent to $7.00 per share before the split. As Figure 5-2 shows, Red Hat's stock has slowly rebounded over the past few years, but its price still remains below its initial offering price of $14. Amidst concerns about the allocation of IPO shares, Google Inc.'s highly publicized 2004 IPO attracted attention because of its size (Google raised $1.67 billion in stock) and the way it was conducted. Rather than having the offer price set by its investment bankers, Google conducted a Dutch auction in which individual investors directly placed bids for shares. In a Dutch auction, the actual transaction price is set at the highest price ("the clearing price") that causes all of the offered shares to be sold. Investors who set their bids at or above the clearing price receive all the shares they subscribed to at the offer price. While Google's IPO was in many ways precedent setting, it remains unclear whether other firms going public in the future will be able, or willing, to use the Dutch auction method to allocate shares in their IPOs. It is important to recognize that firms can go public without raising any additional capital. For example, the Ford Motor Company was once owned 10 See Jay R. Ritter, "The Long-Run Performance of Initial Public Offerings," Journal of Finance, Vol. 46, no. 1 (March 1991), pp. 327. Chapter 5 Financial Markets and Institutions 159 TA B L E 5 - 3 Initial Public Offerings in 2004 PERCENT CHANGE FROM OFFER First Day Trading Through 12/31/04 Issuer The Biggest IPOs Genworth Financial Assurant Google Semiconductor Manufacturing Intl. Freescale Semiconductor China Netcom LG Philips Navteq Dex Media Dreamworks Animation Issue Date U.S. Proceeds (Billions) 05/24/04 02/04/04 08/18/04 03/11/04 07/16/04 11/10/04 07/15/04 08/06/04 07/21/04 10/27/04 $2.86 2.02 1.92 1.80 1.69 1.31 1.06 1.01 1.01 0.93 unch. 12.3% 18.0 11.3 7.9 14.1 6.3 15.0 2.6 38.4 38.5% 38.9 126.8 38.5 37.1 22.6 19.9 110.7 31.4 34.0 Issuer The Best Performers Shanda Interactive Ent 51Job Marchex Volterra Semiconductor eCOST.com Cogent Jed Oil Syneron Medical Kinetic Concepts Kanbay International Issue Date Offer Price U.S. Proceeds (Millions) PERCENT CHANGE FROM OFFER First Day Trading Through 12/31/04 05/12/04 09/28/04 03/30/04 07/28/04 08/27/04 09/23/04 04/05/04 08/05/04 02/23/04 07/22/04 $11.00 14.00 6.50 8.00 5.80 12.00 5.50 12.00 30.00 13.00 $169.0 84.5 26.0 36.5 20.1 248.4 10.5 60.0 621.0 106.9 8.8% 51.1 35.4 3.1 3.5 49.8 103.6 10.4 34.7 16.9 286.4% 271.2 223.1 177.0 175.0 175.0 165.5 155.0 154.3 140.8 Issuer The Worst Performers Xcyte Therapies Staktek Holdings AlphaSmart Corgentech Corcept Therapeutics Daystar Technologies Infosonics Linktone Semiconductor Manufacturing International Cherokee International Issue Date Offer Price U.S. Proceeds (Millions) PERCENT CHANGE FROM OFFER First Day Trading Through 12/31/04 03/16/04 02/05/04 02/06/04 02/12/04 04/14/04 02/05/04 06/16/04 03/03/04 03/11/04 02/19/04 $ 8.00 13.00 6.00 16.00 12.00 5.00 6.00 14.00 17.50 14.50 $ 33.6 145.5 26.4 110.4 54.0 10.6 12.0 86.0 1,803.0 110.1 8.6% 14.5 2.0 20.3 1.9 1.0 2.5 24.4 11.3 13.8 65.5% 64.3 50.8 48.3 47.9 43.0 40.3 40.0 38.5 33.7 Source: "Initial Public Offerings of Stock Bounce Back in 2004," The Wall Street Journal, January 3, 2005, p. R10. 160 Part 2 Fundamental Concepts in Financial Management FIGURE 5-2 Red Hat Inc.'s Stock Price Performance from Its IPO to February 2005 Source: finance.yahoo.com. exclusively by the Ford family. When Henry Ford died, he left a substantial part of his stock to the Ford Foundation. When the Foundation later sold some of it to the general public, the Ford Motor Company went public, even though the company itself raised no capital in the transaction. Differentiate between closely held and publicly owned corporations. Differentiate between primary and secondary markets. What is an IPO? What is a Dutch auction? Why is it used? 5.6 STOCK MARKETS AND RETURNS Anyone who has ever invested in the stock market knows that there can be, and generally are, large differences between expected and realized prices and returns. Figure 5-3 shows how total realized portfolio returns have varied from year to year. As logic would suggest (and as we demonstrate in Chapter 8), a stock's expected return as estimated by investors at the margin is always positive, for otherwise investors would not buy the stock. However, as Figure 5-3 shows, in some years actual returns are negative. Stock Market Reporting Up until a couple of years ago, the best source of stock quotations was the business section of a daily newspaper, such as The Wall Street Journal. One problem with newspapers, however, is that they report yesterday's prices. Now it is possible to obtain quotes all during the day from a wide variety of Internet Chapter 5 Financial Markets and Institutions 161 sources.11 One of the best is Yahoo!, and Figure 5-4 shows a detailed quote for GlaxoSmithKline PLC (GSK). As the heading shows, GlaxoSmithKline is traded on the New York Stock Exchange under the symbol GSK. (The NYSE is just one of many world markets on which the stock trades.) The first two rows of information show that GSK last traded at $45.55, and the stock traded thus far during the day from as low as $45.40 and as high as $45.65. (Note that the price is reported in decimals rather than fractions, reflecting a recent change in trading conventions.) The last trade was at 11:05 A.M. ET on February 4, 2005, and its price range during the past 52 weeks was from $38.80 to $47.59. The next three lines show that GSK opened trading on February 4th at $45.42, that it closed on February 3rd at $44.65, and that its price rose by $0.90 (or a 2.02 percent increase) from the previous close to the current price. So far during the day, 401,700 shares had traded hands. GlaxoSmithKline's average daily trading volume (based on the past three months) was 1,349,318 shares, so trading was relatively light that day. The total value of all of GlaxoSmithKline's stock, called its market cap, was $130.09 billion. The last three lines report other market information for GSK. If it were trading on Nasdaq rather than a listed exchange, the most recent bid and ask quotes from dealers would have been shown. However, because it trades on the NYSE, these data are not available. GSK's P/E ratio (price per share divided by the most recent 12 months' earnings) is 17.16, and its earnings per share for the most recent 12 months was $2.66. (Note that ttm stands for "trailing 12 months"--in other words, the most recent 12 months.) The mean of the analysts' one-year target price for GSK is $49.67. GSK's dividend is $1.46 per share, so the quarterly dividend is $0.365 per share, and the dividend yield, which is the annual dividend divided by the price, is 3.24 percent. FIGURE 5-3 S&P 500 Index, Total Returns: Dividend Yield + Capital Gain or Loss, 19682004 Percent 40 30 20 10 0 10 20 30 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 Years Source: Data taken from various issues of The Wall Street Journal, "Investment Scoreboard" section. 11 Most free sources provide quotes that are delayed by 15 minutes. Real time quotes can be obtained for a fee. 162 Part 2 Fundamental Concepts in Financial Management FIGURE 5-4 Stock Quote for GlaxoSmithKline, February 4, 2005 Source: finance.yahoo.com. In Figure 5.4, the chart to the right plots the stock price during the day; however, the links below the chart allow you to pick different time intervals for plotting data. As you can see, Yahoo! provides a great deal of information in its detailed quote, and even more detail is available on the screen page below the basic quote information. Stock Market Returns In Chapters 8 and 9 we will discuss in detail how stock returns are calculated, the connection between stock market risk and returns, and the techniques that analysts use to value stocks. However, it is useful at this point for you to have a rough idea how stocks have performed in recent years. Figure 5-3 shows how the returns on large U.S. stocks have varied over the past years, and the box entitled "Measuring the Market" provides some information on the major U.S. stock market indices and their performances since the mid-1990s. Since 1968 the market trend has been strongly up, but by no means does it go up every year. Indeed, as we can see from Figure 5-3, the overall market has been down in 9 of the 37 years, including the three consecutive years of 20002002. The stocks of individual companies have likewise gone up and down.12 Of course, even in bad years some individual companies do well, so "the name of the game" in security analysis is to pick the winners. Financial managers attempt to put their companies into the winners' column, but they don't always succeed. In subsequent chapters, we will examine the decisions managers make to increase the odds of their firms performing well in the marketplace. Would you expect a portfolio that consisted of the S&P 500 stocks to be more or less risky than a portfolio of Nasdaq stocks? If we constructed a chart like Figure 5-3 for an average S&P 500 stock, do you think it would show more or less volatility? Explain. 12 If we constructed a graph like Figure 5-3 for individual stocks rather than for the index, far greater variability would be shown. Also, if we constructed a graph like Figure 5-3 for bonds, it would have similar ups and downs, but the bars would be smaller, indicating that gains and losses on bonds are generally smaller than those on stocks. Above-average bond returns occur in years when interest rates decline, losses occur when interest rates rise sharply, but interest payments tend to stabilize bonds' total returns. We will discuss bonds in detail in Chapter 7. Chapter 5 Financial Markets and Institutions 163 5.7 STOCK MARKET EFFICIENCY Figure 1-1 (presented back in Chapter 1) suggests that a stock's price is affected by its intrinsic value, which is determined by the true level and riskiness of the cash flows it is likely to provide, and investors' perceptions about the stock's intrinsic value. In a well-functioning market, investors' perceptions should be closely related to the stock's intrinsic value, in which case the stock price would be a reasonably accurate reflection of its true value. A body of theory called the efficient markets hypothesis (EMH) holds (1) that stocks are always in equilibrium and (2) that it is impossible for an investor to consistently "beat the market." Essentially, those who believe in the EMH note that there are 100,000 or so full-time, highly trained, professional analysts and traders operating in the market, while there are fewer than 3,000 major stocks. Therefore, if each analyst followed 30 stocks (which is about right, as analysts tend to specialize in the stocks in a specific industry), there would on average be 1,000 analysts following each stock. Further, these analysts work for organizations such as Goldman Sachs, Merrill Lynch, Citigroup, Prudential, and the like, which have billions of dollars that can be used to take advantage of bargains. In addition, as a result of SEC disclosure requirements and electronic information networks, as new information about a stock becomes available, these 1,000 analysts generally receive and evaluate it at about the same time. Therefore, the price of a stock will adjust almost immediately to any new development. That makes it very difficult for anyone to consistently pick stocks that will beat the market. Efficient Markets Hypothesis (EMH) The hypothesis that securities are typically in equilibrium--that they are fairly priced in the sense that the price reflects all publicly available information on each security. Levels of Market Efficiency If markets are truly efficient, then stock prices will rapidly adjust to all relevant information as it becomes available. This raises an important question: What types of information are available to investors and, therefore, incorporated into stock prices? Financial theorists have discussed three forms, or levels, of market efficiency. Weak-Form Efficiency The weak form of the EMH states that all information contained in past stock price movements is fully reflected in current market prices. If this were true, then information about recent trends in stock prices would be of no use in selecting stocks--the fact that a stock has risen for the past three days, for example, would give us no useful clues as to what it will do today or tomorrow. People who believe that weak-form efficiency exists also believe that "tape watchers" and "chartists" are wasting their time.13 For example, after studying the past history of the stock market, a chartist might "discover" the following pattern: If a stock falls three consecutive days, its price typically rises 10 percent the following day. The technician would then conclude that investors could make money by purchasing a stock whose price has fallen for three consecutive days. But if this pattern truly existed, wouldn't other investors also discover it, and then why would anyone be willing to sell a stock after it had fallen three consecutive days if he or she knows the stock's price would likely increase by 10 percent the next day? In other words, if a stock were selling at $40 per share after falling three consecutive days, why would investors sell the stock at $40 if they expect it to rise to $44 per share the next day? Those who believe in weakform efficiency argue that if the stock were really likely to rise to $44 per share 13 Tape watchers are people who watch the NYSE tape, while chartists plot past patterns of stock price movements. Both are called "technicians," and both believe that they can tell if something is happening to the stock that will cause its price to move up or down in the near future. 164 Part 2 Fundamental Concepts in Financial Management Measuring the Market Stock indexes are designed to show the performance of the stock market. The problem is that there are many stock indexes, and it is difficult to determine which index best reflects market actions. Some are designed to represent the whole equity market, some to track the returns of certain industry sectors, and others to track the returns of small-cap, mid-cap, or large-cap stocks. We discuss below three of the leading indexes. S&P 500 Index Created in 1926, the S&P 500 Index is widely regarded as the standard for measuring large-cap U.S. stock market performance. The stocks in the S&P 500 are selected by the Standard & Poor's Index Committee as being the leading companies in the leading industries, and for accurately reflecting the U.S. stock market. It is value weighted, so the largest companies (in terms of value) have the greatest influence. The S&P 500 Index is used for benchmarking by 97 percent of all U.S. money managers and pension plan sponsors, and approximately $700 billion is managed so as to obtain the same performance as this index (that is, in indexed funds). Dow Jones Industrial Average Unveiled in 1896 by Charles H. Dow, the Dow Jones Industrial Average (DJIA) provided a benchmark for comparing individual stocks with the overall market, for ascertaining the trend in stock prices over time, and for comparing the market with other economic indicators. The industrial average began with just 10 stocks, was expanded in 1916 to 20 stocks, and then to 30 in 1928. Also in 1928, The Wall Street Journal editors began adjusting the index for stock splits, and making substitutions. Today, the DJIA still includes 30 companies. They represent almost a fifth of the market value of all U.S. stocks, and all are both leading companies in their industries and widely held by individual and institutional investors. Visit http://www.dowjones.com to get more information about the DJIA. You can find out how it is calculated, the current divisor, the companies that make up the DJIA, more history about the DJIA, and other interesting facts. In addition, there is a DJIA time line annotated with historical events. Nasdaq Composite Index The Nasdaq Composite Index measures the performance of all common stocks listed on the Nasdaq stock market. Currently, it includes more than 5,000 companies, and because many of the technologysector companies are traded on the computer-based Nasdaq exchange, this index is generally regarded as an economic indicator of the high-tech industry. Microsoft, Intel, and Cisco Systems are the three largest Nasdaq companies, and they comprise a high percentage of the index's value-weighted market capitalization. For this reason, substantial movements in the same direction by these three companies can move the entire index. tomorrow, its price would actually rise to somewhere near $44 per share immediately, thereby eliminating the trading opportunity. Consequently, weak-form efficiency implies that any information that comes from an examination of past stock prices cannot be used to make money by predicting future stock prices. Semistrong-Form Efficiency The semistrong form of the EMH states that current market prices reflect all publicly available information. Therefore, if semistrong-form efficiency exists, it would do no good to pore over annual reports or yesterday's Wall Street Journal looking at sales and earnings trends and various types of ratios based on historical data because market prices would have adjusted to any good or bad news contained in such Chapter 5 Financial Markets and Institutions 165 Recent Performance The accompanying figure plots the value that an investor would now have if he or she had invested $1.00 in each of the three indexes on January 1, 1995. The returns on the three indexes are compared with an investment strategy that only invests in T-bills. For the returns on T-bills, the one-year Treasury constant maturity rate is used. Over the past 10 years, each of these indexes performed quite well through 1999. However, for a couple years each index stumbled before begin- ning to rebound again in 2003. During the last 10 years the average annualized returns of these indexes ranged from 9.8 percent for the S&P 500 to 10.5 percent for the Nasdaq Composite Index. The Nasdaq experienced a huge bubble in 1999, reflecting overly optimistic valuations of technology companies. However, in 2000 the bubble burst and technology stock valuations spiraled downward, causing the Nasdaq Index to revert back to a level comparable to the S&P 500 and Dow Jones Industrial Average Index. Growth of a $1 Investment Made on January 1, 1995 Value of $1 Investment 7 Nasdaq 6 5 4 3 2 1 0 1995 DJIA S&P 500 T-bills 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Years reports back when the news first came out over the Internet. With semistrongform efficiency, investors should not expect to earn above-average returns except with good luck or information that is not publicly available.14 However, insiders (for example, CEOs and CFOs) who have information that is not publicly available are able to earn above-average returns even under semistrong-form efficiency. Another implication of semistrong-form efficiency is that whenever information is released to the public, stock prices will respond only if the information is different from what had been expected. If, for example, a company announces a 14 Strictly speaking, these returns should be adjusted for risk. We discuss the relationship between risk and return in Chapter 8. 166 Part 2 Fundamental Concepts in Financial Management 30 percent increase in earnings, and if that increase is about what analysts had been expecting, the announcement should have little or no effect on the company's stock price. On the other hand, the stock price would probably fall if analysts had expected earnings to increase by 50 percent, but it probably would rise if they had expected a 10 percent increase. Strong-Form Efficiency The strong form of the EMH states that current market prices reflect all pertinent information, whether publicly available or privately held. If this form holds, even insiders would find it impossible to earn abnormally high returns in the stock market.15 Many empirical studies have been conducted to test for the three forms of market efficiency. Most of these studies suggest that the stock market is indeed highly efficient in the weak form, reasonably efficient in the semistrong form (at least for the larger and more widely followed stocks), but not true for the strong form because abnormally large profits are often earned by those with inside information. Implications of Market Efficiency If the EMH were correct, it would be a waste of time for most of us to seek bargains by analyzing stocks. That follows because, if stock prices already reflect all publicly available information and hence are fairly priced, we can "beat the market" only by luck or with inside information, making it difficult, if not impossible, for most investors to consistently outperform the market averages. To support this viewpoint, efficient market proponents often point out that even the professionals who manage mutual fund portfolios do not, on average, outperform the overall stock market as measured by an index like the S&P 500.16 Indeed, the relatively poor performance of actively managed mutual funds helps explain the growing popularity of indexed funds, where administrative costs are relatively low. Rather than spending time and money trying to find undervalued stocks, index funds try instead to match overall market returns by buying the basket of stocks that makes up a particular index, such as the S&P 500.17 15 Over the years, several cases of illegal insider trading have made the news headlines. These cases involved employees of several major investment banking houses and even an employee of the SEC. In the most famous case, Ivan Boesky admitted to making $50 million by purchasing stocks of firms he knew were about to merge. He went to jail, and he had to pay a large fine, but he helped disprove the strong-form EMH. More recently, Martha Stewart was imprisoned after being convicted on obstruction of justice charges surrounding a federal investigation of insider trading of ImClone Systems Inc. shares. 16 For a discussion of the recent performance of actively managed funds, see Jonathan Clements, "Resisting the Lure of Managed Funds," The Wall Street Journal, February 27, 2001, p. C1. 17 We should also note that some Wall Street pros have consistently beaten the market over many years, which is inconsistent with the EMH. An interesting article in the April 3, 1995, issue of Fortune (Terence P. Par, "Yes, You Can Beat the Market") argued strongly against the EMH. Par suggested that each stock has a fundamental value, but when good or bad news about it is announced, most investors fail to interpret this news correctly. As a result, stocks are generally priced above or below their long-term values. Think of Figure 1-1, which was illustrated in Chapter 1, with stock price on the vertical axis and years on the horizontal axis. A stock's fundamental value might be moving up steadily over time as it retains and reinvests earnings. However, its actual price might fluctuate about the intrinsic value line, overreacting to good or bad news and indicating departures from equilibrium. Successful value investors, according to Par, use fundamental analysis to identify stocks' intrinsic values, and then they buy stocks that are undervalued and sell those that are overvalued. Par's argument implies that stocks are at times systematically out of equilibrium and that investors can act on this knowledge to beat the market. That position may turn out to be correct, but it may also be that the superior performance Par noted simply demonstrates that some people are better at obtaining and interpreting information than others, or have been lucky in the past. Chapter 5 Financial Markets and Institutions 167 It is important to understand that market efficiency does not imply that all stocks are always priced correctly. With hindsight, it is apparent that at any point in time the situation shown in Figure 1-1 back in Chapter 1 tends to hold true, with some stocks overvalued and others undervalued. However, as the efficient markets hypothesis implies, it is hard to identify ahead of time the stocks in each category. To beat the market, you must have above-average information, above-average analytical skills, or above-average luck. Finally, it is important to understand that even if markets are efficient and all stocks are fairly priced, an investor should still be careful when selecting stocks for his or her portfolio. To earn the greatest expected return with the least amount of risk, the portfolio should be diversified, with a mix of stocks from various industries. We will discuss diversification in greater detail in Chapter 8. Is the Stock Market Efficient? During the past 25 years, many empirical studies have been conducted to test the validity of the three forms of market efficiency. Until 10 years ago, most of these studies suggested that the stock market was highly efficient in the weak form and reasonably efficient in the semistrong form, at least for the larger and more widely followed stocks. However, the evidence also suggested that the strong form EMH did not hold, because those who possessed inside information could and did (illegally) make abnormal profits. More recently, the empirical support for the EMH has been somewhat diminished. As we indicate in the behavioral finance box, skeptics point to the recent stock market bubble and suggest that at the height of the boom the prices of the stocks of many companies, particularly in the technology sector, vastly exceeded their intrinsic values. These skeptics suggest that investors are not simply machines that rationally process all available information--rather, a variety of psychological and perhaps irrational factors also come into play. Indeed, researchers have begun to incorporate elements of cognitive psychology in an effort to better understand how individuals and entire markets respond to different circumstances.18 Keep in mind that the EMH does not assume that all investors are rational. Rather, it assumes that whenever stock prices deviate from their intrinsic values due to the availability of new information, investors will quickly take advantage of these mispricings by buying undervalued stocks and selling overvalued stocks. Thus, investors' actions work to drive prices to their equilibrium level. Critics of the EMH stress, however, that the stock market is inherently risky and that rational investors trading in an irrational market can lose a lot of money even if they are ultimately proven to be correct. For example, a "rational" investor in mid-1999 might have concluded that the Nasdaq was overvalued when it was trading at 3,000. If that investor had acted on that assumption, he or she would have lost a lot of money the following year when the Nasdaq soared to over 5,000 as "irrational exuberance" pushed the prices of already overvalued stocks to even higher levels. Ultimately, if our "rational investor" had the courage and patience to hold on, he or she would have been vindicated, because the Nasdaq subsequently fell to about 1,300. 18 Behavioral Finance Incorporates elements of cognitive psychology into finance in an effort to better understand how individuals and entire markets respond to different circumstances. Three noteworthy sources for students interested in behavioral finance are Richard H. Thaler, Editor, Advances in Behavioral Finance (New York: Russell Sage Foundation, 1993); Andrei Shleifer, Inefficient Markets: An Introduction to Behavioral Finance (New York: Oxford University Press, 2000); and Nicholas Barberis and Richard Thaler, "A Survey of Behavioral Finance," Chapter 18, Handbook of the Economics of Finance, edited by George Constantinides, Milt Harris, and Ren Stulz, part of the Handbooks in Economics Series (New York: Elsevier/North-Holland, 2003). Students interested in learning more about the efficient markets hypothesis should consult Burton G. Malkiel, A Random Walk Down Wall Street (New York: W.W. Norton & Company, 1999). 168 Part 2 Fundamental Concepts in Financial Management A Closer Look at Behavioral Finance Theory The efficient markets hypothesis (EMH) remains one of the cornerstones of modern finance theory. It implies that, on average, assets trade at prices equal to their intrinsic values. As we note in the text, the logic behind the EMH is straightforward. If a stock's price is "too low," rational traders will quickly take advantage of this opportunity and will buy the stock. Their actions will quickly push prices back to their equilibrium level. Likewise, if prices are "too high," rational traders will sell the stock, pushing the price down to its equilibrium level. Proponents of the EMH argue that prices cannot be systematically wrong unless you believe that market participants are unable or unwilling to take advantage of profitable trading opportunities. While the logic behind the EMH is compelling, many events in the real world seem to be inconsistent with the EMH. This has spurred a growing field that is called behavioral finance theory. Rather than assuming that investors are rational, behavioral finance theorists borrow insights from psychology to better understand how irrational behavior can be sustained over time. Pioneers in this field include psychologists Daniel Kahneman and Amos Tversky and Richard Thaler, who is a professor of finance at the University of Chicago. Their work has encouraged a growing number of scholars to work in this promising area of research. Professor Thaler and his colleague, Nicholas Barberis, have summarized much of this research in a recent article, which is cited below. They argue that behavioral finance theory's criticism of the EMH rests on two important building blocks. First, it is often difficult or risky for traders to take advantage of mispriced assets. For example, even if you know that a stock's price is too low because investors have overreacted to recent bad news, a trader with limited capital may be reluctant to buy the stock for fear that the same forces that pushed the price down may work to keep it artificially low for a long period of time. On the other side, during the recent stock market bubble, many traders who believed (correctly!) that stock prices were too high lost a lot of money selling stocks in the early stages of the bubble because stock prices went even higher before they eventually collapsed. While the first building block explains why mispricings may persist, the second tries to understand how mispricings can occur in the first place. This component is where the insights from psychology come into play. For example, Kahneman and Tversky suggested that individuals view potential losses and potential gains very differently. If you ask an average person whether he or she would rather have $500 with certainty or flip a fair coin and receive $1,000 if a head comes up and nothing if it comes out tails, most would prefer the certain $500, which suggests an aversion to risk. However, if you ask the same person whether he or she would rather pay $500 with certainty or flip a coin and pay $1,000 if it's heads and nothing if it's tails, most indicate that they would prefer to flip the coin. Other studies suggest that people's willingness to take a gamble depends on recent performance. Gamblers who are ahead tend to take on more risks, whereas those who are behind tend to become more conservative. These experiments suggest that investors and managers behave differently in down markets than they do in up markets, which might explain why those who made money early in the stock market bubble continued to keep investing in these stocks, even as their prices went higher. Other evidence suggests that individuals tend to overestimate their true abilities. For example, a large majority (upward of 90 percent in some studies) of us believe that we have aboveaverage driving ability or above-average ability to get along with others. Barberis and Thaler point out that: Overconfidence may in part stem from two other biases, self-attribution bias and hindsight bias. Self-attribution bias refers to people's tendency to ascribe any success they have in some activity to their own talents, while blaming failure on bad luck, rather than on their ineptitude. Doing this repeatedly will lead people to the pleasing but erroneous conclusion that they are very talented. For example, investors might become overconfident after several quarters of investing success [Gervais and Odean (2001)]. Hindsight bias is the tendency of people to believe, after an event has occurred, that they predicted it before it happened. If people think they predicted the past better than they actually did, they may also believe that they can predict the future better than they actually can. Recent research by Ulrike Malmendier of the Stanford Graduate School of Business and Geoffrey Tate of the Wharton School suggests that overconfidence leads managers to overestimate their ability and the quality of their projects. This result may explain why so many corporate projects fail to live up to their stated expectations. Sources: Nicholas Barberis and Richard Thaler, "A Survey of Behavioral Finance," Chapter 18, Handbook of the Economics of Finance, edited by George Constantinides, Milt Harris, and Ren Stulz, part of the Handbooks in Economics Series (New York: Elsevier/North-Holland, 2003); and Ulrike Malmendier and Geoffrey Tate, "CEO Overconfidence and Corporate Investment," Stanford Graduate School of Business Research Paper #1799, June 2004. Chapter 5 Financial Markets and Institutions 169 The events of recent years, and the new ideas developed by researchers in behavioral finance, suggest that the stock market is not always efficient. Still, the logic behind the EMH is compelling, and most researchers believe that markets are generally efficient in the long run. What is the efficient markets hypothesis (EMH)? What are the differences among the three forms of the EMH: (1) weak form, (2) semistrong form, and (3) strong form? What are the implications of the EMH for financial decisions? What is behavioral finance? What do the new ideas in this area tell us about the stock market? Tying It All Together In this chapter we provided a brief overview of how capital is allocated and the financial markets, instruments, and institutions used in the allocation process. We discussed physical location exchanges and electronic markets for common stocks, stock price reporting, and stock indexes. We demonstrated that security prices are volatile--investors expect to make money, and over time they generally do, but losses can be large in any given year. Finally, we discussed the efficiency of the stock market and developments in behavioral finance. After reading this chapter, you should have a general understanding of the financial environment in which businesses and individuals operate, realize that actual returns are often different from expected returns, and be able to read stock market quotations from either business newspapers or various Internet sites. You should also recognize that the theory of financial markets is a "work in progress," and countless work remains to be done. SELF-TEST QUESTIONS AND PROBLEMS ST-1 Key terms Define each of the following terms: a. Spot markets; futures markets b. Money markets; capital markets c. Primary markets; secondary markets d. Private markets; public markets e. Derivatives f. Investment banking house; commercial banks; financial services corporations g. Mutual funds; money market funds h. Physical location exchanges; over-the-counter market (OTC); dealer market i. Closely held corporation; publicly owned corporation j. Going public; initial public offering (IPO) market k. Efficient markets hypothesis (EMH) l. Behavioral finance 170 Part 2 Fundamental Concepts in Financial Management QUESTIONS 5-1 5-2 5-3 5-4 How does a cost-efficient capital market help to reduce the prices of goods and services? Describe the different ways in which capital can be transferred from suppliers of capital to those who are demanding capital. Is an initial public offering an example of a primary or a secondary market transaction? Indicate whether the following instruments are examples of money market or capital market transactions. a. U.S. Treasury bills b. Long-term corporate bonds c. Common stocks d. Preferred stocks e. Dealer commercial paper What would happen to the U.S. standard of living if people lost faith in the safety of our financial institutions? Why? What types of changes have financial markets experienced during the last two decades? Have they been perceived as positive or negative changes? Explain. Differentiate between dealer markets and stock markets that have a physical location. Identify and briefly compare the two leading stock exchanges in the United States today. Describe the three different forms of market efficiency. Investors expect a company to announce a 10 percent increase in earnings, but instead the company announces a 1 percent increase. If the market is semistrong-form efficient, which of the following would you expect to happen? a. The stock's price increases slightly because the company had a slight increase in earnings. b. The stock's price falls because the earnings increase was less than expected. c. The stock's price stays the same because earnings announcements have no effect if the market is semistrong-form efficient. Explain whether the following statements are true or false. a. Derivative transactions are designed to increase risk and are used almost exclusively by speculators who are looking to capture high returns. b. Hedge funds generally charge higher fees than mutual funds. c. Hedge funds have traditionally been highly regulated. d. The New York Stock Exchange is an example of a stock exchange that has a physical location. e. A larger bid-ask spread means that the dealer will realize a lower profit. f. The efficient market hypothesis assumes that all investors are rational. 5-5 5-6 5-7 5-8 5-9 5-10 5-11 Integrated Case Smyth Barry & Company, Part I 5-1 Financial markets and institutions Assume that you recently graduated with a degree in finance and have just reported to work as an investment advisor at the brokerage firm of Smyth Barry & Co. Your first assignment is to explain the nature of the U.S. financial markets to Michelle Varga, a professional tennis player who has just come to the United States from Mexico. Varga is a highly ranked tennis player who expects to invest substantial amounts of money through Smyth Barry. She is also very bright, and, therefore, she would like to understand in general terms what will happen to her money. Your boss has developed the following set of questions that you must ask and answer to explain the U.S. financial system to Varga. Chapter 5 Financial Markets and Institutions 171 a. b. c. d. e. f. g. h. i. j. Describe the three primary ways in which capital is transferred between savers and borrowers. What is a market? Differentiate between the following types of markets: physical asset versus financial markets, spot versus futures markets, money versus capital markets, primary versus secondary markets, and public versus private markets. Why are financial markets essential for a healthy economy and economic growth? What are derivatives? How can derivatives be used to reduce risk? Can derivatives be used to increase risk? Briefly describe each of the following financial institutions: commercial banks, investment banks, mutual funds, and hedge funds. What are the two leading stock markets? Describe the two basic types of stock markets. If Apple Computer decided to issue additional common stock, and Varga puchased 100 shares of this stock from Smyth Barry, the underwriter, would this transaction be a primary or a secondary market transaction? Would it make a difference if Varga purchased previously outstanding Apple stock in the dealer market? Explain. What is an initial public offering (IPO)? What is the efficient markets hypothesis (EMH), what are its three forms, and what are its implications? After the consultation with Michelle she asked you a few final questions: (1) While in the waiting room of your office, she overheard an analyst on a financial TV network say that a particular medical research company just received FDA approval for one of its products. On the basis of this "hot" information, Michelle wants to buy a lot of that company's stock. Assuming the stock market is semistrong-form efficient, what advice would you give her? (2) She has read a number of newspaper articles about a huge IPO being carried out by a leading technology company. She wants to get as many shares in the IPO as possible, and would even be willing to buy the shares in the open market right after the issue. What advice do you have for her? Please go to the ThomsonNOW Web site to access the Cyberproblems. FINANCIAL ASSETS P A R T 3 6 7 8 9 Interest Rates Bonds and Their Valuation Risk and Rates of Return Stocks and Their Valuation C H APTE R MATT MENDELSOHN/CORBIS 6 INTEREST RATES Low Interest Rates Encourage Investment and Stimulate Consumer Spending The U.S. economy has performed well since the early 1990s. Economic growth has been positive, unemployment fairly low, and inflation under control. One reason for the economy's steady performance has been the low level of interest rates over that period, especially the last few years. Since early 2001, the 10-year Treasury bond rate has generally been at or below 5 percent, a level not seen since the 1960s. Low interest rates reduced the cost of capital for businesses, which has encouraged corporate investment, and they also stimulated consumer spending and the housing market. In the 1980s, 30-year fixed-rate mortgages cost 8 percent or more. At 8 percent, a homeowner who could afford a $1,000 monthly payment for 30 years could borrow $136,283. More recently, with mortgage rates at about 5.5 percent, the same homebuyer could handle a $176,122 loan and thus a lot more house. Or, if this individual borrowed the same $136,283, the monthly payment would decline from $1,000 to $773.80, leaving more funds available for other purchases. The drop in interest rates also led to a surge in mortgage refinancings, where high-rate loans are replaced with lowerrate and possibly larger loans, freeing up money for whatever the borrower chooses to spend it on. The drop in interest rates was due to a number of factors--low inflation, foreign investors' purchases of U.S. securities (which drove their rates down), and effective management of the economy by the Federal Reserve and other government policy makers. While there are reasons for continued optimism, there are also reasons to think that low interest rates may not persist for much longer. Higher oil prices and a weakening dollar could lead to higher inflation, which, in turn, would push up interest rates. Likewise, the growing federal budget deficit and the weakening dollar could cause foreigners to sell U.S. bonds, which would also put upward pressure on rates. Because corporate treasurers--and individuals--are greatly affected by interest rates, this chapter takes a closer look at the major factors that determine rates in the market. Chapter 6 Interest Rates 175 Putting Things In Perspective Companies raise capital in two main forms: debt and equity. In a free economy, capital, like other items, is allocated through a market system, where funds are transferred and prices are established. The interest rate is the price lenders receive and borrowers pay for debt capital. Similarly, equity investors expect to receive dividends and capital gains, the sum of which represents the cost of equity. We will take up the cost of equity in later chapters, but our focus in this chapter is on the cost of debt. We begin by examining the factors that affect the supply of and demand for all investment capital, which, in turn, affects the overall cost of money. We will see that there is no one single interest rate--interest rates on different loans vary depending on the risk of the borrower, the use of the funds borrowed, the type of collateral used to back the loan, and the length of time the money is needed. In this chapter we concentrate mainly on how these various factors affect the cost of debt for individuals, but in later chapters we delve into the firm's cost of debt and its role in investment decisions. As you will see in Chapter 7, the cost of debt is a key determinant of bond prices, and it is also an important component of the cost of corporate capital, which we take up in Chapter 10. 6.1 THE COST OF MONEY The four most fundamental factors affecting the cost of money are (1) production opportunities, (2) time preferences for consumption, (3) risk, and (4) inflation. To see how these factors operate, visualize an isolated island community where the people live on fish. They have a stock of fishing gear that permits them to survive reasonably well, but they would like to have more fish. Now suppose Mr. Crusoe had a bright idea for a new type of fishnet that would enable him to double his daily catch. However, it would take a year to perfect the design, build the net, and learn to use it efficiently, and Mr. Crusoe would probably starve before he could put his new net into operation. Therefore, he might suggest to Ms. Robinson, Mr. Friday, and several others that if they would give him one fish each day for a year, he would return two fish a day during all of the next year. If someone accepted the offer, then the fish that Ms. Robinson or one of the others gave to Mr. Crusoe would constitute savings; these savings would be invested in the fishnet; and the extra fish the net produced would constitute a return on the investment. Obviously, the more productive Mr. Crusoe thought the new fishnet would be, the more he could afford to offer potential investors for their savings. In this example, we assume that Mr. Crusoe thought he would be able to pay, and thus he offered, a 100 percent rate of return--he offered to give back two fish for every one he received. He might have tried to attract savings for less--for example, he might have offered only 1.5 fish per day next year for every one he received this year, which would represent a 50 percent rate of return to Ms. Robinson and the other potential savers. Production Opportunities The investment opportunities in productive (cashgenerating) assets. Time Preferences for Consumption The preferences of consumers for current consumption as opposed to saving for future consumption. Risk In a financial market context, the chance that an investment will provide a low or negative return. Inflation The amount by which prices increase over time. 176 Part 3 Financial Assets How attractive Mr. Crusoe's offer appeared to a potential saver would depend in large part on the saver's time preference for consumption. For example, Ms. Robinson might be thinking of retirement, and she might be willing to trade fish today for fish in the future on a one-for-one basis. On the other hand, Mr. Friday might have a wife and several young children and need his current fish, so he might be unwilling to "lend" a fish today for anything less than three fish next year. Mr. Friday would be said to have a high time preference for current consumption and Ms. Robinson a low time preference. Note also that if the entire population were living right at the subsistence level, time preferences for current consumption would necessarily be high, aggregate savings would be low, interest rates would be high, and capital formation would be difficult. The risk inherent in the fishnet project, and thus in Mr. Crusoe's ability to repay the loan, also affects the return investors require: the higher the perceived risk, the higher the required rate of return. Also, in a more complex society, there are many businesses like Mr. Crusoe's, many goods other than fish, and many savers like Ms. Robinson and Mr. Friday. Therefore, people use money as a medium of exchange rather than barter with fish. When money is used, its value in the future, which is affected by inflation, comes into play: the higher the expected rate of inflation, the larger the required dollar return. We discuss this point in detail later in the chapter. Thus, we see that the interest rate paid to savers depends (1) on the rate of return producers expect to earn on invested capital, (2) on savers' time preferences for current versus future consumption, (3) on the riskiness of the loan, and (4) on the expected future rate of inflation. Producers' expected returns on their business investments set an upper limit to how much they can pay for savings, while consumers' time preferences for consumption establish how much consumption they are willing to defer, hence how much they will save at different interest rates.1 Higher risk and higher inflation also lead to higher interest rates. What is the price paid to borrow debt capital called? What are the two items whose sum is the cost of equity? What four fundamental factors affect the cost of money? 6.2 INTEREST RATE LEVELS Borrowers bid for the available supply of debt capital using interest rates: The firms with the most profitable investment opportunities are willing and able to pay the most for capital, so they tend to attract it away from inefficient firms and firms whose products are not in demand. Of course, our economy is not completely free in the sense of being influenced only by market forces. For example, the federal government has agencies that help designated individuals or groups obtain credit on favorable terms. Among those eligible for this kind of assistance are small businesses, certain minorities, and firms willing to build plants in areas with high unemployment. Still, most capital in the United States is allocated through the price system, where interest is the price. 1 The term "producers" is really too narrow. A better word might be "borrowers," which would include corporations, home purchasers, people borrowing to go to college, or even people borrowing to buy autos or to pay for vacations. Also, the wealth of a society and its demographics influence its people's ability to save and thus their time preferences for current versus future consumption. Chapter 6 Interest Rates 177 FIGURE 6-1 Interest Rates as a Function of Supply and Demand for Funds Market B: High-Risk Securities Interest Rate, r (%) S1 S1 rB = 9 Market A: Low-Risk Securities Interest Rate, r (%) rA = 7 5 D1 D1 D2 0 Dollars 0 Dollars Figure 6-1 shows how supply and demand interact to determine interest rates in two capital markets. Markets A and B represent two of the many capital markets in existence. The going interest rate, designated as r, is initially 7 percent for the low-risk securities in Market A. Borrowers whose credit is strong enough to participate in this market can obtain funds at a cost of 7 percent, and investors who want to put their money to work without much risk can obtain a 7 percent return. Riskier borrowers must obtain higher-cost funds in Market B, where investors who are more willing to take risks expect to earn a 9 percent return but also realize that they might actually receive much less. If the demand for funds declines, as it typically does during business recessions, the demand curves will shift to the left, as shown in curve D2 in Market A. The market-clearing, or equilibrium, interest rate in this example declines to 5 percent. Similarly, you should be able to visualize what would happen if the Federal Reserve tightened credit: The supply curve, S1, would shift to the left, and this would raise interest rates and lower the amount of borrowing in the economy. Capital markets are interdependent. For example, if Markets A and B were in equilibrium before the demand shift to D2 in Market A, then investors were willing to accept the higher risk in Market B in exchange for a risk premium of 9% 7% 2%. After the shift to D2, the risk premium would initially increase to 9% 5% 4%. Immediately, though, this much larger premium would induce some of the lenders in Market A to shift to Market B, which would, in turn, cause the supply curve in Market A to shift to the left (or up) and that in Market B to shift to the right. The transfer of capital between markets would raise the interest rate in Market A and lower it in Market B, thus bringing the risk premium back closer to the original 2 percent. There are many capital markets in the United States. U.S. firms also invest and raise capital throughout the world, and foreigners both borrow and lend in the United States. There are markets for home loans; farm loans; business loans; federal, state, and local government loans; and consumer loans. Within each category, there are regional markets as well as different types of submarkets. For example, in real estate there are separate markets for first and second mortgages 178 Part 3 Financial Assets and for loans on single-family homes, apartments, office buildings, shopping centers, vacant land, and so on. Within the business sector there are dozens of types of debt securities, and there are also several different markets for common stocks. There is a price for each type of capital, and these prices change over time as supply and demand conditions change. Figure 6-2 shows how long- and shortterm interest rates to business borrowers have varied since the early 1970s. Notice that short-term interest rates are especially volatile, rising rapidly during booms and falling equally rapidly during recessions. (The shaded areas of the chart indicate recessions.) When the economy is expanding, firms need capital, and this demand for capital pushes up rates. Also, inflationary pressures are strongest during business booms, and that also exerts upward pressure on rates. Conditions are reversed during recessions. Slack business reduces the demand for credit, the rate of inflation falls, and interest rates drop. Furthermore, the Federal Reserve tends to increase the supply of funds during recessions to help stimulate the economy, and that also lowers rates. These tendencies do not hold exactly, as demonstrated in the period after 1984. Oil prices fell dramatically in 1985 and 1986, reducing inflationary pressures on other prices and easing fears of serious long-term inflation. Earlier, these fears had pushed interest rates to record levels. The economy from 1984 to 1987 was strong, but the declining fears of inflation more than offset the normal FIGURE 6-2 Interest Rate (%) 18 16 14 12 10 8 6 4 2 0 Long- and Short-Term Interest Rates, 19712005 18 16 14 12 Long-Term Rates 10 8 Short-Term Rates 6 4 2 0 2001 2003 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 Notes: a. The shaded areas designate business recessions. b. Short-term rates are measured by 3- to 6-month loans to very large, strong corporations, and long-term rates are measured by AAA corporate bonds. Source: St. Louis Federal Reserve Web site, FRED database, http://research.stlouisfed.org/fred2. Chapter 6 Interest Rates 179 FIGURE 6-3 Percent 16 14 12 10 8 6 4 2 0 Relationship between Annual Inflation Rates and Long-Term Interest Rates, 19712005 16 14 Long-Term Interest Rates 12 10 8 Inflation 6 4 2 0 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 Notes: a. Interest rates are those on AAA long-term corporate bonds. b. Inflation is measured as the annual rate of change in the Consumer Price Index (CPI). Source: St. Louis Federal Reserve Web site, FRED database, http://research.stlouisfed.org/fred2. tendency for interest rates to rise during good economic times, and the net result was lower interest rates.2 The relationship between inflation and long-term interest rates is highlighted in Figure 6-3, which plots inflation over time along with long-term interest rates. In the early 1960s, inflation averaged 1 percent per year, and interest rates on high-quality, long-term bonds averaged 4 percent. Then the Vietnam War heated up, leading to an increase in inflation, and interest rates began an upward climb. When the war ended in the early 1970s, inflation dipped a bit, but then the 1973 Arab oil embargo led to rising oil prices, much higher inflation rates, and sharply higher interest rates. Inflation peaked at about 13 percent in 1980, but interest rates continued to increase into 1981 and 1982, and they remained quite high until 1985, because people feared another increase in inflation. Thus, the "inflationary psychology" created during the 1970s persisted until the mid-1980s. People gradually realized that the Federal Reserve was serious about keeping inflation down, that global competition was keeping U.S. auto producers and other corporations from raising prices as they had in the past, and that constraints on corporate price increases were diminishing labor unions' ability to push through cost-increasing wage hikes. As these realizations set in, interest rates declined. 2 Short-term rates are responsive to current economic conditions, whereas long-term rates primarily reflect long-run expectations for inflation. As a result, short-term rates are sometimes above and sometimes below long-term rates. The relationship between long-term and short-term rates is called the term structure of interest rates, and it is discussed later in this chapter. 180 Part 3 Financial Assets The current interest rate minus the current inflation rate (which is also the gap between the inflation bars and the interest rate curve in Figure 6-3) is defined as the "current real rate of interest." It is called a "real rate" because it shows how much investors really earned after taking out the effects of inflation. The real rate was extremely high during the mid-1980s, but it has generally been in the range of 3 to 4 percent since 1987. In recent years inflation has been about 2.5 percent a year. However, longterm interest rates have been volatile because investors are not sure if inflation is truly under control or is about to jump back to the higher levels of the 1980s. In the years ahead, we can be sure of two things: (1) interest rates will vary, and (2) they will increase if inflation appears to be headed higher and decrease if inflation is expected to decline. We really don't know where interest rates will go, but we do know that they will vary. What role do interest rates play in allocating capital to different potential borrowers? What happens to market-clearing, or equilibrium, interest rates in a capital market when the demand for funds declines? What happens when expected inflation increases or decreases? How does the price of capital tend to change during a boom or a recession? How does risk affect interest rates? If inflation during the last 12 months was 2 percent and the interest rate during that period was 5 percent, what was the real rate of interest? If inflation is expected to average 4 percent during the next year and the real rate is 3 percent, what should the current rate of interest be? (3%; 7%) 6.3 THE DETERMINANTS OF MARKET INTEREST RATES In general, the quoted (or nominal) interest rate on a debt security, r, is composed of a real risk-free rate of interest, r*, plus several premiums that reflect inflation, the security's risk, and its marketability (or liquidity). This relationship can be expressed as follows: Quoted interest rate Here r r* r r* IP DRP LP MRP (6-1) the quoted, or nominal, rate of interest on a given security.3 the real risk-free rate of interest. r* is pronounced "r-star," and it is the rate that would exist on a riskless security in a world with no inflation. 3 The term nominal as it is used here means the stated rate as opposed to the real rate, which is adjusted to remove inflation's effects. If you had bought a 10-year Treasury bond in February 2005, the quoted, or nominal, rate would have been about 4.2 percent, but if inflation averages 2.5 percent over the next 10 years, the real rate would turn out to be about 4.2% 2.5% 1.7%. Also, note that in later chapters, when we discuss both debt and equity, we use the subscripts d and s to designate returns on debt and stock, that is, rd and rs. Chapter 6 Interest Rates 181 rRF IP DRP LP MRP r* IP, and it is the quoted rate on a risk-free security such as a U.S. Treasury bill, which is both very liquid and also free of most types of risk. Note that a premium for expected inflation, IP, is built into rRF. inflation premium. IP is equal to the average expected inflation rate over the life of the security. The expected future inflation rate is not necessarily equal to the current inflation rate, so IP is not necessarily equal to current inflation, as shown back in Figure 6-3. default risk premium. This premium reflects the possibility that the issuer will not pay interest or principal at the stated time and in the stated amount. DRP is zero for U.S. Treasury securities, but it rises as the riskiness of the issuer increases. liquidity (or marketability) premium. This is a premium charged by lenders to reflect the fact that some securities cannot be converted to cash on short notice at a "reasonable" price. LP is very low for Treasury securities and for securities issued by large, strong firms, but it is relatively high on securities issued by small, privately held firms. maturity risk premium. As we will explain later, longer-term bonds, even Treasury bonds, are exposed to a significant risk of price declines due to increases in inflation and interest rates, and a maturity risk premium is charged by lenders to reflect this risk. r* IP, we can rewrite Equation 6-1 as follows: Because rRF Nominal, or quoted, rate r rRF DRP LP MRP We discuss the components whose sum makes up the quoted, or nominal, rate on a given security in the following sections. The Real Risk-Free Rate of Interest, r* The real risk-free rate of interest, r*, is the interest rate that would exist on a riskless security if no inflation were expected, and it may be thought of as the rate of interest on short-term U.S. Treasury securities in an inflation-free world. The real risk-free rate is not static--it changes over time depending on economic conditions, especially (1) on the rate of return corporations and other borrowers expect to earn on productive assets and (2) on people's time preferences for current versus future consumption. Borrowers' expected returns on real asset investments set an upper limit on how much they can afford to pay for borrowed funds, while savers' time preferences for consumption establish how much consumption they are willing to defer, hence the amount of funds they will lend at different interest rates. It is difficult to measure the real risk-free rate precisely, but most experts think that r* has fluctuated in the range of 1 to 5 percent in recent years.4 The best estimate of r* is the rate of return on indexed Treasury bonds, which are discussed in a box later in the chapter. Real Risk-Free Rate of Interest, r* The rate of interest that would exist on default-free U.S. Treasury securities if no inflation were expected. The real rate of interest as discussed here is different from the current real rate as discussed in connection with Figure 6-3. The current real rate is the current interest rate minus the current (or latest past) inflation rate, while the real rate, without the word "current," is the current interest rate minus the expected future inflation rate over the life of the security. For example, suppose the current quoted rate for a one-year Treasury bill is 3 percent, inflation during the latest year was 2 percent, and inflation expected for the coming year is 2.5 percent. Then the current real rate would be 3% 2% 1%, but the expected real rate would be 3% 2.5% 0.5%. The rate on a 10-year bond would be related to the average expected inflation rate over the next 10 years, and so on. In the press, the term "real rate" generally means the current real rate, but in economics and finance, hence in this book unless otherwise noted, the real rate means the one based on expected inflation rates. 4 182 Part 3 Financial Assets The Nominal, or Quoted, Risk-Free Rate of Interest, rRF Nominal (Quoted) Risk-Free Rate, rRF The rate of interest on a security that is free of all risk; rRF is proxied by the T-bill rate or the T-bond rate. rRF includes an inflation premium. The nominal, or quoted, risk-free rate, rRF, is the real risk-free rate plus a premium for expected inflation: rRF r* IP. To be strictly correct, the risk-free rate should mean the interest rate on a totally risk-free security--one that has no default risk, no maturity risk, no liquidity risk, no risk of loss if inflation increases, and no risk of any other type. There is no such security; hence, there is no observable truly risk-free rate. However, there is one security that is free of most risks--an indexed U.S. Treasury security. These securities are free of default, maturity, and liquidity risks, and also of risk due to changes in the general level of interest rates. However, they are not free of changes in the real rate.5 If the term "risk-free rate" is used without either the modifiers "real" or "nominal," people generally mean the quoted (nominal) rate, and we follow that convention in this book. Therefore, when we use the term risk-free rate, rRF, we mean the nominal risk-free rate, which includes an inflation premium equal to the average expected inflation rate over the remaining life of the security. In general, we use the T-bill rate to approximate the short-term risk-free rate, and the T-bond rate to approximate the long-term risk-free rate. So, whenever you see the term "risk-free rate," assume that we are referring either to the quoted U.S. T-bill rate or to the quoted T-bond rate. Inflation Premium (IP) Inflation has a major impact on interest rates because it erodes the dollar's purchasing power and lowers real investment returns. To illustrate, suppose you saved $1,000 and invested it in a Treasury bill that pays a 3 percent interest rate and matures in one year. At the end of the year, you will receive $1,030--your original $1,000 plus $30 of interest. Now suppose the inflation rate during the year turned out to be 3.5 percent, and it affected all goods equally. If heating oil had cost $1 per gallon at the beginning of the year, it would cost $1.035 at the end of the year. Therefore, your $1,000 would have bought $1,000/$1 1,000 gallons at the beginning of the year, but only $1,030/$1.035 995 gallons at the end. In real terms, you would be worse off--you would receive $30 of interest, but it would not be sufficient to offset inflation. You would thus be better off buying 1,000 gallons of heating oil (or some other storable asset such as land, timber, apartment buildings, wheat, or gold) than buying the Treasury bill. Investors are well aware of all this, so when they lend money, they build an inflation premium (IP) equal to the average expected inflation rate over the life of the security into the rate they charge. As discussed previously, the actual interest rate on a short-term, default-free U.S. Treasury bill, rT-bill, would be the real risk-free rate, r*, plus the inflation premium (IP): Inflation Premium (IP) A premium equal to expected inflation that investors add to the real risk-free rate of return. rT-bill rRF r* IP Therefore, if the real risk-free rate were r* 1.7 percent, and if inflation were expected to be 1.5 percent (and hence IP 1.5%) during the next year, then the quoted rate of interest on one-year T-bills would be 1.7% 1.5% 3.2%. It is important to note that the inflation rate built into interest rates is the inflation rate expected in the future, not the rate experienced in the past. Thus, the latest 5 Indexed Treasury securities are the closest thing we have to a riskless security, but even they are not totally riskless, because r* itself can change and cause a decline in the prices of these securities. For example, between its issue date in March 1998 and December 2004, the price of one long-term indexed Treasury bond first declined from 100 to 89, or by almost 10 percent, but then rose to 131. The cause of the initial price decline was an increase in the real rate on long-term securities from 3.625 to 4.4 percent, and the cause of the more recent price increase was a decline in real rates to 1.93 percent. Chapter 6 Interest Rates 183 reported figures might show an annual inflation rate of 3 percent over the past 12 months, but that is for the past year. If people on average expect a 4 percent inflation rate in the future, then 4 percent would be built into the current interest rate. Note also that the inflation rate reflected in the quoted interest rate on any security is the average inflation rate expected over the security's life. Thus, the inflation rate built into a 1-year bond is the expected inflation rate for the next year, but the inflation rate built into a 30-year bond is the average inflation rate expected over the next 30 years.6 Expectations for future inflation are closely, but not perfectly, correlated with rates experienced in the recent past. Therefore, if the inflation rate reported for last month increased, people would tend to raise their expectations for future inflation, and this change in expectations would cause an increase in current rates. Note that Germany, Japan, and Switzerland have over the past several years had lower inflation rates than the United States, hence their interest rates have generally been lower than ours. Italy and most South American countries have experienced higher inflation, and so their rates have been higher than ours. Students should go to www.bloomberg.com/ markets/rates to find current interest rates in the United States, as well as those in Australia, Brazil, Germany, Japan, and Great Britain. Default Risk Premium (DRP) The risk that a borrower will default, which means not make scheduled interest or principal payments, also affects the market interest rate on a bond: the greater the bond's risk of default, the higher the interest rate. Treasury securities have no default risk, hence they carry the lowest interest rates on taxable securities in the United States. For corporate bonds, the higher the bond's rating, the lower its default risk, and, consequently, the lower its interest rate.7 Here are some representative interest rates on long-term bonds during February 2005: Rate U.S. Treasury AAA AA A BBB 4.65% 5.45 5.60 5.78 6.34 DRP -- 0.80 0.95 1.13 1.69 The difference between the quoted interest rate on a T-bond and that on a corporate bond with similar maturity, liquidity, and other features is the default risk premium (DRP). Therefore, if the bonds listed above have the same maturity, liquidity, etc., then the default risk premium would be DRP 5.45% 4.65% 0.8 percentage point for AAA corporate bonds, 5.60% 4.65% 0.95 percentage point for AA, 5.78% 4.65% 1.13 percentage points for A corporate bonds, and so forth. Default risk premiums vary somewhat over time, but the February 2005 figures are representative of levels in recent years. 6 Default Risk Premium (DRP) The difference between the interest rate on a U.S. Treasury bond and a corporate bond of equal maturity and marketability. To be theoretically precise, we should use a geometric average. Also, since millions of investors are active in the market, it is impossible to determine exactly the consensus expected inflation rate. Survey data are available, however, that give us a reasonably good idea of what investors expect over the next few years. For example, in 1980 the University of Michigan's Survey Research Center reported that people expected inflation during the next year to be 11.9 percent and that the average rate of inflation expected over the next 5 to 10 years was 10.5 percent. Those expectations led to record-high interest rates. However, the economy cooled thereafter and, as Figure 6-3 showed, actual inflation dropped sharply. This led to a gradual reduction in the expected future inflation rate, and as inflationary expectations dropped, so did quoted market interest rates. 7 Bond ratings, and bonds' riskiness in general, are discussed in detail in Chapter 7. For now, merely note that bonds rated AAA are judged to have less default risk than bonds rated AA, while AA bonds are less risky than A bonds, and so on. Ratings are designated AAA or Aaa, AA or Aa, and so forth, depending on the rating agency. In this book, the designations are used interchangeably. 184 Part 3 Financial Assets An Almost Riskless Treasury Bond Investors who purchase bonds must constantly worry about inflation. If inflation turns out to be greater than expected, bonds will provide a lower-thanexpected real return. To protect themselves against expected increases in inflation, investors build an inflation risk premium into their required rate of return. This raises borrowers' costs. To provide investors with an inflation-protected bond, and also to reduce the cost of debt to the government, on January 29, 1997, the U.S. Treasury issued $7 billion of 10-year inflation-indexed bonds. These bonds pay an interest rate of 3.375 percent plus an additional amount that is just sufficient to offset inflation. At the end of each six-month period, the principal (originally set at par, or $1,000) is adjusted by the inflation rate. For example, during the first six-month interest period, inflation (as measured by the CPI) was 1.085 percent. The inflationadjusted principal was then calculated as $1,000(1 Inflation) $1,000 1.01085 $1,010.85. So, on July 15, 1997, each bond paid interest of 0.03375/2 $1,010.85 $17.06. Note that the interest rate is Date 7/15/97 1/15/98 7/15/98 1/15/99 7/15/99 1/15/00 7/15/00 1/15/01 7/15/01 1/15/02 7/15/02 1/15/03 7/15/03 1/15/04 7/15/04 1/15/05 divided by two because interest on these (and most other) bonds is paid twice a year. By January 15, 1998, a bit more inflation had occurred, and the inflation-adjusted principal was up to $1,019.69, so on January 15, 1998, each bond paid interest of 0.03375/2 $1,019.69 $17.21. Thus, the total return during the first year consisted of $17.06 $17.21 $34.27 of interest and $1,019.69 $1,000.00 $19.69 of "capital gains," or $34.27 $19.69 $53.96 in total. Thus, the total return was $53.96/$1,000 5.396%. This same adjustment process will continue each year until the bonds mature on January 15, 2007, at which time they will pay the adjusted maturity value. Thus, the cash income provided by the bonds rises by exactly enough to cover inflation, producing a real, inflation-adjusted rate of 3.375 percent. Further, since the principal also rises by the inflation rate, it too is protected from inflation. The accompanying table gives the inflation-adjusted principal and interest paid during the life of these 3 3/8 percent coupon, 10-year, inflation-indexed bonds: Interest Paid $17.06 17.21 17.32 17.47 17.70 17.92 18.24 18.54 18.88 18.91 19.15 19.31 19.56 19.68 20.08 20.34 Inflation-Adjusted Principal $1,010.85 1,019.69 1,026.51 1,035.12 1,049.01 1,061.92 1,080.85 1,098.52 1,118.82 1,120.74 1,134.85 1,144.31 1,159.24 1,166.24 1,189.74 1,205.19 Source: Bureau of the Public Debt's Online, Historical Reference CPI Num3 bers and Daily Index Ratios for 3 /8 percent, 10-year note due January 15, 2007, http://www.publicdebt.treas.gov/of/ofhiscpi.htm. Chapter 6 Interest Rates 185 The Treasury regularly conducts auctions to issue indexed bonds. The 3.375 percent rate was based on the relative supply and demand for the issue, and it will remain fixed over the life of the bond. However, new bonds are issued periodically, and their "coupon" real rates depend on the market at the time the bond is auctioned. In January 2005, 10-year indexed securities had a real rate of 1.625 percent. Federal Reserve Board Chairman Greenspan lobbied in favor of the indexed bonds on the grounds that they would help him and the Fed make better estimates of investors' expectations about inflation. He did not explain his reasoning (to our knowledge), but it might have gone something like this: We know that interest rates in general are determined as follows: r r* IP MRP DRP LP In other words, the market rate on an indexed bond is the real rate. The difference between the yield on a regular 10-year bond and that on an indexed bond is the sum of the 10-year bonds' IP and MRP. Regular 10-year bonds were yielding 6.80 percent when the first indexed bonds were issued in 1997 at a rate of 3.375 percent. The difference, 3.425 percent, was the average expected inflation rate over the next 10 years, plus an MRP for 10-year bonds. The 10-year MRP is about 1.0 percent, and it has been relatively stable in recent years. Therefore, the expected rate of inflation in January 1997 was 3.425% 1.00% 2.425%. Both the annual interest received and the increase in principal are taxed each year as interest income, even though cash from the appreciation will not be received until the bond matures. Therefore, these bonds are not good for accounts subject to current income taxes but are excellent for individual retirement accounts [IRAs and 401(k) plans], which are not taxed until funds are withdrawn. Keep in mind, though, that despite their protection against inflation, indexed bonds are not completely riskless. As we indicated earlier, the real rate can change, and if r* rises, the prices of indexed bonds will decline. This just confirms one more time that there is no such thing as a free lunch or a riskless security! For Treasury bonds, DRP and LP are essentially zero, so for a 10-year bond the rate is rRF r* IP MRP The reason the MRP is not zero is that if inflation increases, interest rates will rise and the price of the bonds will decline. Therefore, "regular" 10-year bonds are exposed to maturity risk, hence a maturity risk premium is built into their market interest rate. The indexed bonds are protected against inflation--if inflation increases, then so will their dollar returns, and as a result, their price will not decline in real terms. Therefore, indexed bonds should have no MRP, hence their market return is rRF r* 0 0 r* Sources: "Inflation Notes Will Offer Fed Forecast Tool," The Wall Street Journal, February 3, 1997, p. C1; and The Wall Street Journal, January 6, 2000, p. C21. 186 Part 3 Financial Assets Liquidity Premium (LP) Liquidity Premium (LP) A premium added to the equilibrium interest rate on a security if that security cannot be converted to cash on short notice and at close to its "fair market value." A "liquid" asset can be converted to cash quickly at a "fair market value." Real assets are generally less liquid than financial assets, but different financial assets vary in their liquidity. Because liquidity is important, investors include a liquidity premium (LP) in the rates charged on different debt securities. Although it is difficult to accurately measure liquidity premiums, a differential of at least two and probably four or five percentage points exists between the least liquid and the most liquid financial assets of similar default risk and maturity. Maturity Risk Premium (MRP) U.S. Treasury securities are free of default risk in the sense that one can be virtually certain that the federal government will pay interest on its bonds and will also pay them off when they mature. Therefore, the default risk premium on Treasury securities is essentially zero. Further, active markets exist for Treasury securities, so their liquidity premiums are also close to zero. Thus, as a first approximation, the rate of interest on a Treasury security should be the risk-free rate, rRF, which is equal to the real risk-free rate, r*, plus an inflation premium, IP. However, the prices of long-term bonds decline whenever interest rates rise, and because interest rates can and do occasionally rise, all long-term bonds, even Treasury bonds, have an element of risk called interest rate risk. As a general rule, the bonds of any organization, from the U.S. government to Delta Airlines, have more interest rate risk the longer the maturity of the bond.8 Therefore, a maturity risk premium (MRP), which is higher the greater the years to maturity, must be included in the required interest rate. The effect of maturity risk premiums is to raise interest rates on long-term bonds relative to those on short-term bonds. This premium, like the others, is difficult to measure, but (1) it varies somewhat over time, rising when interest rates are more volatile and uncertain, then falling when interest rates are more stable, and (2) in recent years, the maturity risk premium on 20-year T-bonds has generally been in the range of one to two percentage points.9 We should also note that although long-term bonds are heavily exposed to interest rate risk, short-term bills are heavily exposed to reinvestment rate risk. When short-term bills mature and the principal must be reinvested, or "rolled over," a decline in interest rates would necessitate reinvestment at a lower rate, and this would result in a decline in interest income. To illustrate, suppose you had $100,000 invested in T-bills and you lived on the income. In 1981, short-term Treasury rates were about 15 percent, so your income would have been about $15,000. However, your income would have declined to about $9,000 by 1983, and to just $2,900 by February 2005. Had you invested your money in long-term T-bonds, your income (but not the value of the principal) would have been stable.10 Thus, although "investing short" preserves one's principal, the interest income provided by short-term T-bills is less stable than the interest income on long-term bonds. 8 Interest Rate Risk The risk of capital losses to which investors are exposed because of changing interest rates. Maturity Risk Premium (MRP) A premium that reflects interest rate risk. Reinvestment Rate Risk The risk that a decline in interest rates will lead to lower income when bonds mature and funds are reinvested. For example, if someone had bought a 20-year Treasury bond for $1,000 in October 1998, when the long-term interest rate was 5.3 percent, and sold it in May 2002, when long-term T-bond rates were about 5.8 percent, the value of the bond would have declined to about $942. That would represent a loss of 5.8 percent, and it demonstrates that long-term bonds, even U.S. Treasury bonds, are not riskless. However, had the investor purchased short-term T-bills in 1998 and subsequently reinvested the principal each time the bills matured, he or she would still have had the original $1,000. This point is discussed in detail in Chapter 7. 9 The MRP for long-term bonds has averaged 1.4 percent over the last 79 years. See Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2005 Yearbook (Chicago: Ibbotson Associates, 2005). 10 Long-term bonds also have some reinvestment rate risk. If one is saving and investing for some future purpose, say, to buy a house or for retirement, then to actually earn the quoted rate on a Chapter 6 Interest Rates 187 Write out an equation for the nominal interest rate on any security. Distinguish between the real risk-free rate of interest, r*, and the nominal, or quoted, risk-free rate of interest, rRF. How do investors deal with inflation when they determine interest rates in the financial markets? Does the interest rate on a T-bond include a default risk premium? Explain. Distinguish between liquid and illiquid assets, and list some assets that are liquid and some that are illiquid. Briefly explain the following statement: "Although long-term bonds are heavily exposed to interest rate risk, short-term T-bills are heavily exposed to reinvestment rate risk. The maturity risk premium reflects the net effects of these two opposing forces." Assume that the real risk-free rate is r* 2% and the average expected inflation rate is 3 percent for each future year. The DRP and LP for Bond X are each 1 percent, and the applicable MRP is 2 percent. What is Bond X's interest rate? Is Bond X (1) a Treasury bond or a corporate bond and (2) more likely to have a 3-month or a 20-year maturity? (9 percent, corporate, 20-year) 6.4 THE TERM STRUCTURE OF INTEREST RATES The term structure of interest rates describes the relationship between long- and short-term rates. The term structure is important both to corporate treasurers deciding whether to borrow by issuing long- or short-term debt and to investors who are deciding whether to buy long- or short-term bonds. Therefore, both borrowers and lenders should understand (1) how long- and short-term rates relate to each other and (2) what causes shifts in their relative levels. Interest rates for bonds with different maturities can be found in a variety of publications, including The Wall Street Journal and the Federal Reserve Bulletin, and on a number of Web sites, including Bloomberg, Yahoo!, CNN Financial, and the Federal Reserve Board. Using interest rate data from these sources, we can determine the term structure at any given point in time. For example, the tabular section below Figure 6-4 presents interest rates for different maturities on three different dates. The set of data for a given date, when plotted on a graph such as Figure 6-4, is called the yield curve for that date. As the figure shows, the yield curve changes both in position and in slope over time. In March 1980, all rates were quite high because high inflation was expected. However, the rate of inflation was expected to decline, so short-term rates were higher than long-term rates and the yield curve was thus downward sloping. By February 2000, inflation had indeed declined and thus all rates were lower, and the yield curve had become humped--medium-term rates were higher (Footnote 10, continued) long-term bond, the interest payments must be reinvested at the quoted rate. However, if interest rates fall, the interest payments must be reinvested at a lower rate; thus, the realized return would be less than the quoted rate. Note, though, that reinvestment rate risk is lower on a long-term bond than on a short-term bond because only the interest payments (rather than interest plus principal) on the long-term bond are exposed to reinvestment rate risk. Zero coupon bonds, which are discussed in Chapter 7, are completely free of reinvestment rate risk during their lifetime. Term Structure of Interest Rates The relationship between bond yields and maturities. Yield Curve A graph showing the relationship between bond yields and maturities. 188 Part 3 Financial Assets FIGURE 6-4 Interest Rate (%) 16 14 U.S. Treasury Bond Interest Rates on Different Dates Yield Curve for March 1980 12 10 8 Yield Curve for February 2000 6 Yield Curve for February 2005 4 2 0 Short Term 5 Intermediate Term 10 15 20 Long Term 25 30 Years to Maturity INTEREST RATE Term to Maturity 6 months 1 year 5 years 10 years 30 years March 1980 15.0% 14.0 13.5 12.8 12.3 February 2000 6.0% 6.2 6.7 6.7 6.3 February 2005 2.9% 3.1 3.8 4.2 4.6 "Normal" Yield Curve An upward-sloping yield curve. Inverted ("Abnormal") Yield Curve A downward-sloping yield curve. than either short- or long-term rates. By February 2005, all rates had fallen below the 2000 levels, and because short-term rates had dropped below long-term rates, the yield curve was upward sloping. Figure 6-4 shows yield curves for U.S. Treasury securities, but we could have constructed curves for bonds issued by GE, IBM, Delta Airlines, or any other company that borrows money over a range of maturities. Had we constructed such corporate yield curves and plotted them on Figure 6-4, they would have been above those for Treasury securities because corporate yields include default risk premiums and somewhat higher liquidity premiums than Treasury bonds. However, the corporate yield curves would have had the same general shape as the Treasury curves. Also, the riskier the corporation, the higher its yield curve, so Delta, which was flirting with bankruptcy, would have a higher yield curve than GE or IBM. Historically, long-term rates are generally above short-term rates because of the maturity premium, so the yield curve usually slopes upward. For this reason, people often call an upward-sloping yield curve a "normal" yield curve and a yield curve that slopes downward an inverted, or "abnormal" curve. Chapter 6 Interest Rates 189 Thus, in Figure 6-4 the yield curve for March 1980 was inverted, while the yield curve in February 2005 was normal. However, the February 2000 curve was humped, which means that interest rates on medium-term maturities were higher than rates on both short- and long-term maturities. We explain in detail in the next section why an upward slope is the normal situation, but briefly, the reason is that short-term securities have less interest rate risk than longer-term securities, hence smaller MRPs. Therefore, short-term rates are normally lower than long-term rates. Humped Yield Curve A yield curve where interest rates on medium-term maturities are higher than rates on both short- and long-term maturities. What is a yield curve, and what information would you need to draw this curve? Distinguish among the shapes of a "normal" yield curve, an "abnormal" curve, and a "humped" curve. If the interest rates on 1-, 5-, 10-, and 30-year bonds are 4, 5, 6, and 7 percent, respectively, how would you describe the yield curve? If the rates were reversed, how would you describe it? 6.5 WHAT DETERMINES THE SHAPE OF THE YIELD CURVE? Because maturity risk premiums are positive, then if other things were held constant, long-term bonds would always have higher interest rates than shortterm bonds. However, market interest rates also depend on expected inflation, default risk, and liquidity, and each of these factors can vary with maturity. Expected inflation has an especially important effect on the yield curve's shape, especially the curve for U.S. Treasury securities. Treasuries have essentially no default or liquidity risk, so the yield on a Treasury bond that matures in t years can be expressed as follows: T-bond yield r*t IPt MRPt While the real risk-free rate, r*, varies somewhat over time because of changes in the economy and demographics, these changes are random rather than predictable, so the best forecast for the future value of r* is its current value. However, the inflation premium, IP, does vary significantly over time, and in a somewhat predictable manner. Recall that the inflation premium is simply the average level of expected inflation over the life of the bond. Thus, if the market expects inflation to increase in the future, say, from 3 to 4 to 5 percent over the next three years, the inflation premium will be higher on a three-year bond than on a one-year bond. On the other hand, if the market expects inflation to decline in the future, long-term bonds will have a smaller inflation premium than shortterm bonds. Finally, since investors consider long-term bonds to be riskier than short-term bonds because of interest rate risk, the maturity risk premium always increases with maturity. Panel a of Figure 6-5 shows the yield curve when inflation is expected to increase. Here long-term bonds have higher yields for two reasons: (1) Inflation is expected to be higher in the future, and (2) there is a positive maturity risk premium. Panel b of the figure shows the yield curve when inflation is expected to decline. Such a downward sloping yield curve often foreshadows an economic 190 Part 3 Financial Assets FIGURE 6-5 Illustrative Treasury Yield Curves b. When Inflation Is Expected to Decrease Interest Rate (%) a. When Inflation Is Expected to Increase Interest Rate (%) 8 7 6 5 4 3 2 1 0 10 20 30 Years to Maturity Maturity Risk Premium 8 7 6 Maturity Risk Premium Inflation Premium Inflation Premium 5 4 3 2 Real RiskFree Rate 1 0 10 20 30 Years to Maturity Real RiskFree Rate WITH INFLATION EXPECTED TO INCREASE Maturity 1 year 5 years 10 years 20 years 30 years r* 2.50% 2.50 2.50 2.50 2.50 IP 3.00% 3.40 4.00 4.50 4.67 MRP 0.00% 0.18 0.28 0.42 0.53 Yield 5.50% 6.08 6.78 7.42 7.70 Maturity 1 year 5 years 10 years 20 years 30 years r* WITH INFLATION EXPECTED TO DECREASE IP 5.00% 4.60 4.00 3.50 3.33 MRP 0.00% 0.18 0.28 0.42 0.53 Yield 7.50% 7.28 6.78 6.42 6.36 2.50% 2.50 2.50 2.50 2.50 downturn, because weaker economic conditions generally lead to declining inflation, which, in turn, results in lower long-term rates.11 Now let's consider the yield curve for corporate bonds. Recall that corporate bonds include a default risk premium (DRP) and a liquidity premium (LP). Therefore, the yield on a corporate bond that matures in t years can be expressed as follows: Corporate bond yield r*t IPt MRPt DRPt LPt Corporate bonds' default and liquidity risks are affected by their maturities. For example, the default risk on Coca-Cola's short-term debt is very small, since there is almost no chance that Coca-Cola will go bankrupt over the next few years. However, Coke has some bonds that have a maturity of almost 100 years, and while the odds of Coke defaulting on these bonds still might not be very 11 Note that yield curves tend to rise or fall relatively sharply for 5 to 10 years, and then flatten out. One reason this occurs is that when forecasting future interest rates people often predict varying changes in inflation for the next 5 to 10 years after which they assume a long-run constant inflation rate. Consequently, the short end of the yield curve tends to have more volatility because there are more variations in the year-to-year interest rate forecasts. By contrast, the long end of the yield curve tends to be more stable because of the assumption of constant inflation rates. Chapter 6 Interest Rates 191 FIGURE 6-6 Illustrative Corporate and Treasury Yield Curves Interest Rate (%) 12 BBB-Rated Bond 10 AA-Rated Bond 8 Treasury Bond 6 4 2 0 10 20 30 Years to Maturity INTEREST RATE Term to Maturity 1 year 5 years 10 years 20 years 30 years Treasury Bond 5.5% 6.1 6.8 7.4 7.7 AA-Rated Bond 6.7% 7.4 8.2 9.2 9.8 BBB-Rated Bond 7.4% 8.1 9.1 10.2 11.1 high, there is still a higher probability of default risk on Coke's long-term bonds than on its short-term ones. Longer-term corporate bonds are also less liquid than shorter-term bonds. Since short-term debt has less default risk, someone can buy a short-term bond without as much credit checking as would be necessary before buying a longterm bond. Thus, people can move in and out of short-term corporate debt more rapidly than long-term debt. As a result, a corporation's short-term bonds are more liquid and thus have lower liquidity premiums than its long-term bonds. Figure 6-6 shows yield curves for two hypothetical corporate bonds, an AA-rated bond with minimal default risk and a BBB-rated bond with more default risk, along with the yield curve for Treasury securities as taken from Panel a of Figure 6-5. Here we assume that inflation is expected to increase, so the Treasury yield curve is upward sloping. Because of their additional default and liquidity risk, corporate bonds always yield more than Treasury bonds with the same maturity, and BBB-rated bonds yield more than AA-rated bonds. Finally, note that the yield spread between corporate bonds and Treasury bonds is larger the longer the maturity. This occurs because longer-term corporate bonds have more default and liquidity risk than shorter-term bonds, and both of these premiums are absent in Treasury bonds. 192 Part 3 Financial Assets The Links between Expected Inflation and Interest Rates: A Closer Look Throughout the text, we use the following equation to describe the link between expected inflation and the nominal risk-free rate of interest, rRF : rRF r* IP With these concerns in mind, let's compare the dollar cost of 100 loaves of bread today to the cost of 103 loaves next year. Given the current price, 100 loaves of bread today would cost $100. Since expected inflation is 5 percent, this means that a loaf of bread is expected to cost $1.05 next year. Consequently, 103 loaves of bread are expected to cost $108.15 next year (103 $1.05). So, if consumers were to deposit $100 in a bank today, they would need to earn 8.15 percent to realize a real return of 3 percent. Putting this all together, we see that the one-year nominal interest rate can be calculated as follows: rRF (1 r*)(1 I) 1 (1.03)(1.05) 1 0.0815 8.15% Recall that r* is the real risk-free interest rate, and IP is the corresponding inflation premium. This equation suggests that there is a simple direct link between expected inflation and nominal interest rates. It turns out, however, that this link is a bit more complex. To fully understand this relationship, first recognize that individuals get utility through the consumption of real goods and services such as bread, water, haircuts, pizza, and textbooks. When we save money we are giving up the opportunity to consume these goods today in return for being able to consume more in the future. Our gain in purchasing power is measured by the real rate of interest, r*. To illustrate this point consider the following example. Assume that a loaf of bread costs $1.00 today. Also assume that the real rate of interest is 3 percent and that inflation is expected to be 5 percent over the next year. The 3 percent real rate indicates that the average consumer is willing to trade 100 loaves of bread today for 103 loaves next year. If there were a "bread bank," consumers who wanted to defer consumption until next year could deposit 100 loaves today and withdraw 103 loaves next year. In practice, most of us do not directly trade real goods such as bread--instead we purchase these goods with money because in a well-functioning economy it is much more efficient to exchange money than goods. However, when we lend money over time we worry that borrowers might pay us back with dollars that aren't worth as much due to inflation. To compensate for this risk, lenders build in a premium for expected inflation. How does this expression compare with the original equation we used for the nominal risk-free rate of interest? Note that the above expression can be rewritten as rRF r* I (r* I) This equation is identical to our original expression for the nominal risk-free rate except it includes a "cross-term," r* I. When real interest rates and expected inflation are relatively low, the cross-term turns out to be quite small and thus it is often ignored. With this point in mind, in the text we will disregard the cross-term unless we state otherwise. One last point--you should recognize that while it may be reasonable to ignore the cross-term when interest rates are low (as they are today), it is a mistake to do so when investing in a market where interest rates and inflation are quite high, as is often the case in many emerging markets. In these markets, the cross-term can be significant and thus should not be disregarded. How do maturity risk premiums affect the yield curve? If the inflation rate is expected to increase, would this increase or decrease the slope of the yield curve? If the inflation rate is expected to remain constant at the current level in the future, would the yield curve slope up, down, or be horizontal? Consider all factors that affect the yield curve, not just inflation. Chapter 6 Interest Rates 193 Explain why corporate bonds' default and liquidity premiums are likely to increase with their maturity. Explain why corporate bonds always yield more than Treasury bonds and why BBB-rated bonds always yield more than AA-rated bonds. 6.6 USING THE YIELD CURVE TO ESTIMATE FUTURE INTEREST RATES12 In the last section we saw that the slope of the yield curve depends primarily on two factors: (1) expectations about future inflation and (2) the effects of maturity on bonds' risk. We also saw how to calculate the yield curve, given inflation and maturity-related risks. Note, though, that investors can reverse the process: They plot the yield curve and then use information embedded in it to estimate the market's expectations regarding future inflation and risk. This process of using the yield curve to estimate future expected interest rates is straightforward, provided (1) we focus on Treasury bonds, and (2) we assume that all Treasury bonds have the same risk, that is, that there is no maturity risk premium. While this second assumption may not be reasonable, it enables us for the time being to take out the effects of risk and focus exclusively on how expectations about future interest rates affect the shape of the yield curve. Later on, we will show what happens when we once again assume that there is a maturity risk premium. In fact, while most evidence suggests that there is a positive maturity risk premium, some academics and practitioners contend that this second assumption is reasonable, at least as an approximation. They argue that the market is dominated by large bond traders who buy and sell securities of different maturities each day, that these traders focus only on short-term returns, and that they are not concerned with maturity risk. According to this view, a bond trader is just as willing to buy a 20-year bond to pick up a short-term profit as he or she would be to buy a three-month security. Strict proponents of this view argue that the shape of the Treasury yield curve is therefore determined only by market expectations about future interest rates. This position has been called the pure expectations theory of the term structure of interest rates. The pure expectations theory (often simply referred to as the "expectations theory") assumes that bond traders establish bond prices and interest rates strictly on the basis of expectations for future interest rates, and they are indifferent to maturity because they do not view long-term bonds as being riskier than short-term bonds. If this were true, then the maturity risk premium (MRP) would be zero, and long-term interest rates would simply be a weighted average of current and expected future short-term interest rates. To illustrate this point, assume that one-year Treasury securities currently yield 5 percent, while two-year Treasury securities yield 5.5 percent. Investors with a two-year horizon have two primary options: Option 1: Buy a two-year security and hold it for two years. Option 2: Buy a one-year security, hold it for one year, and then at the end of the year reinvest the proceeds in another one-year security. If they select Option 1, for every dollar they invest today, they will have accumulated $1.113025 by the end of Year 2: Pure Expectations Theory A theory that states that the shape of the yield curve depends on investors` expectations about future interest rates. Funds at end of Year 2 12 $1 (1.055)2 $1.113025 This section is relatively technical, but instructors can omit it without loss of continuity. 194 Part 3 Financial Assets If they select Option 2, they should end up with the same amount, but this equation is used to find the ending amount: Funds at end of Year 2 $1 (1.05) (1 X) Here X is the expected interest rate on a one-year Treasury security one year from now. If the expectations theory is correct, each option must provide the same amount of cash at the end of two years, which implies that (1.05)(1 X) (1.055)2 We can rearrange this equation and then solve for X: 1 X X (1.055)2/1.05 (1.055)2/1.05 1 0.0600238 6.00238% Thus, if the expectations theory is correct, the current yield curve would indicate that the market expects the one-year rate to be 6.00238 percent one year from now. We can use yield curve data to help predict future short-term interest rates. In the absence of maturity risk premiums, an upward sloping Treasury yield curve implies that the market expects future short-term rates to increase. Also, notice that the two-year rate of 5.5 percent is a geometric average of the current and expected one-year rates.13 To understand the logic behind the averaging process, ask yourself what would happen if long-term yields were not an average of expected short-term yields. For example, suppose investors expected the one-year Treasury rate to be 6.00238 percent a year from now, but two-year bonds yielded only 5.25 percent. Bond traders would be able to earn a profit by adopting the following strategy: 1. Borrow money for two years at an annual cost of 5.25 percent. 2. Invest the money in a series of one-year securities. The annual expected return over the two-year period would be [(1.05) (1.0600238)]1/2 1 5.5%. Earning 5.5 percent when the cost is 5.25 percent is a good deal, so bond traders would rush to borrow money (demand funds) in the two-year market and invest (or supply funds) in the one-year market. Recall from Figure 6-1 that an increase in the demand for funds raises interest rates, whereas an increase in the supply of funds reduces interest rates. Therefore, bond traders would push up the twoyear yield but reduce the yield on one-year bonds. The net effect would be a market equilibrium in which the two-year rate is a weighted average of expected future one-year rates. The preceding analysis was based on the assumption that the maturity risk premium is zero, but most evidence suggests that there is a positive maturity risk premium. For example, assume once again that one- and two-year maturities yield 5.0 and 5.5 percent respectively, so we have a rising yield curve. However, now assume that the maturity risk premium on the two-year bond is 13 The geometric average of the current and expected one-year rates can be expressed as: [(1.05) (1.0600238)]1/2 1 0.055 or 5.50%. The arithmetic average of the two rates is (5% 6.00238%)/2 5.50119%. The geometric average is theoretically superior, but the difference is only 0.00119%. With interest rates at the levels they have been in the United States and most other nations in recent years, the geometric and arithmetic averages are so close that many people simply use the arithmetic average, especially given the other assumptions that underlie the estimation of future one-year rates. Chapter 6 Interest Rates 195 0.2 percent versus zero for the one-year bond. This premium means that in equilibrium the expected annual return on a two-year bond (5.5 percent) must be 0.2 percent higher than the expected return on a series of two one-year bonds (5 percent and X percent), so the expected return on the series must be 5.5% 0.2% 5.3%: Expected return on 2-year series 0.055 0.002 Rate on 2-year bond 0.053 5.3% MRP Now recall that the annual expected return from the series of two one-year securities can be expressed as follows, where X is the one-year rate next year: (1.05)(1 X) (1 Expected return on 2-year series)2 1.05 0.0560086 5.60086% (1.053)2 1.05X X (1.053)2 0.0588090 1.05 Therefore, in this scenario market participants must expect the one-year rate next year to be 5.60086 percent. Note that the yield curve rises by 0.5 percent when the years to maturity increases from one to two: 5.5% 5.0% 0.5%. Of this 0.5 percent increase, 0.2 percent is attributable to the MRP and the remaining 0.3 percent is due to the increase in expected one-year rates next year. Putting all this together, we see that we can use the yield curve to predict the short-term rates that will exist for next year, but to do this we must have an estimate of the maturity risk premium. If our estimate of the MRP is incorrect, then so will be our yield-curve-based interest-rate forecast. Thus, while the yield curve can be used to obtain insights into the direction of future interest rates, we cannot back out expected interest rates with precision unless either the pure expectations theory holds exactly or else we know with certainty the exact maturity risk premium. As neither of these conditions holds, forecasts of future interest rates are only approximations, though they may be good approximations. What key assumption underlies the pure expectations theory? Assuming that the pure expectations theory is correct, how are expected short-term rates used to calculate expected long-term rates? According to the pure expectations theory, what would happen if long-term rates were not an average of expected short-term rates? Most evidence suggests that a positive maturity risk premium exists. How would this affect your calculations when determining interest rates? Assume the interest rate on a one-year T-bond is currently 7 percent and the rate on a two-year bond is 9 percent. If the maturity risk premium is zero, what is a reasonable forecast of the rate on a oneyear bond next year? What would the forecast be if the maturity risk premium on the two-year bond were 0.5 percent and it was zero for the one-year bond? (11.04 percent; 10.02 percent) 196 Part 3 Financial Assets 6.7 OTHER FACTORS THAT INFLUENCE INTEREST RATE LEVELS Four additional factors that influence both the general level of interest rates and the shape of the yield curve are (1) the Federal Reserve policy; (2) the federal budget deficit or surplus; (3) international factors, including the foreign trade balance and interest rates in other countries; and (4) the level of business activity. Federal Reserve Policy As you probably learned in your economics courses, (1) the money supply has a significant effect on the level of economic activity, inflation rate, and interest rates, and (2) in the United States, the Federal Reserve Board controls the money supply. If the Fed wants to stimulate the economy, it increases growth in the money supply. The initial effect of this action is to cause interest rates to decline. However, a larger money supply may also lead to an increase in the expected inflation rate, which could push up interest rates in spite of the Fed's desire to lower them. The reverse holds if the Fed tightens the money supply. To illustrate, in 1981 inflation was extremely high, so the Fed tightened the money supply. The Fed deals primarily in the short-term end of the market, so its tightening had the direct effect of pushing up short-term rates sharply. At the same time, the very fact that the Fed was taking strong action to reduce inflation led to a decline in expectations for long-run inflation, which caused long-term bond yields to decline even as short-term rates rose. The situation in 1991 was just the reverse. To combat the recession, the Fed took actions that caused short-term rates to fall sharply. These lower rates benefited companies that used debt--lower rates helped companies finance capital expenditures, which stimulated the economy. At the same time, lower rates led to home mortgage refinancings, which lowered mortgage payments and thus put additional dollars into consumers' pockets, which also stimulated the economy. Savers, of course, lost out, but the net effect of lower interest rates was a stronger economy. Lower rates also cause foreigners who hold U.S. bonds to sell those bonds. These investors are paid dollars, which they then sell in order to buy other currencies. The sale of dollars and the purchase of other currencies lowers the value of the dollar relative to other currencies, and that makes U.S. goods less expensive, which helps our manufacturers and thus lowers the trade deficit. Note, though, that during periods when the Fed is actively intervening in the markets, the yield curve may be temporarily distorted. Short-term rates may be driven below the equilibrium level if the Fed is easing credit and above equilibrium if it is tightening credit. Long-term rates are not affected as much by Fed intervention. During 2004, in order to bring interest rates back to levels more consistent with inflation, the Federal Reserve increased short-term interest rates five times, causing short-term rates to rise by 1.25 percentage points. However, long-term rates (as measured by the 10-year Treasury note) remained level. The home page for the Board of Governors of the Federal Reserve System can be found at http://www .federalreserve.gov/. You can access general information about the Federal Reserve, including press releases, speeches, and monetary policy. Federal Budget Deficits or Surpluses If the federal government spends more than it takes in from taxes, it runs a deficit, and that deficit must be covered by additional borrowing or by printing money. If the government borrows, this increases the demand for funds and thus pushes up interest rates. If it prints money, investors believe that with "more money chasing a given amount of goods," the result will be increased inflation, which will also increase interest rates. So, the larger the federal deficit, other things held constant, the higher the level of interest rates. Chapter 6 Interest Rates 197 Over the past several decades, the federal government has usually run large budget deficits. There were some surpluses in the late 1990s, but the September 11, 2001, terrorist attacks, the subsequent recession, and the Iraq war all boosted government spending and caused the deficits to return. International Factors Businesses and individuals in the United States buy from and sell to people and firms all around the globe. If we buy more than we sell (that is, if we import more than we export), we are said to be running a foreign trade deficit. When trade deficits occur, they must be financed, and this generally means borrowing from nations with export surpluses. In other words, if we import $200 billion of goods but export only $100 billion, we run a trade deficit of $100 billion, while other countries would share in a $100 billion trade surplus. We would probably borrow the $100 billion from the surplus nations.14 At any rate, the larger our trade deficit, the more we must borrow. Foreigners will hold U.S. debt if and only if the rates on U.S. securities are competitive with rates in other countries. So, our interest rates are highly dependent on rates in other parts of the world. This interdependency limits the ability of the Federal Reserve to use monetary policy to control economic activity in the United States. For example, if the Fed attempts to lower U.S. interest rates in the United States, and this causes our rates to fall below rates abroad, then foreigners will begin selling U.S. bonds. Those sales will depress bond prices, and that will push up rates in the U.S. Thus, a large trade deficit hinders the Fed's ability to combat a recession by lowering interest rates. For 25 or so years following World War II the United States ran large trade surpluses, and the rest of the world owed us many billions of dollars. However, the situation changed, and we have been running trade deficits since the mid1970s. The cumulative effect of these deficits has been to change the United States from being the largest creditor nation to being the largest debtor nation of all time. As a result, our interest rates are very much influenced by interest rates in other countries--higher or lower rates abroad lead to higher or lower U.S. rates. Because of all this, U.S. corporate treasurers and everyone else who is affected by interest rates should keep up with developments in the world economy. Foreign Trade Deficit The situation that exists when a country imports more than it exports. Business Activity Figure 6-2, presented in Section 6.2, can be examined to see how business conditions influence interest rates. Here are the key points revealed by the graph: 1. Because inflation increased from 1971 to 1981, the general tendency during that period was toward higher interest rates. However, since the 1981 peak, the trend has generally been downward. 2. The shaded areas in the graph represent recessions, during which (a) both the demand for money and the rate of inflation tend to fall and (b) the Federal Reserve tends to increase the money supply in an effort to stimulate the economy. As a result, there is a tendency for interest rates to decline during recessions. For example, the economy began to slow down in 2000, and we entered a mild recession in 2001. In response to this economic weakness, the Federal Reserve cut interest rates. However, in 2004 the economy began to rebound, so the Fed began to raise rates. 3. During recessions, short-term rates decline more sharply than long-term rates. This occurs because (a) the Fed operates mainly in the short-term sector, so its 14 The deficit could also be financed by selling assets, including gold, corporate stocks, entire companies, and real estate. The United States has financed its massive trade deficits by all of these means in recent years, but the primary method has been by borrowing from foreigners. 198 Part 3 Financial Assets G L O B A L P E R S P E C T I V E S Measuring Country Risk Various forecasting services measure the level of country risk in different countries and provide indexes that indicate factors such as each country's expected economic performance, access to world capital markets, political stability, and level of internal conflict. Country risk analysts use sophisticated models to measure risk, thus providing corporate managers and investors with a way to judge both the relative and absolute risk of investing in different countries. A sample of recent country risk estimates compiled by Institutional Investor is presented in the accompanying table. The higher the country's score, the lower its country risk. The maximum possible score is 100. The countries with the least country risk all have strong, market-based economies, ready access to worldwide capital markets, relatively little social unrest, and a stable political climate. Switzerland's top ranking may surprise you, but that country's ranking is the result of its strong economic performance and political stability. You may also be surprised that the United States was ranked third, below both Switzerland and Luxembourg. Arguably, there are fewer surprises when looking at the bottom five. Each of these countries has considerable social and political unrest and no marketbased economic system. An investment in any of these countries is clearly a risky proposition. Top Five Countries (Least Amount of Country Risk) Rank 1 2 3* 4* 5 Country Switzerland Luxembourg United States Norway United Kingdom Total Score (Maximum Possible 95.2 93.9 93.7 93.7 93.6 100) Bottom Five Countries (Greatest Amount of Country Risk) Rank 169 170 171 172 173 Country Afghanistan Liberia Sierra Leone North Korea Somalia Total Score (Minimum Possible 11.0 9.4 9.3 8.9 8.2 0) *Ranking was determined before rounding total score. Source: "Country Ratings by Region," Institutional Investor, www.institutionalinvestor.com, September 2004. intervention has the strongest effect there, and (b) long-term rates reflect the average expected inflation rate over the next 20 to 30 years, and this expectation generally does not change much, even when the current inflation rate is low because of a recession or high because of a boom. So, short-term rates are more volatile than long-term rates. Taking another look at Figure 6-2, we indeed see that short-term rates have declined much more than long-term rates. Other than inflationary expectations, name some additional factors that influence interest rates, and explain the effects of each. Chapter 6 Interest Rates 199 How does the Fed stimulate the economy? How does the Fed affect interest rates? Does the Fed have complete control over U.S. interest rates; that is, can it set rates at any level it chooses? Why or why not? 6.8 INVESTING OVERSEAS Investors should consider additional risk factors if they invest overseas. First, there is country risk, which refers to the risk that is attributable to investing in a particular country. This risk depends on the country's economic, political, and social environment. Some countries provide a safer investment climate, and therefore less country risk, than others. Examples of country risk include the risk that property will be expropriated without adequate compensation plus risks associated with changes in tax rates, regulations, and currency repatriation. Country risk also includes changes in host-country requirements regarding local production and employment, as well as the danger of damage due to internal strife. It is especially important to keep in mind when investing overseas that securities are often denominated in a currency other than the dollar, which means that returns on the investment will depend on what happens to exchange rates. This is known as exchange rate risk. For example, if a U.S. investor purchases a Japanese bond, interest will probably be paid in yen, which must then be converted into dollars before the investor can spend his or her money in the United States. If the yen weakens relative to the dollar, then it will buy fewer dollars, hence fewer dollars will be received when funds are repatriated. However, if the yen strengthens, this will increase the effective investment return. It therefore follows that returns on a foreign investment depend on both the performance of the foreign security and on changes in exchange rates. Country Risk The risk that arises from investing or doing business in a particular country. Exchange Rate Risk The risk that exchange rate changes will reduce the number of dollars provided by a given amount of a foreign currency. What is country risk? What is exchange rate risk? On what two factors does the return on a foreign investment depend? 6.9 INTEREST RATES AND BUSINESS DECISIONS The yield curve for February 2005, shown earlier in Figure 6-4 in Section 6.4, indicates how much the U.S. government had to pay in February 2005 to borrow money for 1 year, 5 years, 10 years, and so on. A business borrower would have had to pay somewhat more, but assume for the moment that it is February 2005 and that the yield curve shown for that year applies to your company. Now suppose your company has decided to build a new plant with a 30-year life that will cost $1 million, and to raise the $1 million by borrowing rather than by issuing new stock. If you borrowed in February 2005 on a short-term basis--say, for one year--your interest cost would be only 3.1 percent, or $31,000. On the other hand, if you used long-term financing, your cost would be 4.6 percent, or $46,000. Therefore, at first glance, it would seem that you should use short-term debt. However, this could prove to be a horrible mistake. If you use short-term debt, you will have to renew your loan every year, and the rate charged on each new loan will reflect the then-current short-term rate. Interest rates could return to their previous highs, in which case you would be paying 14 percent, or 200 Part 3 Financial Assets $140,000, per year. Those high interest payments would cut into and perhaps eliminate your profits. Your reduced profitability could increase your firm's risk to the point where your bond rating was lowered, causing lenders to increase the risk premium built into your interest rate. That would further increase your interest payments, which would further reduce your profitability, worry lenders still more, and make them reluctant to even renew your loan. If your lenders refused to renew the loan and demanded its repayment, as they would have every right to do, you might have to sell assets at a loss, which could result in bankruptcy. On the other hand, if you used long-term financing in 2005, your interest costs would remain constant at $46,000 per year, so an increase in interest rates in the economy would not hurt you. You might even be able to acquire some of your bankrupt competitors at bargain prices--bankruptcies increase dramatically when interest rates rise, primarily because many firms do use so much short-term debt. Does all this suggest that firms should always avoid short-term debt? Not at all. If inflation falls over the next few years, so will interest rates. If you had borrowed on a long-term basis for 4.6 percent in February 2005, your company would be at a disadvantage if it were locked into 4.6 percent debt while its competitors (who used short-term debt in 2005) had a borrowing cost of only 3 percent or so. Financing decisions would be easy if we could make accurate forecasts of future interest rates. Unfortunately, predicting interest rates with consistent accuracy is nearly impossible. However, even if it is difficult to predict future interest rate levels, it is easy to predict that interest rates will fluctuate--they always have, and they always will. This being the case, sound financial policy calls for using a mix of long- and short-term debt, as well as equity, to position the firm so that it can survive in any interest rate environment. Further, the optimal financial policy depends in an important way on the nature of the firm's assets--the easier it is to sell off assets to generate cash, the more feasible it is to use more short-term debt. This makes it more feasible for a firm to finance current assets like inventories and receivables with short-term debt than fixed assets like buildings. We will return to this issue later in the book, when we discuss working capital policy. Changes in interest rates also have implications for savers. For example, if you had a 401(k) plan--and someday most of you will--you would probably want to invest some of your money in a bond mutual fund. You could choose a fund that had an average maturity of 25 years, 20 years, on down to only a few months (a money market fund). How would your choice affect your investment results, hence your retirement income? First, your annual interest income would be affected. For example, if the yield curve were upward sloping, as it normally is, you would earn more interest if you chose a fund that held long-term bonds. Note, though, that if you chose a long-term fund and interest rates then rose, the market value of the bonds in the fund would decline. For example, as we will see in Chapter 7, if you had $100,000 in a fund whose average bond had a maturity of 25 years and a coupon rate of 6 percent, and if interest rates then rose from 6 to 10 percent, the market value of your fund would decline from $100,000 to about $64,000. On the other hand, if rates declined, your fund would increase in value. In any event, your choice of maturity would have a major effect on your investment performance, hence on your future income. If short-term interest rates are lower than long-term rates, why might a borrower still choose to finance with long-term debt? Explain the following statement: "The optimal financial policy depends in an important way on the nature of the firm's assets." Chapter 6 Interest Rates 201 Tying It All Together In this chapter, we discussed how interest rates are determined, the term structure of interest rates, and some of the ways interest rates affect business decisions. We saw that the interest rate on a given bond, r, is based on this equation: r r* IP DRP LP MRP where r* is the real risk-free rate, IP is the premium for expected inflation, DRP is the premium for potential default risk, LP is the premium for lack of liquidity (or marketability), and MRP is the premium to compensate for the risk inherent in bonds with long maturities. Both r* and the various premiums can and do change over time, depending on economic conditions, Federal Reserve actions, and the like. Since changes in these factors are difficult to predict, it is hard to forecast the future direction of interest rates. The yield curve, which relates bonds' interest rates to their maturities, can slope up or down, and it changes in both slope and level over time. The main determinants of the slope of the curve are expectations for inflation in future years and the MRP. We can analyze yield curve data to estimate what market participants think future interest rates are likely to be. We will use the insights gained from this chapter in later chapters, when we analyze the values of bonds and stocks and also when we examine various corporate investment and financing decisions. SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) ST-1 Key terms Define each of the following terms: a. Production opportunities; time preferences for consumption; risk; inflation b. Real risk-free rate of interest, r*; nominal (quoted) risk-free rate of interest, rRF c. Inflation premium (IP) d. Default risk premium (DRP) e. Liquidity premium (LP); maturity risk premium (MRP) f. Interest rate risk; reinvestment rate risk g. Term structure of interest rates; yield curve h. "Normal" yield curve; inverted ("abnormal") yield curve; humped yield curve i. Pure expectations theory j. Foreign trade deficit; country risk; exchange rate risk Inflation and interest rates The real risk-free rate of interest, r*, is 3 percent, and it is expected to remain constant over time. Inflation is expected to be 2 percent per year for the next 3 years, and 4 percent per year for the next 5 years. The maturity risk premium is equal to 0.1(t 1)%, where t the bond's maturity. The default risk premium for a BBB-rated bond is 1.3 percent. a. What is the average expected inflation rate over the next 4 years? b. What is the yield on a 4-year Treasury bond? c. What is the yield on a 4-year BBB-rated corporate bond with a liquidity premium of 0.5 percent? ST-2 202 Part 3 Financial Assets d. e. f. What is the yield on an 8-year Treasury bond? What is the yield on an 8-year BBB-rated corporate bond with a liquidity premium of 0.5 percent? If the yield on a 9-year Treasury bond is 7.3 percent, what does that imply about expected inflation in 9 years? ST-3 Pure expectations theory The yield on one-year Treasury securities is 6 percent, 2-year securities yield 6.2 percent, and three-year securities yield 6.3 percent. There is no maturity risk premium. Using expectations theory, forecast the yields on the following securities: a. A 1-year security, 1 year from now? b. A 1-year security, 2 years from now? c. A 2-year security, 1 year from now? QUESTIONS 6-1 Suppose interest rates on residential mortgages of equal risk were 5.5 percent in California and 7.0 percent in New York. Could this differential persist? What forces might tend to equalize rates? Would differentials in borrowing costs for businesses of equal risk located in California and New York be more or less likely to exist than differentials in residential mortgage rates? Would differentials in the cost of money for New York and California firms be more likely to exist if the firms being compared were very large or if they were very small? What are the implications of all this with respect to nationwide branching? Which fluctuate more, long-term or short-term interest rates? Why? Suppose you believe that the economy is just entering a recession. Your firm must raise capital immediately, and debt will be used. Should you borrow on a long-term or a short-term basis? Why? Suppose the population of Area Y is relatively young while that of Area O is relatively old, but everything else about the two areas is equal. a. Would interest rates likely be the same or different in the two areas? Explain. b. Would a trend toward nationwide branching by banks and savings and loans, and the development of nationwide diversified financial corporations, affect your answer to part a? Suppose a new process was developed that could be used to make oil out of seawater. The equipment required is quite expensive, but it would, in time, lead to very low prices for gasoline, electricity, and other types of energy. What effect would this have on interest rates? Suppose a new and much more liberal Congress and administration were elected, and their first order of business was to take away the independence of the Federal Reserve System and to force the Fed to greatly expand the money supply. What effect would this have a. On the level and slope of the yield curve immediately after the announcement? b. On the level and slope of the yield curve that would exist two or three years in the future? It is a fact that the federal government (1) encouraged the development of the savings and loan industry; (2) virtually forced the industry to make long-term, fixed-interest-rate mortgages; and (3) forced the savings and loans to obtain most of their capital as deposits that were withdrawable on demand. a. Would the savings and loans have higher profits in a world with a "normal" or an inverted yield curve? b. Would the savings and loan industry be better off if the individual institutions sold their mortgages to federal agencies and then collected servicing fees or if the institutions held the mortgages that they originated? Suppose interest rates on Treasury bonds rose from 5 to 9 percent as a result of higher interest rates in Europe. What effect would this have on the price of an average company's common stock? What does it mean when it is said that the United States is running a trade deficit? What impact will a trade deficit have on interest rates? 6-2 6-3 6-4 6-5 6-6 6-7 6-8 6-9 Chapter 6 Interest Rates 203 PROBLEMS Easy Problems 17 6-1 Yield curves The following yields on U.S. Treasury securities were taken from a recent financial publication: Term 6 months 1 year 2 years 3 years 4 years 5 years 10 years 20 years 30 years Rate 5.1% 5.5 5.6 5.7 5.8 6.0 6.1 6.5 6.3 a. b. c. d. Plot a yield curve based on these data. What type of yield curve is shown? What information does this graph tell you? Based on this yield curve, if you needed to borrow money for longer than one year, would it make sense for you to borrow short term and renew the loan or borrow long term? Explain. 6-2 Real risk-free rate You read in The Wall Street Journal that 30-day T-bills are currently yielding 5.5 percent. Your brother-in-law, a broker at Safe and Sound Securities, has given you the following estimates of current interest rate premiums: Inflation premium 3.25% Liquidity premium 0.6% Maturity risk premium 1.8% Default risk premium 2.15% On the basis of these data, what is the real risk-free rate of return? 6-3 Expected interest rate The real risk-free rate is 3 percent. Inflation is expected to be 2 percent this year and 4 percent during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities? Default risk premium A Treasury bond that matures in 10 years has a yield of 6 percent. A 10-year corporate bond has a yield of 8 percent. Assume that the liquidity premium on the corporate bond is 0.5 percent. What is the default risk premium on the corporate bond? Maturity risk premium The real risk-free rate is 3 percent, and inflation is expected to be 3 percent for the next 2 years. A 2-year Treasury security yields 6.2 percent. What is the maturity risk premium for the 2-year security? Inflation cross-product An analyst is evaluating securities in a developing nation where the inflation rate is very high. As a result, the analyst has been warned not to ignore the cross-product between the real rate and inflation. If the real risk-free rate is 5 percent and inflation is expected to be 16 percent each of the next 4 years, what is the yield on a 4-year security with no maturity, default, or liquidity risk? (Hint: Refer to the box titled "The Links Between Expected Inflation and Interest Rates: A Closer Look.") Expectations theory One-year Treasury securities yield 5 percent. The market anticipates that 1 year from now, 1-year Treasury securities will yield 6 percent. If the pure expectations theory is correct, what is the yield today for 2-year Treasury securities? Expectations theory Interest rates on 4-year Treasury securities are currently 7 percent, while 6-year Treasury securities yield 7.5 percent. If the pure expectations theory is correct, what does the market believe that 2-year securities will be yielding 4 years from now? Expected interest rate The real risk-free rate is 3 percent. Inflation is expected to be 3 percent this year, 4 percent next year, and then 3.5 percent thereafter. The maturity risk premium is estimated to be 0.05 (t 1)%, where t number of years to maturity. What is the yield on a 7-year Treasury note? 6-4 6-5 6-6 6-7 Intermediate Problems 816 6-8 6-9 204 Part 3 Financial Assets 6-10 Inflation Due to a recession, expected inflation this year is only 3 percent. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3 percent. Assume that the expectations theory holds and the real risk-free rate is r* 2%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 2 percent, what inflation rate is expected after Year 1? Default risk premium A company's 5-year bonds are yielding 7.75 percent per year. Treasury bonds with the same maturity are yielding 5.2 percent per year, and the real risk-free rate (r*) is 2.3 percent. The average inflation premium is 2.5 percent, and the maturity risk premium is estimated to be 0.1 (t 1)%, where t number of years to maturity. If the liquidity premium is 1 percent, what is the default risk premium on the corporate bonds? Maturity risk premium An investor in Treasury securities expects inflation to be 2.5 percent in Year 1, 3.2 percent in Year 2, and 3.6 percent each year thereafter. Assume that the real risk-free rate is 2.75 percent, and that this rate will remain constant. Three-year Treasury securities yield 6.25 percent, while 5-year Treasury securities yield 6.80 percent. What is the difference in the maturity risk premiums (MRPs) on the two securities; that is, what is MRP5 MRP3? Default risk premium The real risk-free rate, r*, is 2.5 percent. Inflation is expected to average 2.8 percent a year for the next 4 years, after which time inflation is expected to average 3.75 percent a year. Assume that there is no maturity risk premium. An 8-year corporate bond has a yield of 8.3 percent, which includes a liquidity premium of 0.75 percent. What is its default risk premium? Expectations theory and inflation Suppose 2-year Treasury bonds yield 4.5 percent, while 1-year bonds yield 3 percent. r* is 1 percent, and the maturity risk premium is zero. a. Using the expectations theory, what is the yield on a 1-year bond, 1 year from now? b. What is the expected inflation rate in Year 1? Year 2? Expectations theory Assume that the real risk-free rate is 2 percent and that the maturity risk premium is zero. If the 1-year bond yield is 5 percent and a 2-year bond (of similar risk) yields 7 percent, what is the 1-year interest rate that is expected for Year 2? What inflation rate is expected during Year 2? Comment on why the average interest rate during the 2-year period differs from the 1-year interest rate expected for Year 2. Inflation cross-product An analyst is evaluating securities in a developing nation where the inflation rate is very high. As a result, the analyst has been warned not to ignore the crossproduct between the real rate and inflation. A 6-year security with no maturity, default, or liquidity risk has a yield of 20.84 percent. If the real risk-free rate is 6 percent, what average rate of inflation is expected in this country over the next 6 years? (Hint: Refer to the box titled, "The Links Between Expected Inflation and Interest Rates: A Closer Look.") Interest rate premiums A 5-year Treasury bond has a 5.2 percent yield. A 10-year Treasury bond yields 6.4 percent, and a 10-year corporate bond yields 8.4 percent. The market expects that inflation will average 2.5 percent over the next 10 years (IP10 2.5%). Assume that there is no maturity risk premium (MRP 0), and that the annual real riskfree rate, r*, will remain constant over the next 10 years. (Hint: Remember that the default risk premium and the liquidity premium are zero for Treasury securities: DRP LP 0.) A 5-year corporate bond has the same default risk premium and liquidity premium as the 10-year corporate bond described above. What is the yield on this 5-year corporate bond? Yield curves Suppose the inflation rate is expected to be 7 percent next year, 5 percent the following year, and 3 percent thereafter. Assume that the real risk-free rate, r*, will remain at 2 percent and that maturity risk premiums on Treasury securities rise from zero on very short-term bonds (those that mature in a few days) to 0.2 percent for 1-year securities. Furthermore, maturity risk premiums increase 0.2 percent for each year to maturity, up to a limit of 1.0 percent on 5-year or longer-term T-bonds. a. Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, 10-, and 20-year Treasury securities, and plot the yield curve. b. Now suppose ExxonMobil, a AAA-rated company, had bonds with the same maturities as the Treasury bonds. As an approximation, plot an ExxonMobil yield curve on the same graph with the Treasury bond yield curve. (Hint: Think about the default risk premium on ExxonMobil's long-term versus its short-term bonds.) c. Now plot the approximate yield curve of Exelon Corp., a risky nuclear utility. Inflation and interest rates In late 1980, the U.S. Commerce Department released new data showing inflation was 15 percent. At the time, the prime rate of interest was 21 percent, a record high. However, many investors expected the new Reagan administration to be more effective in controlling inflation than the Carter administration had been. Moreover, many observers believed that the extremely high interest rates and generally 6-11 6-12 6-13 6-14 6-15 6-16 Challenging Problems 1719 6-17 6-18 6-19 Chapter 6 Interest Rates 205 tight credit, which resulted from the Federal Reserve System's attempts to curb the inflation rate, would lead to a recession, which, in turn, would lead to a decline in inflation and interest rates. Assume that at the beginning of 1981, the expected inflation rate for 1981 was 13 percent; for 1982, 9 percent; for 1983, 7 percent; and for 1984 and thereafter, 6 percent. a. What was the average expected inflation rate over the 5-year period 19811985? (Use the arithmetic average.) b. What average nominal interest rate would, over the 5-year period, be expected to produce a 2 percent real risk-free return on 5-year Treasury securities? c. Assuming a real risk-free rate of 2 percent and a maturity risk premium that equals 0.1 (t)%, where t is the number of years to maturity, estimate the interest rate in January 1981 on bonds that mature in 1, 2, 5, 10, and 20 years, and draw a yield curve based on these data. d. Describe the general economic conditions that could lead to an upward-sloping yield curve. e. If investors in early 1981 expected the inflation rate for every future year was 10 percent (that is, It It+1 10% for t 1 to ), what would the yield curve have looked like? Consider all the factors that are likely to affect the curve. Does your answer here make you question the yield curve you drew in part c? COMPREHENSIVE/SPREADSHEET PROBLEM 6-20 Interest rate determination and yield curves a. What effect would each of the following events likely have on the level of nominal interest rates? (1) Households dramatically increase their savings rate. (2) Corporations increase their demand for funds following an increase in investment opportunities. (3) The government runs a larger than expected budget deficit. (4) There is an increase in expected inflation. b. Suppose you are considering two possible investment opportunities: a 12-year Treasury bond and a 7-year, A-rated corporate bond. The current real risk-free rate is 4 percent, and inflation is expected to be 2 percent for the next 2 years, 3 percent for the following 4 years, and 4 percent thereafter. The maturity risk premium is estimated by this formula: MRP 0.1(t 1)%. The liquidity premium for the corporate bond is estimated to be 0.7 percent. Finally, you may determine the default risk premium, given the company's bond rating, from the default risk premium table in the text. What yield would you predict for each of these two investments? c. Given the following Treasury bond yield information from a recent financial publication, construct a graph of the yield curve. Maturity 1 year 2 years 3 years 4 years 5 years 10 years 20 years 30 years Yield 5.37% 5.47 5.65 5.71 5.64 5.75 6.33 5.94 d. e. f. Based on the information about the corporate bond that was given in part b, calculate yields and then construct a new yield curve graph that shows both the Treasury and the corporate bonds. Which part of the yield curve (the left side or right side) is likely to be the most volatile over time? Using the Treasury yield information above, calculate the following rates: (1) The 1-year rate, 1 year from now. (2) The 5-year rate, 5 years from now. (3) The 10-year rate, 10 years from now. (4) The 10-year rate, 20 years from now. 206 Part 3 Financial Assets Integrated Case Smyth Barry & Company, Part II 6-21 Interest rate determination In Part I of this case, presented in Chapter 5, you were asked to describe the U.S. financial system to Michelle Varga. Varga is a professional tennis player, and your firm (Smyth Barry) manages her money. Varga was impressed with your discussion and has asked you to give her more information about what determines the level of various interest rates. Once again, your boss has prepared some questions for you to consider. a. What are the four most fundamental factors that affect the cost of money, or the general level of interest rates, in the economy? b. What is the real risk-free rate of interest (r*) and the nominal risk-free rate (rRF)? How are these two rates measured? c. Define the terms inflation premium (IP), default risk premium (DRP), liquidity premium (LP), and maturity risk premium (MRP). Which of these premiums is included when determining the interest rate on (1) short-term U.S. Treasury securities, (2) long-term U.S. Treasury securities, (3) short-term corporate securities, and (4) long-term corporate securities? Explain how the premiums would vary over time and among the different securities listed above. d. What is the term structure of interest rates? What is a yield curve? e. Suppose most investors expect the inflation rate to be 5 percent next year, 6 percent the following year, and 8 percent thereafter. The real risk-free rate is 3 percent. The maturity risk premium is zero for bonds that mature in 1 year or less, 0.1 percent for 2-year bonds, and then the MRP increases by 0.1 percent per year thereafter for 20 years, after which it is stable. What is the interest rate on 1-, 10-, and 20-year Treasury bonds? Draw a yield curve with these data. What factors can explain why this constructed yield curve is upward sloping? f. At any given time, how would the yield curve facing a AAA-rated company compare with the yield curve for U.S. Treasury securities? At any given time, how would the yield curve facing a BB-rated company compare with the yield curve for U.S. Treasury securities? Draw a graph to illustrate your answer. g. What is the pure expectations theory? What does the pure expectations theory imply about the term structure of interest rates? h. Suppose that you observe the following term structure for Treasury securities: Maturity 1 year 2 years 3 years 4 years 5 years Yield 6.0% 6.2 6.4 6.5 6.5 i. Assume that the pure expectations theory of the term structure is correct. (This implies that you can use the yield curve given above to "back out" the market's expectations about future interest rates.) What does the market expect will be the interest rate on 1-year securities 1 year from now? What does the market expect will be the interest rate on 3-year securities 2 years from now? Finally, Varga is also interested in investing in countries other than the United States. Describe the various types of risks that arise when investing overseas. Please go to the ThomsonNOW Web site to access the Cyberproblems. C H APTE R 7 BONDS AND THEIR VALUATION Sizing Up Risk in the Bond Market Many investors view Treasury securities as a safe but lackluster place to invest their funds. Treasuries are among the safest investments; nevertheless, in any given year, changing interest rates can cause significant changes in bond values, particularly for long-term bonds. For example, long-term Treasuries lost nearly 9 percent in 1999. More recently, Treasury bonds have performed quite well--indeed, they outperformed stocks in three of the five years between 2000 and 2004. All bonds don't move in the same direction. Because of call and default risks, corporate bonds have higher yields than Treasuries. The yield spread between high-grade corporate and Treasury bonds is fairly small, but it is quite wide for companies with lower credit ratings and thus higher default risk. Indeed, changes in a firm's credit situation can cause dramatic shifts in its yield spreads. For example, amidst concerns about WorldCom's long-term viability, the spread on its five-year bonds that once had been just 1.67 percent jumped to over 20 percent in mid-2002. These bonds subsequently defaulted, which is what the huge spread predicted. When all is going well in the economy, corporate bonds generally return more to investors than Treasuries. However, when the economy weakens and concerns about defaults rise, corporate bonds do worse than Treasuries. For example, from the beginning of 2000 to the end of 2002, a sluggish economy and the string of accounting scandals led to some major corporate defaults, which worried investors. Corporate bond prices declined relative to Treasury prices, and the result was an increase in the average yield spread. Since the beginning of 2003, though, the spread has declined as the economy rebounded. AP PHOTO/JACQUELINE ROGGENBRODT 208 Part 3 Financial Assets To deal with these various risks, a recent BusinessWeek Online article gave investors the following useful advice: Take the same diversified approach to bonds as you do with stocks. Blend in U.S. government, corporate--both high-quality and high-yield--and perhaps even some foreign government debt. If you're investing taxable dollars, consider tax-exempt municipal bonds. And it doesn't hurt to layer in some inflation-indexed bonds. Sources: Susan Scherreik, "Getting the Most Bang Out of Your Bonds," BusinessWeek Online, November 12, 2001; and Stocks, Bonds, Bills, and Inflation: 2005 Yearbook (Valuation Edition), (Chicago: Ibbotson Associates, 2005). Putting Things In Perspective Bonds are one of the most important securities. If you skim through The Wall Street Journal, you will see references to a wide variety of bonds. This variety may seem confusing, but in actuality only a few characteristics distinguish the various types of bonds. In this chapter, we discuss the types of bonds companies and governments issue, the terms built into bond contracts, the procedures for determining bond prices and rates of return, and the types of risk bond investors and issuers face. 7.1 WHO ISSUES BONDS? Bond A long-term debt instrument. A bond is a long-term contract under which a borrower agrees to make payments of interest and principal, on specific dates, to the holders of the bond. For example, on January 3, 2006, Allied Food Products borrowed $50 million by issuing $50 million of bonds. For convenience, we assume that Allied sold 50,000 individual bonds for $1,000 each. Actually, it could have sold one $50 million bond, 10 bonds each with a $5 million face value, or any other combination that totals to $50 million. In any event, Allied received the $50 million, and in exchange it promised to make annual interest payments and to repay the $50 million on a specified maturity date. Until the 1970s, most bonds were beautifully engraved pieces of paper, and their key terms, including their face values, were spelled out on the bonds themselves. Today, though, virtually all bonds are represented by electronic data stored in secure computers, much like the "money" in a bank checking account.1 1 The Internal Revenue Service put pressure on corporations to move from paper bonds to "book entry" bonds for two reasons: (1) With paper bonds, there was no systematic record of who received interest payments, hence it was relatively easy for bondholders to cheat on their income taxes. (2) People could store unregistered paper bonds in safe-deposit boxes, and when they died, their heirs could simply remove them and thereby evade estate taxes. Book entry prevents these evasions. Chapter 7 Bonds and Their Valuation 209 Investors have many choices when investing in bonds, but bonds are classified into four main types: Treasury, corporate, municipal, and foreign. Each differs with respect to risk and consequently to its expected return. Treasury bonds, generally called Treasuries and sometimes referred to as government bonds, are issued by the federal government.2 It is reasonable to assume that the federal government will make good on its promised payments, so Treasuries have no default risk. However, these bonds' prices decline when interest rates rise, so they are not completely risk free. Corporate bonds, as the name implies, are issued by corporations. Unlike Treasuries, corporate bonds are exposed to default risk--if the issuing company gets into trouble, it may be unable to make the promised interest and principal payments. Different corporate bonds have different levels of default risk, depending on the issuing company's characteristics and on the terms of the specific bond. Default risk is often referred to as "credit risk," and, as we saw in Chapter 6, the larger the default risk, the higher the interest rate investors demand. Municipal bonds, or "munis," are issued by state and local governments. Like corporates, munis are exposed to some default risk. However, munis offer one major advantage over all other bonds: As we discussed in Chapter 3, the interest earned on most munis is exempt from federal taxes, and also from state taxes if the holder is a resident of the issuing state. Consequently, the interest rates on munis are considerably lower than on corporates of equivalent risk. Foreign bonds are issued by foreign governments or foreign corporations. Foreign corporate bonds are, of course, exposed to default risk, and so are the bonds of some foreign governments. An additional risk exists if the bonds are denominated in a currency other than that of the investor's home currency. For example, if you purchase a corporate bond denominated in Japanese yen, even if the company does not default you still could lose money if the Japanese yen falls relative to the dollar. Treasury Bonds Bonds issued by the federal government, sometimes referred to as government bonds. Corporate Bonds Bonds issued by corporations. Municipal Bonds Bonds issued by state and local governments. Foreign Bonds Bonds issued by either foreign governments or foreign corporations. What is a bond? What are the four main types of bonds? Why are U.S. Treasury bonds not completely riskless? In addition to default risk, what key risk do investors in foreign bonds face? 7.2 KEY CHARACTERISTICS OF BONDS Although all bonds have some common characteristics, different bonds also have some different contractual features. For example, most corporate bonds have provisions for early repayment (call features), but the specific call provisions can vary widely among different bonds. Similarly, some bonds are backed by specific assets that must be turned over to the bondholders if the issuer defaults, while other bonds have no such collateral backup. Differences in contractual provisions, and in the fundamental, underlying financial strength of the 2 The U.S. Treasury actually calls its debt "bills," "notes," or "bonds." T-bills generally have maturities of 1 year or less at the time of issue, notes generally have original maturities of 2 to 7 years, and bonds mature in 8 to 30 years. There are technical differences between bills, notes, and bonds, but they are not important for our purposes, so we generally call all Treasury securities "bonds." Note too that a 30-year T-bond at the time of issue becomes a 29-year bond the next year, and it becomes a 1-year bond after 29 years. 210 Part 3 Financial Assets companies backing the bonds, lead to differences in bonds' risks, prices, and expected returns. To understand bonds, it is essential that you understand the following terms. Par Value Par Value The face value of a bond. The par value is the stated face value of the bond; for illustrative purposes we generally assume a par value of $1,000, although any multiple of $1,000 (for example, $5,000 or $5 million) can be used. The par value generally represents the amount of money the firm borrows and promises to repay on the maturity date. Coupon Interest Rate Coupon Payment The specified number of dollars of interest paid each year. Coupon Interest Rate The stated annual interest rate on a bond. Floating-Rate Bond A bond whose interest rate fluctuates with shifts in the general level of interest rates. Zero Coupon Bond A bond that pays no annual interest but is sold at a discount below par, thus providing compensation to investors in the form of capital appreciation. Original Issue Discount (OID) Bond Any bond originally offered at a price below its par value. Maturity Date A specified date on which the par value of a bond must be repaid. Allied Food Products' bonds require the company to pay a fixed number of dollars of interest each year. When this annual coupon payment, as it is called, is divided by the par value, the result is the coupon interest rate. For example, Allied's bonds have a $1,000 par value, and they pay $100 in interest each year. The bond's coupon payment is $100, so its coupon interest rate is $100/$1,000 10%. The $100 is the annual "rent" on the $1,000 loan. This payment, which is set at the time the bond is issued, remains in force during the bond's life.3 Typically, at the time a bond is issued, its coupon payment is set at a level that will induce investors to buy the bond at or near its par value. Most of the examples and problems throughout this text will focus on bonds with fixed coupon rates. In some cases, however, a bond's coupon payment will be allowed to vary over time. These floating-rate bonds work as follows. The coupon rate is set for an initial period, often six months, after which it is adjusted every six months based on some open market rate. For example, many corporate issues are tied to the 10-year Treasury bond rate. Other provisions can be included in these bonds. For example, some are convertible at the holders' option to fixed-rate debt, whereas others have upper and lower limits ("caps" and "floors") on how high or low the rate can go. Some bonds pay no coupons at all, but are offered at a discount below their par values and hence provide capital appreciation rather than interest income. These securities are called zero coupon bonds (zeros). Other bonds pay some coupon interest, but not enough to allow them to be issued at par. In general, any bond originally offered at a price significantly below its par value is called an original issue discount (OID) bond. Some of the details associated with issuing or investing in zero coupon bonds are discussed more fully in Web Appendix 7A. Maturity Date Bonds generally have a specified maturity date on which the par value must be repaid. Allied's bonds, which were issued on January 3, 2006, will mature on January 2, 2021; thus, they had a 15-year maturity at the time they were issued. 3 Back when bonds were pieces of paper, the "main bond" had a number of small (1/2- by 2-inch), dated, coupons attached to them, and on each interest payment date, the owner would "clip the coupon" for that date, send it to the company's paying agent, and receive a check for the interest. A 30-year, semiannual bond would start with 60 coupons, whereas a 5-year, annual payment, bond would start with only 5 coupons. Today, no physical coupons are involved, and interest checks are mailed automatically to the bonds' registered owners. Even so, people continue to use the terms coupon and coupon interest rate when discussing bonds. Chapter 7 Bonds and Their Valuation 211 Most bonds have original maturities (the maturity at the time the bond is issued) ranging from 10 to 40 years, but any maturity is legally permissible.4 Of course, the effective maturity of a bond declines each year after it has been issued. Thus, Allied's bonds had a 15-year original maturity, but in 2007, a year later, they will have a 14-year maturity, and so on. Original Maturity The number of years to maturity at the time a bond is issued. Call Provisions Most corporate and municipal bonds, but not Treasury bonds, contain a call provision, which gives the issuer the right to call the bonds for redemption.5 The call provision generally states that the issuer must pay the bondholders an amount greater than the par value if they are called. The additional sum, which is termed a call premium, is often set equal to one year's interest. For example, the call premium on a 10-year bond with a 10 percent annual coupon and a par value of $1,000 would be $100, which means that the issuer would have to pay investors $1,100 (the par value plus the call premium) if they wanted to call the bonds. In most cases the provisions in the bond contract are set so that the call premium declines over time as the bonds approach maturity. Also, while some bonds are immediately callable, in most cases bonds are often not callable until several years (generally 5 to 10) after issue. This is known as a deferred call, and the bonds are said to have call protection. Suppose a company sold bonds when interest rates were relatively high. Provided the issue is callable, the company could sell a new issue of low-yielding securities if and when interest rates drop, use the proceeds of the new issue to retire the high-rate issue, and thus reduce its interest expense. This process is called a refunding operation. Thus, the call privilege is valuable to the firm but detrimental to long-term investors, who will be forced to reinvest the amount they receive at the new and lower rates. Accordingly, the interest rate on new issues of callable bonds will exceed that on new noncallable bonds. For example, on August 30, 2005, Pacific Timber Company sold a bond issue yielding 8 percent; these bonds were callable immediately. On the same day, Northwest Milling Company sold an issue of similar risk and maturity that yielded only 7.5 percent; its bonds were noncallable for 10 years. Investors were willing to accept a 0.5 percent lower interest rate on Northwest's bonds for the assurance that the 7.5 percent interest rate would be earned for at least 10 years. Pacific, on the other hand, had to incur a 0.5 percent higher annual interest rate to obtain the option of calling the bonds in the event of a decline in rates. Call Provision A provision in a bond contract that gives the issuer the right to redeem the bonds under specified terms prior to the normal maturity date. Sinking Funds Some bonds also include a sinking fund provision that facilitates the orderly retirement of the bond issue. Years ago, firms were required to deposit money with a trustee, which invested the funds and then used the accumulated sum to retire the bonds when they matured. Today, though, sinking fund provisions Sinking Fund Provision A provision in a bond contract that requires the issuer to retire a portion of the bond issue each year. 4 In July 1993, Walt Disney Co., attempting to lock in a low interest rate, issued the first 100-year bonds to be sold by any borrower in modern times. Soon after, Coca-Cola became the second company to stretch the meaning of "long-term bond" by selling $150 million worth of 100-year bonds. 5 The number of new corporate issues with call provisions attached has declined somewhat in recent years. In the 1980s, nearly 80 percent of new issues contained call provisions; however, in recent years this number has fallen to about 35 percent. The use of call provisions also varies with credit quality. Roughly 25 percent of investment-grade bonds issued in recent years have call provisions. By contrast, about 75 percent of recent non-investment-grade bond issues include a call provision. For more information on the use of callable bonds, see Levent Gntay, N. R. Prabhala, and Haluk Unal, "Callable Bonds and Hedging," a Wharton Financial Institutions Center working paper. 212 Part 3 Financial Assets require the issuer to buy back a specified percentage of the issue each year. A failure to meet the sinking fund requirement constitutes a default, which may throw the company into bankruptcy. Therefore, a sinking fund puts a significant cash drain on the firm. In most cases, the issuer can handle the sinking fund in either of two ways: 1. The company can call in for redemption (at par value) a certain percentage of the bonds each year; for example, it might call 5 percent of the total original amount of the issue at a price of $1,000 per bond. The bonds are numbered serially, and those called for redemption are determined by a lottery administered by the trustee. 2. Alternatively, the company can buy the required bonds on the open market. The firm will choose the least-cost method. If interest rates have risen since the bond was issued, then the bond will sell at a price below its par value, so the firm will buy bonds in the open market at a discount. On the other hand, if interest rates have fallen and the bond's price has risen above par, it will use the call option. Note that a call for sinking fund purposes is quite different from a refunding call--a sinking fund call requires no call premium, but only a small percentage of the issue is normally callable in a given year.6 Although sinking funds are designed to protect investors by ensuring that the bonds are retired in an orderly fashion, you should recognize that sinking funds can work to the detriment of bondholders. For example, suppose the bond carries a 10 percent interest rate, but yields on similar bonds have fallen to 7.5 percent. A sinking fund call at par would require a long-term investor to give up a bond that pays $100 of interest and then to reinvest in a bond that pays only $75 per year. This is an obvious disadvantage to those bondholders whose bonds are called. On balance, however, bonds that have a sinking fund are regarded as being safer than those without such a provision, so at the time they are issued sinking fund bonds have lower coupon rates than otherwise similar bonds without sinking funds. Other Features Convertible Bond A bond that is exchangeable, at the option of the holder, for the issuing firm's common stock. Warrant A long-term option to buy a stated number of shares of common stock at a specified price. Putable Bond A bond with provisions that allow its investor to sell it back to the company prior to maturity at a prearranged price. Income Bond A bond that pays interest only if it is earned. Several other types of bonds are used sufficiently often to warrant mention.7 First, convertible bonds are bonds that are exchangeable into shares of common stock, at a fixed price, at the option of the bondholder. Convertibles have lower coupon rates than nonconvertible debt with similar credit risk, but they offer investors the chance for capital gains as compensation for the lower coupon rate. Bonds issued with warrants are similar to convertibles. Warrants are options that permit the holder to buy stock for a stated price, thereby providing a capital gain if the stock's price rises. Bonds issued with warrants, like convertibles, carry lower coupon rates than regular bonds. Unlike callable bonds that give the issuer the option to buy back their debt prior to maturity, putable bonds allow investors to sell the bonds back to the company prior to maturity at a specified price. If interest rates rise, then investors will put these bonds back to the company and reinvest in higher coupon bonds. Another variation is the income bond, which pays interest only if the interest is earned. Thus, income bonds cannot bankrupt a company, but from an investor's standpoint they are riskier than "regular" bonds. Yet another bond 6 7 Some sinking funds require the issuer to pay a call premium. A recent article by John D. Finnerty and Douglas R. Emery reviews new types of debt (and other) securities that have been created in recent years. See "Corporate Securities Innovations: An Update," Journal of Applied Finance: Theory, Practice, Education, Vol. 12, no. 1 (Spring/Summer 2002), pp. 2147. Chapter 7 Bonds and Their Valuation 213 is the indexed, or purchasing power, bond. The interest rate is based on an inflation index such as the consumer price index, so the interest paid rises automatically when the inflation rate rises, thus protecting bondholders against inflation. The U.S. Treasury is the main issuer of indexed bonds, and today (2005) they generally pay from 1 to 2 percent, plus the rate of inflation during the past year. Indexed (Purchasing Power) Bond A bond that has interest payments based on an inflation index so as to protect the holder from inflation. Define floating-rate bonds, zero coupon bonds, putable bonds, income bonds, convertible bonds, and inflation indexed bonds. How is the rate on a floating-rate bond determined? On an indexed bond? What are the two ways sinking funds can be handled? Which alternative will be used if interest rates have risen? Which if interest rates have fallen? 7.3 BOND VALUATION The value of any financial asset--a stock, a bond, a lease, or even physical assets such as apartment buildings or pieces of machinery--is simply the present value of the cash flows the asset is expected to produce. The cash flows for a standard coupon-bearing bond, like those of Allied Foods', consist of interest payments during the bond's 15-year life plus the amount borrowed (generally the par value) when the bond matures. In the case of a floating-rate bond, the interest payments vary over time. For zero coupon bonds, there are no interest payments, so the only cash flow is the face amount when the bond matures. For a "regular" bond with a fixed coupon rate, like Allied's, here is the situation: 0 Bond's value rd 1 INT 2 INT 3 INT N INT M Here rd the bond's market rate of interest 10 percent. This is the discount rate used to calculate the present value of the bond's cash flows, which is also its price. In Chapter 6 we discussed in detail the various factors that determine market interest rates. Note that rd is not the coupon interest rate, and it is equal to the coupon rate if and only if (as in this case) the bond is selling at par. the number of years before the bond matures 15. N declines each year after the bond has been issued, so a bond that had a maturity of 15 years when it was issued (original maturity 15) will have N 14 after one year, N 13 after two years, and so on. At this point we assume that the bond pays interest once a year, or annually, so N is measured in years. Later on, we will analyze semiannual payment bonds, which pay interest each six months. dollars of interest paid each year Coupon rate Par value 0.10($1,000) $100. In calculator terminology, INT PMT 100. If the N INT 214 Part 3 Financial Assets M bond had been a semiannual payment bond, the payment would have been $50 each six months. The payment would be zero if Allied had issued zero coupon bonds, and it would vary if the bond had been a "floater." the par, or maturity, value of the bond $1,000. This amount must be paid at maturity. We can now redraw the time line to show the numerical values for all variables except the bond's value, VB: 0 VB 10% 1 100 2 100 3 100 15 100 1,000 1,100 The following general equation can be solved to find the value of any bond: Bond's value, VB INT 11 rd 2 1 INT a 11 r 2 t t 1 d 15 N INT 11 rd 2 2 M 11 rd 2 N ### INT 11 rd 2 N M 11 rd 2 N (7-1) Inserting values for our particular bond, we have VB $100 a 11.102 t t 1 $1,000 11.102 15 The cash flows consist of an annuity of N years plus a lump sum payment at the end of Year N, and this fact is reflected in Equation 7-1. We could simply discount each cash flow back to the present and sum these PVs to find the bond's value; see Figure 7-1 for an example. However, this procedure is not very efficient, especially if the bond has many years to maturity. Therefore, we use a financial calculator to solve the problem. Here is the setup: Inputs: 15 10 100 1000 N Output: I/YR PV = 1,000 PMT FV Simply input N 15, rd I/YR 10, INT PMT 100, M FV 1000, and then press the PV key to find the bond's value, $1,000.8 Since the PV is an outflow to the investor, it is shown with a negative sign. The calculator is programmed to solve Equation 7-1: It finds the PV of an annuity of $100 per year for 15 years, discounted at 10 percent, then it finds the PV of the $1,000 maturity payment, and then it adds these two PVs to find the bond's value. In this example the bond is selling at a price equal to its par value. Whenever the going rate of interest, rd, is equal to the coupon rate, a fixed-rate bond 8 Spreadsheets can also be used to solve for the bond's value, as we show in the Excel model for this chapter. Chapter 7 Bonds and Their Valuation 215 FIGURE 7-1 Time Line for Allied Food Products' Bonds, 10% Interest Rate 1/3/07 1/08 1/09 1/10 1/11 100 100 100 1/12 1/13 1/14 1/15 100 100 100 100 1/16 1/17 100 100 1/18 1/19 1/20 100 100 100 1/2/2021 100 1,000 Payments 90.91 82.64 75.13 68.30 62.09 56.45 51.32 46.65 42.41 38.55 35.05 31.86 28.97 26.33 23.94 Present Value 239.39 100 100 1,000.00 when rd 10% will sell at its par value. Normally, the coupon rate is set at the going rate when a bond is issued, causing it to sell at par initially. The coupon rate remains fixed after the bond is issued, but interest rates in the market move up and down. Looking at Equation 7-1, we see that an increase in the market interest rate (rd) will cause the price of an outstanding bond to fall, whereas a decrease in rates will cause the bond's price to rise. For example, if the market interest rate on Allied's bond increased to 15 percent immediately after it was issued, we would recalculate the price with the new market interest rate as follows: Inputs: 15 15 100 1000 N Output: I/YR PV = 707.63 PMT FV The price would fall to $707.63. Notice that the bond would then sell at a price below its par value. Whenever the going rate of interest rises above the coupon rate, a fixed-rate bond's price will fall below its par value, and it is called a discount bond. On the other hand, bond prices rise when market interest rates fall. For example, if the market interest rate on Allied's bond decreased to 5 percent, we would once again recalculate its price: Inputs: Discount Bond A bond that sells below its par value; occurs whenever the going rate of interest is above the coupon rate. 15 5 100 1000 N Output: I/YR PV = 1,518.98 PMT FV 216 Part 3 Financial Assets Premium Bond A bond that sells above its par value; occurs whenever the going rate of interest is below the coupon rate. In this case the price rises to $1,518.98. In general, whenever the going interest rate falls below the coupon rate, a fixed-rate bond's price will rise above its par value, and it is called a premium bond. A bond that matures in eight years has a par value of $1,000, an annual coupon payment of $70, and a market interest rate of 9 percent. What is its price? ($889.30) A bond that matures in 12 years has a par value of $1,000, an annual coupon of 10 percent, and a market interest rate of 8 percent. What is its price? ($1,150.72) Which of these bonds is a "discount bond," and which is a "premium bond"? 7.4 BOND YIELDS If you examine the bond market table of The Wall Street Journal or a price sheet put out by a bond dealer, you will typically see information regarding each bond's maturity date, price, and coupon interest rate. You will also see the bond's reported yield. Unlike the coupon interest rate, which is fixed, the bond's reported yield varies from day to day depending on current market conditions. Moreover, the yield can be calculated in three different ways, as we explain in the following sections. Yield to Maturity Suppose you were offered a 14-year, 10 percent annual coupon, $1,000 par value bond at a price of $1,494.93. What rate of interest would you earn on your investment if you bought the bond and held it to maturity? This rate is called the bond's yield to maturity (YTM), and it is the interest rate generally discussed by investors when they talk about rates of return and the rate reported by The Wall Street Journal. To find the YTM, all you need to do is solve Equation 7-1 for rd: Yield to Maturity (YTM) The rate of return earned on a bond if it is held to maturity. VB $1,494.93 $100 11 rd 2 1 ### $100 11 rd 2 14 $1,000 11 rd 2 14 You could substitute values for rd until you find a value that "works" and forces the sum of the PVs on the right side of the equation to equal $1,494.93. However, finding rd YTM by trial and error would be a tedious, time-consuming process that is, as you might guess, easy with a financial calculator.9 Here is the setup: Inputs: 14 1494.93 100 1000 N Output: I/YR =5 PV PMT FV 9 You could also find the YTM with a spreadsheet. In Excel, you would use the Rate function, inputting Nper 14, Pmt 100, Pv 1494.93, Fv 1000, 0 for Type, and leave Guess blank. Chapter 7 Bonds and Their Valuation 217 Simply enter N 14, PV 1494.93, PMT 100, and FV 1000, and then press the I/YR key. The answer, 5 percent, will then appear. The yield to maturity can also be viewed as the bond's promised rate of return, which is the return that investors will receive if all the promised payments are made. However, the yield to maturity equals the expected rate of return only if (1) the probability of default is zero and (2) the bond cannot be called. If there is some default risk, or if the bond may be called, then there is some probability that the promised payments to maturity will not be received, in which case the calculated yield to maturity will differ from the expected return. Note also that a bond's yield to maturity changes whenever interest rates in the economy change, and this is almost daily. An investor who purchases a bond and holds it until it matures will receive the YTM that existed on the purchase date, but the bond's calculated YTM will change frequently between the purchase date and the maturity date. Yield to Call If you purchased a bond that was callable and the company called it, you would not have the option of holding it until it matured. Therefore, the yield to maturity would not be earned. For example, if Allied's 10 percent coupon bonds were callable, and if interest rates fell from 10 to 5 percent, then the company could call in the 10 percent bonds, replace them with 5 percent bonds, and save $100 $50 $50 interest per bond per year. This would be beneficial to the company, but not to its bondholders. If current interest rates are well below an outstanding bond's coupon rate, then a callable bond is likely to be called, and investors will estimate its expected rate of return as the yield to call (YTC) rather than as the yield to maturity. To calculate the YTC, solve this equation for rd: N Price of callable bond a 11 t 1 INT rd 2 t Call price 11 rd 2 N (7-2) Yield to Call (YTC) The rate of return earned on a bond if it is called before its maturity date. Here N is the number of years until the company can call the bond; call price is the price the company must pay in order to call the bond (it is often set equal to the par value plus one year's interest); and rd is the YTC. To illustrate, suppose Allied's bonds had a provision that permitted the company, if it desired, to call them 10 years after their issue date at a price of $1,100. Suppose further that interest rates had fallen, and one year after issuance the going interest rate had declined, causing their price to rise to $1,494.93. Here is the time line and the setup for finding the bonds' YTC with a financial calculator: 0 1,494.93 YTC = ? 1 100 2 100 8 100 9 100 1,100 Inputs: 9 1494.93 100 1100 N Output: I/YR 4.21 = YTC PV PMT FV The YTC is 4.21 percent--this is the return you would earn if you bought an Allied bond at a price of $1,494.93 and it was called nine years from today. (It could not be called until 10 years after issuance, and 1 year has gone by, so there are 9 years left until the first call date.) 218 Part 3 Financial Assets Do you think Allied will call its 10 percent bonds when they become callable? Allied's action will depend on what the going interest rate is when they become callable. If the going rate remains at rd 5%, then Allied could save 10% 5% 5%, or $50 per bond per year, so it would call the 10 percent bonds and replace them with a new 5 percent issue. There would be some costs to the company to refund the bonds, but the interest savings would almost certainly be worth the cost, so Allied would almost certainly refund them. Therefore, you should expect to earn the YTC 4.21% rather than the YTM 5% if you bought the bond under the indicated conditions. In the balance of this chapter, we assume that bonds are not callable unless otherwise noted, but some of the end-of-chapter problems deal with yield to call. Current Yield Current Yield The annual interest payment on a bond divided by the bond's current price. Brokerage house reports on bonds often refer to the current yield, which is defined as the annual interest payment divided by the bond's current price. For example, if Allied's 10 percent coupon bonds were currently selling for $985, the current yield would be $100/$985 10.15%. Unlike the yield to maturity, the current yield does not represent the total return that investors should expect to receive from the bond because it does not take account of the capital gain or loss that will be realized if the bond is held until its maturity (or call). It does provide information regarding the amount of cash income that will be generated in a given year, but it does not provide an accurate measure of the total expected return. This point can be illustrated with a zero coupon bond. Because zeros pay no annual interest, they always have a zero current yield. However, zeros appreciate in value over time, so their total rate of return clearly exceeds zero. Explain the difference between yield to maturity and yield to call. Halley Enterprises' bonds currently sell for $975. They have a sevenyear maturity, an annual coupon of $90, and a par value of $1,000. What is their yield to maturity? Their current yield? (9.51%; 9.23%) The Henderson Company's bonds currently sell for $1,275. They pay a $120 annual coupon and have a 20-year maturity, but they can be called in 5 years at $1,120. What is their YTM and their YTC, and which is "more relevant" in the sense that investors should expect to earn it? (8.99%; 7.31%; YTC) 7.5 CHANGES IN BOND VALUES OVER TIME When a coupon bond is issued, the coupon is generally set at a level that causes the bond's market price to equal its par value. If a lower coupon were set, investors would not be willing to pay $1,000 for the bond, while if a higher coupon were set, investors would clamor for it and bid its price up over $1,000. Investment bankers can judge quite precisely the coupon rate that causes a bond to sell at its $1,000 par value. A bond that has just been issued is known as a new issue. Once it has been issued, it is an outstanding bond, also called a seasoned issue. Newly issued bonds generally sell at prices very close to par, but the prices of outstanding bonds can vary widely from par. Except for floating-rate bonds, coupon payments are constant, so when economic conditions change, a bond with a $100 coupon that sold Chapter 7 Bonds and Their Valuation 219 at its $1,000 par value when it was issued will sell for more or less than $1,000 thereafter. Among its outstanding bonds, Allied currently has three issues that will all mature in 15 years: As we have been discussing, Allied just issued 15-year bonds with a 10 percent coupon rate. These bonds were issued at par, which means that the market interest rate on the bonds was also 10 percent. Because the coupon rate equals the market interest rate, these bonds are trading at par, hence their price is $1,000. Five years ago, Allied issued 20-year bonds with a 7 percent coupon rate. These bonds currently have 15 years remaining until maturity. The bonds were originally issued at par, which means that 5 years ago when these bonds were issued, the market interest rate was 7 percent. For these bonds, the coupon rate is less than the market interest rate, so they sell at a discount. Using a financial calculator or spreadsheet, we can quickly find that they have a price of $771.82. (Set N 15, I/YR 10, PMT 70, FV 1000, and solve for the PV to get the price.) Ten years ago, Allied issued 25-year bonds with a 13 percent coupon rate. These bonds currently have 15 years remaining until maturity. They were originally issued at par, which means that 10 years ago the market interest rate must have been 13 percent. Because the coupon rate on these bonds is greater than the current market interest rate, they sell at a premium. Using a financial calculator or spreadsheet, we can find that their price is $1,228.18. (Set N 15, I/YR 10, PMT 130, FV 1000, and solve for the PV to get the price.) Each of these three bonds has a 15-year maturity, each has the same credit risk, and thus each has the same market interest rate, 10 percent. However, the bonds have different prices because of their different coupon rates. Now let's consider what would happen to the prices of these bonds over time, assuming that market interest rates remained constant at 10 percent and Allied does not default on its bonds. Table 7-1 demonstrates how the prices of each of these bonds will change over time if market interest rates remain at 10 percent. One year from now, each bond will have a maturity of 14 years--that is, N 14. With a financial calculator, just override N 15 with N 14, press the PV key, and you find the value of each bond one year from now. Continuing, set N 13, N 12, and so forth, to see how the prices change over time. Table 7-1 also shows the current yield, the capital gains yield, and the total return over time. For any given year, the capital gains yield is calculated as the bond's annual change in price divided by the beginning-of-year price. For example, if a bond were selling for $1,000 at the beginning of the year and $1,035 at the end of the year, its capital gains yield for the year would be $35/$1,000 3.5%. (If the bond were selling at a premium, then its price would decline over time, and the capital gains yield would be negative but offset by a high current yield.) A bond's total return is equal to the current yield plus the capital gains yield. In the absence of default risk, it is also equal to YTM and the market interest rate, which in our example is 10 percent. Using the information from Table 7-1, Figure 7-2 plots the predicted changes in bond prices for the 7, 10, and 13 percent coupon bonds. Notice that the bonds have very different price paths over time, but at maturity all three bonds will sell at their par value of $1,000. Here are some points about the prices of the bonds over time: The price of the 10 percent coupon bond trading at par would remain at $1,000 if the market interest rate remains at 10 percent, so its current yield would remain at 10 percent and its capital gains yield would be zero each year. 220 TA B L E 7 - 1 Calculation of Current Yields, Capital Gains Yields, and Total Returns for 7%, 10%, and 13% Coupon Bonds When the Market Rate Remains Constant at 10% 7% COUPON BOND 10% COUPON BOND 13% COUPON BOND Number of Years until Maturity Expected Current Yieldb Pricea $1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00 10.0% 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 0.0% 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10.0% 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 $1,228.18 1,221.00 1,213.10 1,204.41 1,194.85 1,184.34 1,172.77 1,160.05 1,146.05 1,130.66 1,113.72 1,095.10 1,074.61 1,052.07 1,027.27 1,000.00 10.6% 10.6 10.7 10.8 10.9 11.0 11.1 11.2 11.3 11.5 11.7 11.9 12.1 12.4 12.7 Pricea 9.1% 9.0 8.9 8.8 8.7 8.6 8.5 8.3 8.2 8.1 7.9 7.7 7.6 7.4 7.2 0.9% 1.0 1.1 1.2 1.3 1.4 1.5 1.7 1.8 1.9 2.1 2.3 2.4 2.6 2.8 10.0% 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 Expected Total Returnd Expected Current Yieldb Expected Total Returnd Expected Current Yieldb Pricea Expected Capital Gains Yieldc Expected Capital Gains Yieldc Expected Capital Gains Yieldc 0.6% 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.5 1.7 1.9 2.1 2.4 2.7 Expected Total Returnd 10.0% 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 $ 771.82 779.00 786.90 795.59 805.15 815.66 827.23 839.95 853.95 869.34 886.28 904.90 925.39 947.93 972.73 1,000.00 Notes: a Using a financial calculator, the price of each bond is calculated by entering the data for N, I/YR, PMT, and FV, then solving for PV the bond's value. b The expected current yield is calculated as the annual interest divided by the price of the bond. c The expected capital gains yield is calculated as the difference between the end-of-year bond price and the beginning-of-year bond price divided by the beginning-ofyear price. d The expected total return is the sum of the expected current yield and the expected capital gains yield. Chapter 7 Bonds and Their Valuation 221 FIGURE 7-2 Time Paths of 7%, 10%, and 13% Coupon Bonds When the Market Rate Remains Constant at 10% Bond Value ($) 1,500 1,250 Coupon = 13% Coupon = 10% 1,000 750 Coupon = 7% 500 0 15 12 9 6 3 0 Years Remaining until Maturity The 7 percent bond trades at a discount, but its price must approach its par value as the maturity date approaches. At maturity it must sell for its par value, because that is the amount the company must give to its holders. So, its price must rise over time. The 13 percent coupon bond trades at a premium, but its price must be equal to its par value at maturity, so it must decline over time. While the prices of the 7 and 13 percent coupon bonds move in opposite directions over time, each bond provides investors with the same total return, 10 percent, which is also the total return on the 10 percent coupon bond that sells at par. The discount bond has a lower coupon rate (and therefore a lower current yield), but it provides a capital gain each year. In contrast, the premium bond has a higher current yield, but it has an expected capital loss each year.10 What is meant by the terms "new issue" and "seasoned issue"? Last year a firm issued 20-year, 8 percent annual coupon bonds at a par value of $1,000. (1) Suppose that one year later the going rate had dropped to 6 percent. What is the new price of the bonds, assuming that they now have 19 years to maturity? ($1,223.16) 10 In this example (and throughout the text) we ignore the tax effects associated with purchasing different types of bonds. For coupon bonds, under the current Tax Code, coupon payments are taxed as ordinary income, whereas capital gains are taxed at the capital gains tax rate. As we mentioned in Chapter 3, for most investors the capital gains tax rate is lower than the personal tax rate. Moreover, while coupon payments are taxed each year, capital gains taxes are deferred until the bond is sold or matures. Consequently, all else equal, investors would end up paying lower taxes on discount bonds, because a greater percentage of their total return comes in the form of capital gains. For details on the tax treatment of zero coupon bonds, see Web Appendix 7A. 222 Part 3 Financial Assets (2) Suppose that one year after issue the going interest rate had been 10 percent (rather than 6 percent). What would the price have been? ($832.70) Why do the prices of fixed-rate bonds fall if expectations for inflation rise? 7.6 BONDS WITH SEMIANNUAL COUPONS Although some bonds pay interest annually, the vast majority actually make payments semiannually. To evaluate semiannual bonds, we must modify the valuation model (Equation 7-1) as follows: 1. Divide the annual coupon interest payment by 2 to determine the dollars of interest paid each six months. 2. Multiply the years to maturity, N, by 2 to determine the number of semiannual periods. 3. Divide the nominal (quoted) interest rate, rd, by 2 to determine the periodic (semiannual) interest rate. Making these changes results in the following equation for finding a semiannual bond's value: 2N VB a 11 t 1 INT>2 rd>22 t 11 M rd>22 2N (7-1a) To illustrate, now assume the Allied Food bonds discussed in Section 7.3 pay $50 of interest each six months rather than $100 at the end of each year. Thus, each interest payment is only half as large, but there are twice as many of them. The coupon rate is thus stated to be "10 percent with semiannual payments."11 When the going (nominal) rate of interest is rd 5% with semiannual compounding, the value of a 15-year, 10 percent semiannual coupon, bond that pays $50 interest every six months, is found as follows: 30 2.5 50 1000 Inputs: N Output: I/YR PV = 1,523.26 PMT FV Enter N 30, rd I/YR 2.5, PMT 50, FV 1000, and then press the PV key to obtain the bond's value, $1,523.26. The value with semiannual interest payments is slightly larger than $1,518.98, the value when interest is paid annually 11 In this situation, the coupon rate of "10 percent paid semiannually," is the rate that bond dealers, corporate treasurers, and investors generally would discuss. Of course, if this bond were issued at par, its effective annual rate would be higher than 10 percent: EAR EFF% a1 rNOM M b M 1 a1 0.10 2 b 2 1 11.052 2 1 10.25% Since 10 percent with annual payments is quite different from 10 percent with semiannual payments, we have assumed a change in effective rates in this section from the situation in Section 7.3, where we assumed 10 percent with annual payments. Chapter 7 Bonds and Their Valuation 223 as we calculated in Section 7.3. This higher value occurs because each interest payment is received somewhat faster under semiannual compounding. Describe how the annual payment bond valuation formula is changed to evaluate semiannual coupon bonds, and write out the revised formula. Hartwell Corporation bonds have a 20-year maturity, an 8 percent semiannual coupon, and a face value of $1,000. The going interest rate (rd) is 7 percent, based on semiannual compounding. What is the bond's price? ($1,106.78) 7.7 ASSESSING A BOND'S RISKINESS Interest Rate Risk As we saw in Chapter 6, interest rates fluctuate over time, and an increase in rates leads to a decline in the value of an outstanding bond. This risk of a decline in bond values due to an increase in interest rates is called interest rate risk (or interest rate price risk). To illustrate, refer back to Allied's bonds, assume once more that they have a 10 percent annual coupon, and assume that you bought one of these bonds at its par value, $1,000. Shortly after your purchase, the going interest rate rises from 10 to 15 percent.12 As we saw in Section 7.3, this interest rate increase would cause the bond's price to fall from $1,000 to $707.63, so you would have a loss of $292.37 on the bond.13 Interest rates can and do rise, and rising rates cause a loss of value for bondholders. Thus, people or firms who invest in bonds are exposed to risk from increasing interest rates. Interest rate risk is higher on bonds with long maturities than on those maturing in the near future.14 This follows because the longer the maturity, the longer before it is paid off and the bondholder can replace it with one with a higher coupon. This point can be demonstrated numerically by showing how the value of a 1-year bond with a 10 percent annual coupon fluctuates with changes in rd, and then comparing these changes with those on a 15-year bond Interest Rate (Price) Risk The risk of a decline in a bond's price due to an increase in interest rates. 12 An immediate increase in rates from 10 to 15 percent would be quite unusual, and it would occur only if something quite bad were revealed about the company or happened in the economy. Smaller but still significant rate increases that adversely affect bondholders do occur fairly often. 13 You would have an accounting (and tax) loss only if you sold the bond; if you held it to maturity, you would not have such a loss. However, even if you did not sell, you would still have suffered a real economic loss in an opportunity cost sense because you would have lost the opportunity to invest at 15 percent and would be stuck with a 10 percent bond in a 15 percent market. In an economic sense, "paper losses" are just as bad as realized accounting losses. 14 Actually, a bond's maturity and coupon rate both affect interest rate risk. Low coupons mean that most of the bond's return will come from repayment of principal, whereas on a high-coupon bond with the same maturity, more of the cash flows will come in during the early years due to the relatively large coupon payments. A measurement called "duration," which finds the average number of years the bond's PV of cash flows remain outstanding, has been developed to combine maturity and coupons. A zero coupon bond, which has no interest payments and whose payments all come at maturity, has a duration equal to its maturity. Coupon bonds all have durations that are shorter than maturity, and the higher the coupon rate, the shorter the duration. Bonds with longer duration are exposed to more interest rate risk. A discussion of duration would go beyond the scope of this book, but see any investments text for a discussion of the concept. 224 Part 3 Financial Assets as calculated previously. The one-year bond's values at different interest rates are shown here: Value of a one-year bond at rd = 5%: Inputs: 1 5 100 1000 N Output (Bond Value): rd = 10%: I/YR PV 1,047.62 PMT FV Inputs: 1 10 100 1000 N Output (Bond Value): rd = 15%: I/YR PV 1,000.00 PMT FV Inputs: 1 15 100 1000 N Output (Bond Value): I/YR PV 956.52 PMT FV You would obtain the first value with a financial calculator by entering N 1, I/YR 5, PMT 100, and FV 1000, and then pressing PV to get $1,047.62. With everything still in your calculator, enter I/YR 10 to override the old I/YR 5, and press PV to find the bond's value at a 10 percent market rate; it drops to $1,000. Then enter I/YR 15 and press the PV key to find the last bond value, $956.52. The effects of increasing rates on the 15-year bond as found earlier can be compared with the just-calculated effects for the 1-year bond. This comparison is shown in Figure 7-3, where we show bond prices at several rates and then plot those prices in the graph. Note how much more sensitive the price of the 15-year bond is to changes in interest rates. At a 10 percent interest rate, both the 15-year and the 1-year bonds are valued at $1,000. When rates rise to 15 percent, the 15-year bond falls to $707.63, but the 1-year bond only falls to $956.52. The price decline for the 1-year bond is only 4.35 percent, while that for the 15-year bond is 29.24 percent. For bonds with similar coupons, this differential interest rate sensitivity always holds true--the longer its maturity, the more its price changes in response to a given change in interest rates. Thus, even if the risk of default on two bonds is exactly the same, the one with the longer maturity is typically exposed to more risk from a rise in interest rates.15 The logical explanation for this difference in interest rate risk is simple. Suppose you bought a 15-year bond that yielded 10 percent, or $100 a year. Now suppose interest rates on comparable-risk bonds rose to 15 percent. You would be stuck with only $100 of interest for the next 15 years. On the other hand, had you bought a 1-year bond, you would have a low return for only 1 year. At the 15 If a 10-year bond were plotted in Figure 7-3, its curve would lie between those of the 15-year and the 1-year bonds. The curve of a one-month bond would be almost horizontal, indicating that its price would change very little in response to an interest rate change, but a 100-year bond would have a very steep slope, and the slope of a perpetuity would be even steeper. Also, a zero coupon bond's price is quite sensitive to interest rate changes, and the longer its maturity, the greater its price sensitivity. Therefore, a 30-year zero coupon bond would have a huge amount of interest rate risk. Chapter 7 Bonds and Their Valuation 225 FIGURE 7-3 Values of Long- and Short-Term 10% Annual Coupon Bonds at Different Market Interest Rates Bond Value ($) 2,500 2,000 1,500 15-Year Bond 1,000 1-Year Bond 500 0 5 10 15 20 25 Interest Rate (%) VALUE OF Current Market Interest Rate, rd 5% 10 15 20 25 1-Year Bond $1,047.62 1,000.00 956.52 916.67 880.00 15-Year Bond $1,518.98 1,000.00 707.63 532.45 421.11 Note: Bond values were calculated using a financial calculator assuming annual, or once-a-year, compounding. end of the year, you would receive your $1,000 back, and you could then reinvest it and earn 15 percent, or $150 per year, for the next 14 years. Thus, interest rate risk reflects the length of time you are committed to a given investment. Reinvestment Rate Risk As we saw in the preceding section, an increase in interest rates will hurt bondholders because it will lead to a decline in the value of a bond portfolio. But can a decrease in interest rates also hurt bondholders? Actually, the answer is yes, because if interest rates fall, long-term bondholders will suffer a reduction in income. For example, consider a retiree who has a bond portfolio and lives off the income it produces. The bonds in the portfolio, on average, have coupon rates of 10 percent. Now suppose interest rates decline to 5 percent. Many of the bonds will be called, and as calls occur, the bondholder will have to replace 226 Part 3 Financial Assets Reinvestment Rate Risk The risk that a decline in interest rates will lead to a decline in income from a bond portfolio. 10 percent bonds with 5 percent bonds. Even bonds that are not callable will mature, and when they do, they too will have to be replaced with lower-yielding bonds. Thus, our retiree will suffer a reduction of income. The risk of an income decline due to a drop in interest rates is called reinvestment rate risk, and its importance has been demonstrated to all bondholders in recent years as a result of the sharp drop in rates since the mid-1980s. Reinvestment rate risk is obviously high on callable bonds. It is also high on shortterm bonds, because the shorter the bond's maturity, the fewer the years before the relatively high old-coupon bonds will be replaced with the new low-coupon issues. Thus, retirees whose primary holdings are short-term bonds or other debt securities will be hurt badly by a decline in rates, but holders of noncallable longterm bonds will continue to enjoy the old high rates. Comparing Interest Rate and Reinvestment Rate Risk Note that interest rate risk relates to the value of the bond portfolio, while reinvestment rate risk relates to the income the portfolio produces. If you hold longterm bonds, you will face significant interest rate risk because the value of your portfolio will decline if interest rates rise, but you will not face much reinvestment rate risk because your income will be stable. On the other hand, if you hold short-term bonds, you will not be exposed to much interest rate price risk, but you will be exposed to significant reinvestment rate risk. Which type of risk is "more relevant" to a given investor depends critically on how long the investor plans to hold the bonds--this is often referred to as the investment horizon. To illustrate, consider first an investor who has a relatively short, one-year investment horizon--say, the investor plans to go to graduate school a year from now and needs money for tuition and expenses. Reinvestment rate risk is of minimal concern to this investor, because there is little time for reinvestment. The investor could eliminate interest rate risk by buying a oneyear Treasury security, since he or she would be assured of receiving the face value of the bond one year from now (the investment horizon). However, if this investor were to buy a long-term Treasury security, he or she would bear a considerable amount of interest rate risk because, as we have seen, long-term bond prices decline if interest rates rise. Consequently, investors with shorter investment horizons should view long-term bonds as being especially risky. By contrast, the reinvestment risk inherent in short-term bonds is especially relevant to investors with longer investment horizons. Consider a retiree who is living on income from his or her portfolio. If this investor buys one-year bonds, he or she will have to "roll them over" every year, and if rates fall, his or her income in subsequent years will likewise decline. A younger couple saving for something like their own retirement or their children's college costs would be affected similarly, because if they buy short-term bonds they too will have to roll their portfolio at possibly much lower rates. Since there is uncertainty today about the rates that will be earned on these reinvested cash flows, long-term investors should be especially concerned about the reinvestment rate risk inherent in short-term bonds. One simple way to minimize both interest rate and reinvestment rate risk is to buy a zero coupon Treasury bond with a maturity that matches the investor's investment horizon. For example, assume your investment horizon is 10 years. If you buy a 10-year zero, you will receive a guaranteed payment in 10 years equal to the bond's face value, hence you face no interest rate price risk. Moreover, as there are no coupons to reinvest, there is no reinvestment rate risk. This Investment Horizon The period of time an investor plans to hold a particular investment. Chapter 7 Bonds and Their Valuation 227 feature explains why investors with specific goals often invest in zero coupon bonds.16 Recall from Chapter 6 that maturity risk premiums are generally positive. Moreover, a positive maturity risk premium implies that investors on average regard longer-term bonds as being riskier than shorter-term bonds. That, in turn, suggests that the average investor is most concerned with interest rate price risk. Still, it is appropriate for each individual investor to consider his or her situation, to recognize the risks inherent in bonds with different maturities, and to construct a portfolio that deals best with the investor's most relevant risk. Differentiate between interest rate risk and reinvestment rate risk. To which type of risk are holders of long-term bonds more exposed? Short-term bondholders? What type of security can be used to minimize both interest rate and reinvestment rate risk for an investor with a fixed investment horizon? 7.8 DEFAULT RISK Potential default is another important risk faced by bondholders. If the issuer defaults, investors will receive less than the promised return. Recall from Chapter 6 that the quoted interest rate includes a default risk premium--the higher the probability of default, the higher the premium and thus the yield to maturity. Default risk on Treasuries is zero, but this risk is substantial for lower-grade corporate and municipal bonds. To illustrate, suppose two bonds have the same promised cash flows--their coupon rates, maturities, liquidity, and inflation exposures are identical, but one has more default risk than the other. Investors will naturally pay more for the one with less chance of default. As a result, bonds with higher default risk will have higher market rates: rd r* IP DRP LP MRP. If its default risk changes, this will affect rd and thus the price. Thus, if the default risk on Allied's bonds increases, their price will fall and the yield to maturity (YTM rd) will increase. In the next sections we consider some issues related to default risk. First, we show that corporations can influence default risk by changing the types of bonds they issue. Second, we discuss bond ratings, which are used to help judge default risk. Finally, we consider bankruptcy and reorganization, which affect how much an investor can expect to recover if a default occurs. 16 Two words of caution about zeros are in order. First, as we show in Web Appendix 7A, investors in zeros must pay taxes each year on their accrued gain in value, even though the bonds don't pay any cash until they mature. Second, buying a zero coupon with a maturity equal to your investment horizon enables you to lock in nominal cash flow, but the value of that cash flow will still depend on what happens to inflation during your investment horizon. What we need is an inflationindexed zero coupon Treasury bond, but to date no such bond exists. Also, the fact that maturity risk premiums are positive suggests that most investors have relatively short investment horizons. See Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2005 Yearbook (Chicago: Ibbotson Associates, 2005), which finds that the maturity risk premium for long-term bonds has averaged 1.4 percent over the past 79 years. 228 Part 3 Financial Assets Various Types of Corporate Bonds Default risk is influenced by both the financial strength of the issuer and the terms of the bond contract, including whether or not collateral has been pledged to secure the bond. Some types of bonds are described in this section. Mortgage Bonds Mortgage Bond A bond backed by fixed assets. First mortgage bonds are senior in priority to claims of second mortgage bonds. Indenture A formal agreement between the issuer and the bondholders. Under a mortgage bond, the corporation pledges specific assets as security for the bond. To illustrate, in 2005, Billingham Corporation needed $10 million to build a regional distribution center. Bonds in the amount of $4 million, secured by a first mortgage on the property, were issued. (The remaining $6 million was financed with equity capital.) If Billingham defaults on the bonds, the bondholders can foreclose on the property and sell it to satisfy their claims. If Billingham had chosen to, it could have issued second mortgage bonds secured by the same $10 million of assets. In the event of liquidation, the holders of the second mortgage bonds would have a claim against the property, but only after the first mortgage bondholders had been paid off in full. Thus, second mortgages are sometimes called junior mortgages because they are junior in priority to the claims of senior mortgages, or first mortgage bonds. All mortgage bonds are subject to an indenture, which is a legal document that spells out in detail the rights of both the bondholders and the corporation. The indentures of many major corporations were written 20, 30, 40, or more years ago. These indentures are generally "open ended," meaning that new bonds can be issued from time to time under the same indenture. However, the amount of new bonds that can be issued is virtually always limited to a specified percentage of the firm's total "bondable property," which generally includes all land, plant, and equipment. For example, in the past Savannah Electric Company had provisions in its bond indenture that allowed it to issue first mortgage bonds totaling up to 60 percent of its net fixed assets. If its fixed assets totaled $1 billion, and if it had $500 million of first mortgage bonds outstanding, it could, by the property test, issue another $100 million of bonds (60 percent of $1 billion $600 million). At times, Savannah Electric was unable to issue any new first mortgage bonds because of another indenture provision: its times-interest-earned (TIE) ratio was required to be greater than 2.5, and at times earnings declined to the point where the minimum was violated. Thus, although Savannah Electric passed the property test, it failed the coverage test, so it could not issue any more first mortgage bonds. Savannah Electric then had to finance with junior bonds. Since its first mortgage bonds carried lower interest rates than its junior long-term debt, this restriction was costly. Savannah Electric's neighbor, Georgia Power Company, had more flexibility under its indenture--its interest coverage requirement was only 2.0. In hearings before the Georgia Public Service Commission, it was suggested that Savannah Electric should change its indenture coverage to 2.0 so it could issue more first mortgage bonds. However, this was simply not possible--the holders of the outstanding bonds would have to approve the change, and it is inconceivable that they would vote for a change that would seriously weaken their position. Debentures Debenture A long-term bond that is not secured by a mortgage on specific property. A debenture is an unsecured bond, and as such it provides no specific collateral as security for the obligation. Debenture holders are, therefore, general creditors whose claims are protected by property not otherwise pledged. In practice, the use of debentures depends both on the nature of the firm's assets and on its general credit strength. Extremely strong companies such as General Electric and Chapter 7 Bonds and Their Valuation 229 ExxonMobil can use debentures because they simply do not need to put up property as security for their debt. Debentures are also issued by weak companies that have already pledged most of their assets as collateral for mortgage loans. In this latter case, the debentures are quite risky, and that risk will be reflected in their interest rates. Subordinated Debentures The term subordinate means "below," or "inferior to," and, in the event of bankruptcy, subordinated debt has a claim on assets only after senior debt has been paid in full. Subordinated debentures may be subordinated either to designated notes payable (usually bank loans) or to all other debt. In the event of liquidation or reorganization, holders of subordinated debentures receive nothing until all senior debt, as named in the debentures' indenture, has been paid. Precisely how subordination works, and how it strengthens the position of senior debtholders, is explained in detail in Web Appendix 7B. Subordinated Debenture A bond having a claim on assets only after the senior debt has been paid off in the event of liquidation. Bond Ratings Since the early 1900s, bonds have been assigned quality ratings that reflect their probability of going into default. The three major rating agencies are Moody's Investors Service (Moody's), Standard & Poor's Corporation (S&P), and Fitch Investor's Service. Moody's and S&P's rating designations are shown in Table 7-2.17 The triple- and double-A bonds are extremely safe. Single-A and triple-B bonds are also strong enough to be called investment-grade bonds, and they are the lowest-rated bonds that many banks and other institutional investors are permitted by law to hold. Double-B and lower bonds are speculative, or junk, bonds, and they have a significant probability of going into default. Bond Rating Criteria Bond ratings are based on both qualitative and quantitative factors, some of which are listed below: 1. Various ratios, including the debt ratio and the times-interest-earned ratio. The better the ratios, the higher the rating. Investment-Grade Bonds Bonds rated triple-B or higher; many banks and other institutional investors are permitted by law to hold only investment-grade bonds. Junk Bond A high-risk, high-yield bond. TA B L E 7 - 2 Moody's and S&P Bond Ratings INVESTMENT GRADE JUNK BONDS Baa BBB Ba BB B B Caa CCC C C Moody's S&P Aaa AAA Aa AA A A Note: Both Moody's and S&P use "modifiers" for bonds rated below triple-A. S&P uses a plus and minus system; thus, A designates the strongest A-rated bonds and A the weakest. Moody's uses a 1, 2, or 3 designation, with 1 denoting the strongest and 3 the weakest; thus, within the double-A category, Aa1 is the best, Aa2 is average, and Aa3 is the weakest. 17 In the discussion to follow, reference to the S&P rating is intended to imply the Moody's and Fitch's ratings as well. Thus, triple-B bonds mean both BBB and Baa bonds; double-B bonds mean both BB and Ba bonds; and so on. 230 Part 3 Financial Assets 2. Mortgage provisions: Is the bond secured by a mortgage? If it is, and if the property has a high value relative to the amount of bonded debt, the rating is enhanced. 3. Subordination provisions: Is the bond subordinated to other debt? If so, it will be rated at least one notch below the rating it would have if it were not subordinated. Conversely, a bond with other debt subordinated to it will have a somewhat higher rating. 4. Guarantee provisions: Some bonds are guaranteed by other firms. If a weak company's debt is guaranteed by a strong company (usually the weak company's parent), the bond will be given the strong company's rating. 5. Sinking fund: Does the bond have a sinking fund to ensure systematic repayment? This feature is a plus factor to the rating agencies. 6. Maturity: Other things the same, a bond with a shorter maturity will be judged less risky than a longer-term bond, and this will be reflected in the ratings. 7. Stability: Are the issuer's sales and earnings stable? 8. Regulation: Is the issuer regulated, and could an adverse regulatory climate cause the company's economic position to decline? Regulation is especially important for utility, telephone, and insurance companies. 9. Antitrust: Are any antitrust actions pending against the firm that could erode its position? 10. Overseas operations: What percentage of the firm's sales, assets, and profits are from overseas operations, and what is the political climate in the host countries? 11. Environmental factors: Is the firm likely to face heavy expenditures for pollution remediation? 12. Product liability: Are the firm's products safe? The tobacco companies have for some time been under pressure, and so are their bond ratings. 13. Pension liabilities: Does the firm have unfunded pension and/or employee health insurance liabilities that could pose a future problem? 14. Labor unrest: Are there potential labor problems on the horizon that could weaken the firm's position? As we write this, a number of airlines face this problem, and it has caused their ratings to be lowered. 15. Accounting policies: If a firm's accounting policies, and thus its reported earnings, are questionable, this will have a negative effect on its bond ratings. As we were working on this chapter, the policies of American International Group (AIG) came into question, and its bonds were downgraded shortly after its problems were revealed. Representatives of the rating agencies have consistently stated that no precise formula is used to set a firm's rating: all the factors listed, plus others, are taken into account, but not in a mathematically precise manner. Statistical studies have borne out this contention, for researchers who have tried to predict bond ratings on the basis of quantitative data have had only limited success, indicating that the agencies use subjective judgment when establishing a firm's rating.18 Nevertheless, as we see in Table 7-3, there is a strong correlation between bond ratings and many of the ratios that we described in Chapter 4. Not surprisingly, companies with lower debt ratios, higher free cash flow to debt, higher returns on invested capital, higher EBITDA coverage ratios, and higher TIE ratios typically have higher bond ratings. Importance of Bond Ratings Bond ratings are important both to firms and to investors. First, because a bond's rating is an indicator of its default risk, the rating has a direct, measurable 18 See Amed Belkaoui, Industrial Bonds and the Rating Process (London: Quorum Books, 1983). Chapter 7 Bonds and Their Valuation 231 TA B L E 7 - 3 Bond Rating Criteria; Three-Year (19982000) Median Financial Ratios for Different Bond Rating Classifications of Industrial Companiesa AAA AA 10.1 12.9 55.4% 25.2 21.7 22.1 28.2 37.7 A 6.1 9.1 43.2% 15.0 19.4 18.6 33.9 42.5 BBB 3.7 5.8 30.8% 8.5 13.6 15.4 42.5 48.2 BB 2.1 3.4 18.8% 2.6 11.6 15.9 57.2 62.6 B 0.8 1.8 7.8% (3.2) 6.6 11.9 69.7 74.8 CCC 0.1 1.3 1.6% (12.9) 1.0 11.9 68.8 87.7 Times-interest-earned (EBIT/Interest) EBITDA interest coverage (EBITDA/Interest) Net cash flow/Total debt Free cash flow/Total debt Return on capital Operating income/Salesb Long-term debt/Total capital Total debt/Total capital 21.4 26.5 128.8% 84.2 34.9 27.0 13.3 22.9 Notes: a Somewhat different criteria are applied to firms in different industries, such as utilities and financial corporations. This table pertains to industrial companies, which include manufacturers, retailers, and service firms. b Operating income here is defined as sales minus cost of goods manufactured (before depreciation and amortization), selling, general and administrative, and research and development costs. Source: Adapted from "Adjusted Key Industrial Financial Ratios," Standard & Poor's 2002 Corporate Ratings Criteria, July 21, 2003, p. 54. influence on the bond's interest rate and the firm's cost of debt. Second, most bonds are purchased by institutional investors rather than individuals, and many institutions are restricted to investment-grade securities. Thus, if a firm's bonds fall below BBB, it will have a difficult time selling new bonds because many potential purchasers will not be allowed to buy them. As a result of their higher risk and more restricted market, lower-grade bonds have higher required rates of return, rd, than high-grade bonds. Figure 7-4 illustrates this point. In each of the years shown on the graph, U.S. government bonds have had the lowest yields, AAA bonds have been next, and BBB bonds have had the highest yields. The figure also shows that the gaps between yields on the three types of bonds vary over time, indicating that the cost differentials, or yield spreads, fluctuate from year to year. This point is highlighted in Figure 7-5, which gives the yields on the three types of bonds and the yield spreads for AAA and BBB bonds over Treasuries in May 2002 and January 2005.19 Note first from Figure 7-5 that the risk-free rate, or vertical axis intercept, was lower in early 2005 than it was in May 2002, primarily reflecting the decline in 19 A yield spread is related to but not identical to risk premiums on corporate bonds. The true risk premium reflects only the difference in expected (and required) returns between two securities that results from differences in their risk. However, yield spreads reflect (1) a true risk premium; (2) a liquidity premium, which reflects the fact that U.S. Treasury bonds are more readily marketable than most corporate bonds; (3) a call premium, because most Treasury bonds are not callable whereas corporate bonds are; and (4) an expected loss differential, which reflects the probability of loss on the corporate bonds. As an example of the last point, suppose the yield to maturity on a BBB bond was 6.0 percent versus 4.8 percent on government bonds, but there was a 5 percent probability of total default loss on the corporate bond. In this case, the expected return on the BBB bond would be 0.95(6.0%) 0.05(0%) 5.7%, and the yield spread would be 0.9%, not the full 1.2 percentage points difference in "promised" yields to maturity. 232 Part 3 Financial Assets FIGURE 7-4 Yield (%) 10 Yields on Selected Long-Term Bonds, 19942005 Narrow Spread Corporate BBB 10 8 8 6 6 4 U.S. Government Corporate AAA Wide Spread 4 0 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 0 2005 Source: Federal Reserve Statistical Release, Selected Interest Rates (Historical Data), http://www .federalreserve.gov/releases/H15/data.htm. both real rates and expected inflation over the past few years. Second, the slope of the line has also decreased, indicating a decrease in investors' risk aversion. Thus, the penalty for having a low credit rating varies over time. Occasionally, as in 2002, the penalty is quite large, but at times like 1995 (shown in Figure 7-4) and in 2005 (shown in Figures 7-4 and 7-5) it is small. These spread differences reflect both investors' risk aversion and also their optimism or pessimism regarding the economy and corporate profits. In 2002, as more and more corporate scandals were being revealed, investors were both pessimistic and risk averse, so spreads were quite high. Changes in Ratings Changes in a firm's bond rating affect both the firm's ability to borrow funds capital and its cost of that capital. Rating agencies review outstanding bonds on a periodic basis, occasionally upgrading or downgrading a bond as a result of its issuer's changed circumstances. For example, the February 10, 2005, issue of Standard & Poor's CreditWeek Focus reported that Gap Inc.'s corporate credit rating was upgraded from BB to BBB . The improved rating moved Gap's bonds into the investment-grade category. The rating upgrade reflected Gap's improved operating performance and its continued strong liquidity. On the other hand, a little more than a week later, CreditWeek Focus warned that it might have to downgrade the bonds of New York Times Co. The warning cited fears that the Times may have taken on too much debt to finance a recent acquisition. In the Chapter 7 Bonds and Their Valuation 233 FIGURE 7-5 Relationship between Bond Ratings and Bond Yields, 2002 and 2005 Yield (%) 9.0 8.0 7.0 6.0 5.0 4.0 3.0 May 2002 Yield SpreadBBB = 2.3% Yield SpreadAAA = 1.0% January 2005 Yield SpreadBBB = 1.2% Yield SpreadAAA = 0.6% U.S. Treasury Bonds Long-Term Government Bonds (Default-Free) (1) May 2002 January 2005 5.8% 4.8 AAA BBB Bond Ratings AAA Corporate Bonds (2) 6.8% 5.4 BBB Corporate Bonds (3) 8.1% 6.0 AAA (4) (2) YIELD SPREADS BBB (1) (5) (3) 2.3% 1.2 (1) 1.0% 0.6 Source: Federal Reserve Statistical Release, Selected Interest Rates (Historical Data), http://www.federalreserve.gov/releases/H15/data.htm. months that follow, the company may choose to strengthen its balance sheet in order to avoid a downgrade. On balance, it is fair to say that ratings agencies generally do a good job of measuring the average credit risk of bonds, and that they do their best to change ratings whenever they perceive a change in credit quality. At the same time, it is important to understand that ratings do not adjust immediately to changes in credit quality, and in some cases there can be a considerable lag between a change in credit quality and a change in rating. For example, the rating agencies were caught off guard by Enron's rapid decline. Enron declared bankruptcy on a Sunday in December 2001, and the preceding Friday its bonds still carried an investment-grade rating. Bankruptcy and Reorganization When a business becomes insolvent, this means that it doesn't have enough cash to meet its interest and principal payments. A decision must then be made whether to dissolve the firm through liquidation or to permit it to reorganize and thus stay alive. These issues are addressed in Chapters 7 and 11 of the federal bankruptcy statutes, and the final decision is made by a federal bankruptcy court judge. 234 Part 3 Financial Assets The decision to force a firm to liquidate versus permitting it to reorganize depends on whether the value of the reorganized firm is likely to be greater than the value of its assets if they were sold off piecemeal. In a reorganization, the firm's creditors negotiate with management on the terms of a potential reorganization. The reorganization plan may call for restructuring the debt, in which case the interest rate may be reduced, the term to maturity lengthened, or some of the debt may be exchanged for equity. The point of the restructuring is to reduce the financial charges to a level that is supportable by the firm's cash flows. Of course, the common stockholders also have to "take a haircut"--they generally see their position diluted as a result of additional shares being given to debtholders in exchange for accepting a reduced amount of debt principal and interest. A trustee may be appointed by the court to oversee the reorganization, but generally the existing management is allowed to retain control. Liquidation occurs if the company is deemed to be worth more dead than alive. If the bankruptcy court orders a liquidation, assets are auctioned off and the cash obtained is distributed as specified in Chapter 7 of the Bankruptcy Act. Web Appendix 7B provides an illustration of how a firm's assets are distributed after liquidation. For now, you should know that (1) the federal bankruptcy statutes govern both reorganization and liquidation, (2) bankruptcies occur frequently, (3) a priority of the specified claims must be followed when distributing the assets of a liquidated firm, (4) bondholders' treatment depends on the terms of the bond, and (5) stockholders generally receive little in reorganizations and nothing in liquidations because the assets are generally worth less than the amount of debt outstanding. Differentiate between mortgage bonds and debentures. Name the major rating agencies, and list some factors that affect bond ratings. Why are bond ratings important both to firms and to investors? Do bond ratings adjust immediately to changes in credit quality? Explain. Differentiate between Chapter 7 liquidations and Chapter 11 reorganizations. When should each be used? 7.9 BOND MARKETS Corporate bonds are traded primarily in the over-the-counter market. Most bonds are owned by and traded among large financial institutions (for example, life insurance companies, mutual funds, and pension funds, all of which deal in very large blocks of securities), and it is relatively easy for the over-the-counter bond dealers to arrange the transfer of large blocks of bonds among the relatively few holders of the bonds. It would be much more difficult to conduct similar operations in the stock market among the literally millions of large and small stockholders, so a higher percentage of stock trades occur on the exchanges. Information on bond trades in the over-the-counter market is not published, but a representative group of bonds is listed and traded on the bond division of the NYSE. Table 7-4 reprints the "Corporate Bonds" section from The Wall Street Journal that shows the 40 most active issues that traded on March 11, 2005, in descending order of sales volume. Chapter 7 Bonds and Their Valuation 235 TA B L E 7 - 4 The 40 Most Active Fixed-Coupon Corporate Bonds, March 11, 2005 Source: "Corporate Bonds," The Wall Street Journal, March 14, 2005, p. C12. If you look at the first issue shown in Table 7-4, you will see that General Motors had the most actively traded issue on March 11, 2005. These bonds have an 8.375 percent coupon and will mature on July 15, 2033. On March 11, 2005, their price was 94.965 percent of par, or 0.94965 $1,000 $949.65, and their yield to maturity was 8.861 percent. (Thus, similarly rated bonds with a similar maturity would have required a coupon of roughly 8.86 percent on March 11 to sell at par.) Their estimated spread was 405 basis points over 30-year Treasuries. (If you looked at The Wall Street Journal for March 14, 2005, you would see that the 5.375 percent February 2031 Treasury issue's yield on March 11 was 4.81 percent, and 8.86% 4.81% 4.05%, which is the 405 basis points spread shown in Table 7-4.) The last column shows the estimated trading volume on March 11, which was $207,068,000. 236 Part 3 Financial Assets If you examined the table closely, you would note that the GM bonds at the top of the list also have the highest yield and the largest yield spread over Treasuries. This reflects two things: First, the GM bonds at the top of the list have a very long maturity--2033--and when the yield curve is sharply upward sloping, long-term bonds have high yields. However, maturity doesn't explain the high yield spread over Treasuries--that is explained by the fact that GM is now (2005) in financial trouble, and its bonds were just downgraded to junk status. Seven other GM bonds are in the table, and they also have relatively high yields and yield spreads relative to their maturities. Ford also has several bonds in the table, and their yield spreads are second only to those of GM, reflecting its poor financial condition. At the other end of the spectrum we see Time Warner, with a yield of only 3.239 percent and a yield spread so low that it is not even measurable. TW's bonds mature in only six weeks, and investors regard it as inconceivable that the company could go bankrupt in that short time. All the other data in the table have similar logical explanations. As we noted earlier, coupon rates are generally set at levels that reflect the "going rate of interest" on the day the bonds are issued. If the rates were set lower, investors simply would not buy the bonds at the $1,000 par value, so the company could not borrow the money it needed. Thus, bonds generally sell at their par values on the day they are issued, but their prices fluctuate thereafter as interest rates change. Thus, the prices of the bonds in the table range from a low 93.804 (percent of par) for Ford to a high of 132.794 for Sprint, which issued bonds with a high yield but then gained strength (the opposite of GM) and saw its yields fall and its bond prices rise. Why do most bond trades occur in the over-the-counter market? If a bond issue is to be sold at par, at what rate must its coupon rate be set? Explain. Tying It All Together This chapter described the different types of bonds governments and corporations issue, explained how bond prices are established, and discussed how investors estimate the rates of return on bonds. It also discussed the various types of risks that investors face when they buy bonds. It is important to remember that when an investor purchases a company's bonds, the investor is providing the company with capital. Therefore, when a firm issues bonds, the return that investors require on the bonds represents the cost of debt capital to the firm. This point is extended in Chapter 7 Bonds and Their Valuation 237 Chapter 10, where the ideas developed in this chapter are used to help determine a company's overall cost of capital, which is a basic component in the capital budgeting process. In recent years many companies have used zero coupon bonds to raise billions of dollars, while bankruptcy is an important consideration for both companies that issue debt and investors. Therefore, these two related issues are discussed in detail in Web Appendixes 7A and 7B. Please go to the ThomsonNOW Web site to access these appendixes. SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) ST-1 Key terms Define each of the following terms: a. b. c. d. e. f. g. h. i. j. k. l. Bond; treasury bond; corporate bond; municipal bond; foreign bond Par value; maturity date; original maturity Coupon payment; coupon interest rate Floating-rate bond; zero coupon bond; original issue discount (OID) bond Call provision; sinking fund provision; indenture Convertible bond; warrant; putable bond; income bond; indexed, or purchasing power, bond Discount bond; premium bond Yield to maturity (YTM); yield to call (YTC); current yield; total return; yield spread Interest rate risk; reinvestment rate risk; investment horizon Default risk; credit risk Mortgage bond; debenture; subordinated debenture Investment-grade bond; junk bond ST-2 Bond valuation The Pennington Corporation issued a new series of bonds on January 1, 1982. The bonds were sold at par ($1,000), had a 12 percent coupon, and matured in 30 years, on December 31, 2011. Coupon payments are made semiannually (on June 30 and December 31). a. b. c. d. e. What was the YTM on January 1, 1982? What was the price of the bonds on January 1, 1987, 5 years later, assuming that interest rates had fallen to 10 percent? Find the current yield, capital gains yield, and total return on January 1, 1987, given the price as determined in part b. On July 1, 2005, 6.5 years before maturity, Pennington's bonds sold for $916.42. What was the YTM, the current yield, the capital gains yield, and the total return at that time? Now, assume that you plan to purchase an outstanding Pennington bond on March 1, 2005, when the going rate of interest given its risk was 15.5 percent. How large a check must you write to complete the transaction? This is a hard question. 238 Part 3 Financial Assets ST-3 Sinking fund The Vancouver Development Company (VDC) is planning to sell a $100 million, 10-year, 12 percent, annual payment, bond issue. Provisions for a sinking fund to retire the issue over its life will be included in the indenture. Sinking fund payments will be made at the end of each year, and each payment must be sufficient to retire 10 percent of the original amount of the issue. The last sinking fund payment will retire the last of the bonds. The bonds to be retired each period can either be purchased on the open market or obtained by calling up to 5 percent of the original issue at par, at VDC's option. a. How large must each sinking fund payment be if the company (1) uses the option to call bonds at par or (2) decides to buy bonds on the open market? For part (2), you can only answer in words. b. What will happen to debt service requirements per year associated with this issue over its 10-year life? c. Now consider an alternative plan, where VDC sets up its sinking fund so that equal annual amounts are paid into a sinking fund trust held by a bank, with the proceeds being used to buy government bonds that are expected to pay 7 percent annual interest. The payments, plus accumulated interest, must total to $100 million at the end of 10 years, when the proceeds will be used to retire the issue. How large must the annual sinking fund payments be? Is this amount known with certainty, or might it be higher or lower? d. What are the annual cash requirements for covering bond service costs under the trusteeship arrangement described in part c? (Note: Interest must be paid on Vancouver's outstanding bonds but not on bonds that have been retired.) Assume level interest rates for purposes of answering this question. e. What would have to happen to interest rates to cause the company to buy bonds on the open market rather than call them under the plan where some bonds are retired each year? QUESTIONS 7-1 A sinking fund can be set up in one of two ways: a. The corporation makes annual payments to the trustee, who invests the proceeds in securities (frequently government bonds) and uses the accumulated total to retire the bond issue at maturity. b. The trustee uses the annual payments to retire a portion of the issue each year, either calling a given percentage of the issue by a lottery and paying a specified price per bond or buying bonds on the open market, whichever is cheaper. What are the advantages and disadvantages of each procedure from the viewpoint of (a) the firm and (b) the bondholders? 7-2 Is it true that the following equation can be used to find the value of a bond with N years to maturity that pays interest once a year? Assume that the bond was issued several years ago. N VB a t Annual interest 11 rd 2 t 1 Par value 11 rd 2 N 7-3 "The values of outstanding bonds change whenever the going rate of interest changes. In general, short-term interest rates are more volatile than long-term interest rates. Therefore, short-term bond prices are more sensitive to interest rate changes than are long-term bond prices." Is this statement true or false? Explain. (Hint: Make up a "reasonable" example based on a 1-year and a 20-year bond to help answer the question.) If interest rates rise after a bond issue, what will happen to the bond's price and YTM? Does the time to maturity affect the extent to which interest rate changes affect the bond's price? (Again, an example might help you answer this question.) 7-4 Chapter 7 Bonds and Their Valuation 239 7-5 7-6 If you buy a callable bond and interest rates decline, will the value of your bond rise by as much as it would have risen if the bond had not been callable? Explain. Assume that you have a short investment horizon (less than 1 year). You are considering two investments: a 1-year Treasury security and a 20-year Treasury security. Which of the two investments would you view as being more risky? Explain. Indicate whether each of the following actions will increase or decrease a bond's yield to maturity: a. b. c. d. e. The bond's price increases. The bond is downgraded by the rating agencies. A change in the bankruptcy code makes it more difficult for bondholders to receive payments in the event the firm declares bankruptcy. The economy seems to be shifting from a boom to a recession. Discuss the effects of the firm's credit strength in your answer. Investors learn that these bonds are subordinated to another debt issue. 7-7 7-8 7-9 7-10 7-11 7-12 7-13 Why is a call provision advantageous to a bond issuer? When would the issuer be likely to initiate a refunding call? Are securities that provide for a sinking fund more or less risky from the bondholder's perspective than those without this type of provision? Explain. What's the difference between a call for sinking fund purposes and a refunding call? Why are convertibles and bonds with warrants typically offered with lower coupons than similarly rated straight bonds? Explain whether the following statement is true or false: "Only weak companies issue debentures." Would the yield spread on a corporate bond over a Treasury bond with the same maturity tend to become wider or narrower if the economy appeared to be heading into a recession? Would the change in the spread for a given company be affected by the firm's credit strength? A bond's expected return is sometimes estimated by its YTM and sometimes by its YTC. Under what conditions would the YTM provide a better estimate, and when would the YTC be better? 7-14 PROBLEMS Easy Problems 14 7-1 Bond valuation Callaghan Motors' bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8 percent; and the yield to maturity is 9 percent. What is the bond's current market price? Current yield and yield to maturity A bond has a $1,000 par value, 10 years to maturity, a 7 percent annual coupon, and sells for $985. a. b. c. What is its current yield? What is its yield to maturity (YTM)? Assume that the yield to maturity remains constant for the next 3 years. What will the price be 3 years from today? 7-2 7-3 Bond valuation Nungesser Corporation's outstanding bonds have a $1,000 par value, a 9 percent semiannual coupon, 8 years to maturity, and an 8.5 percent YTM. What is the bond's price? Yield to maturity A firm's bonds have a maturity of 10 years with a $1,000 face value, an 8 percent semiannual coupon, are callable in 5 years at $1,050, and currently sell at a price of $1,100. What are their yield to maturity and their yield to call? What return should investors expect to earn on this bond? 7-4 240 Part 3 Financial Assets Intermediate Problems 515 7-5 Bond valuation An investor has two bonds in his portfolio that both have a face value of $1,000 and pay a 10 percent annual coupon. Bond L matures in 15 years, while Bond S matures in 1 year. a. What will the value of each bond be if the going interest rate is 5 percent, 8 percent, and 12 percent? Assume that there is only one more interest payment to be made on Bond S, at its maturity, and 15 more payments on Bond L. b. Why does the longer-term bond's price vary more when interest rates change than does that of the shorter-term bond? Bond valuation An investor has two bonds in his or her portfolio, Bond C and Bond Z. Each matures in 4 years, has a face value of $1,000, and has a yield to maturity of 9.6 percent. Bond C pays a 10 percent annual coupon, while Bond Z is a zero coupon bond. a. Assuming that the yield to maturity of each bond remains at 9.6 percent over the next 4 years, calculate the price of the bonds at the following years to maturity and fill in the following table: Years to Maturity 4 3 2 1 0 Price of Bond C _________ _________ _________ _________ _________ Price of Bond Z _________ _________ _________ _________ _________ 7-6 b. Plot the time path of prices for each bond. 7-7 Interest rate sensitivity An investor purchased the following 5 bonds. Each of them had an 8 percent yield to maturity on the purchase day. Immediately after she purchased them, interest rates fell and each then had a new YTM of 7 percent. What is the percentage change in price for each bond after the decline in interest rates? Fill in the following table: Price @ 8% 10-year, 10% annual coupon 10-year zero 5-year zero 30-year zero $100 perpetuity _______ _______ _______ _______ _______ Price @ 7% _______ _______ _______ _______ _______ Percentage Change _______ _______ _______ _______ _______ 7-8 Yield to call Six years ago, the Singleton Company issued 20-year bonds with a 14 percent annual coupon rate at their $1,000 par value. The bonds had a 9 percent call premium, with 5 years of call protection. Today, Singleton called the bonds. Compute the realized rate of return for an investor who purchased the bonds when they were issued and held them until they were called. Explain why the investor should or should not be happy that Singleton called them. Yield to maturity Heymann Company bonds have 4 years left to maturity. Interest is paid annually, and the bonds have a $1,000 par value and a coupon rate of 9 percent. a. What is the yield to maturity at a current market price of (1) $829 or (2) $1,104? b. Would you pay $829 for each bond if you thought that a "fair" market interest rate for such bonds was 12 percent--that is, if rd 12 percent? Explain your answer. Current yield, capital gains yield, and yield to maturity Hooper Printing Inc. has bonds outstanding with 9 years left to maturity. The bonds have an 8 percent annual coupon rate and were issued 1 year ago at their par value of $1,000, but due to changes in interest rates, the bond's market price has fallen to $901.40. The capital gains yield last year was 9.86 percent. a. What is the yield to maturity? b. For the coming year, what is the expected current yield and the expected capital gains yield? c. Will the actual realized yields be equal to the expected yields if interest rates change? If not, how will they differ? Bond yields Last year Clark Company issued a 10-year, 12 percent semiannual coupon bond at its par value of $1,000. The bond can be called in 4 years at a price of $1,060, and it now sells for $1,100. 7-9 7-10 7-11 Chapter 7 Bonds and Their Valuation 241 a. b. c. What are the bond's yield to maturity and its yield to call? Would an investor be more likely to actually earn the YTM or the YTC? What is the current yield? Is this yield affected by whether or not the bond is likely to be called? What is the expected capital gains (or loss) yield for the coming year? Is this yield dependent on whether or not the bond is expected to be called? 7-12 Yield to call It is now January 1, 2006, and you are considering the purchase of an outstanding bond that was issued on January 1, 2004. It has a 9.5 percent annual coupon and had a 30-year original maturity. (It matures on December 31, 2033.) There was 5 years of call protection (until December 31, 2008), after which time it can be called at 109 (that is, at 109 percent of par, or $1,090). Interest rates have declined since it was issued, and it is now selling at 116.575 percent of par, or $1,165.75. a. What is the yield to maturity? What is the yield to call? b. If you bought this bond, which return do you think you would actually earn? Explain your reasoning. c. Suppose the bond had been selling at a discount rather than a premium. Would the yield to maturity then have been the most likely actual return, or would the yield to call have been most likely? Price and yield An 8 percent semiannual coupon bond matures in 5 years. The bond has a face value of $1,000 and a current yield of 8.21 percent. What are the bond's price and YTM? Current yield A semiannual coupon bond that matures in 7 years sells for $1,020. It has a face value of $1,000 and a yield to maturity of 10.5883 percent. What is its current yield? Expected interest rate Lloyd Corporation's 14 percent coupon rate, semiannual payment, $1,000 par value bonds, which mature in 30 years, are callable 5 years from today at $1,050. They sell at a price of $1,353.54, and the yield curve is flat. Assume interest rates are expected to remain at their current level. a. What is the best estimate of these bonds' remaining life? b. If Lloyd plans to raise additional capital and wants to use debt financing, what coupon rate would it have to set in order to issue new bonds at par? Bond valuation Bond X is noncallable, has 20 years to maturity, a 9 percent annual coupon, and a $1,000 par value. Your required return on Bond X is 10 percent, and if you buy it you plan to hold it for 5 years. You, and the market, have expectations that in 5 years the yield to maturity on a 15-year bond with similar risk will be 8.5 percent. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Bond valuation You are considering a 10-year, $1,000 par value bond. Its coupon rate is 9 percent, and interest is paid semiannually. If you require an "effective" annual interest rate (not a nominal rate) of 8.16 percent, then how much should you be willing to pay for the bond? Bond returns Last year, Joan purchased a $1,000 face value corporate bond with an 11 percent annual coupon rate and a 10-year maturity. At the time of the purchase, it had an expected yield to maturity of 9.79 percent. If Joan sold the bond today for $1,060.49, what rate of return would she have earned for the past year? Bond reporting Look back at Table 7-4, and examine the Albertson's and Ford Motor Co. bonds that mature in 2031. a. If these companies were to sell new $1,000 par value long-term bonds, approximately what coupon interest rate would they have to set if they wanted to bring them out at par? b. If you had $10,000 and wanted to invest in the Ford bonds, what return would you expect to earn? What about the Albertson's bonds? Just based on the data in the table, would you have more confidence about earning your expected rate of return if you bought the Ford or Albertson's bonds? Explain. Yield to maturity and yield to call Kaufman Enterprises has bonds outstanding with a $1,000 face value and 10 years left until maturity. They have an 11 percent annual coupon payment and their current price is $1,175. The bonds may be called in 5 years at 109 percent of face value (Call price $1,090). 7-13 7-14 7-15 Challenging Problems 1620 7-16 7-17 7-18 7-19 7-20 242 Part 3 Financial Assets a. b. c. d. What is the yield to maturity? What is the yield to call, if they are called in 5 years? Which yield might investors expect to earn on these bonds, and why? The bond's indenture indicates that the call provision gives the firm the right to call them at the end of each year beginning in Year 5. In Year 5, they may be called at 109 percent of face value, but in each of the next 4 years the call percentage will decline by 1 percent. Thus, in Year 6 they may be called at 108 percent of face value, in Year 7 they may be called at 107 percent of face value, and so on. If the yield curve is horizontal and interest rates remain at their current level, when is the latest that investors might expect the firm to call the bonds? COMPREHENSIVE/SPREADSHEET PROBLEM 7-21 Bond valuation Clifford Clark is a recent retiree who is interested in investing some of his savings in corporate bonds. His financial planner has suggested the following bonds: Bond A has a 7 percent annual coupon, matures in 12 years, and has a $1,000 face value. Bond B has a 9 percent annual coupon, matures in 12 years, and has a $1,000 face value. Bond C has an 11 percent annual coupon, matures in 12 years, and has a $1,000 face value. Each bond has a yield to maturity of 9 percent. a. Before calculating the prices of the bonds, indicate whether each bond is trading at a premium, discount, or at par. b. Calculate the price of each of the three bonds. c. Calculate the current yield for each of the three bonds. d. If the yield to maturity for each bond remains at 9 percent, what will be the price of each bond 1 year from now? What is the expected capital gains yield for each bond? What is the expected total return for each bond? e. Mr. Clark is considering another bond, Bond D. It has an 8 percent semiannual coupon and a $1,000 face value (that is, it pays a $40 coupon every 6 months). Bond D is scheduled to mature in 9 years and has a price of $1,150. It is also callable in 5 years at a call price of $1,040. (1) What is the bond's nominal yield to maturity? (2) What is the bond's nominal yield to call? (3) If Mr. Clark were to purchase this bond, would he be more likely to receive the yield to maturity or yield to call? Explain your Register to View AnswerExplain briefly the difference between interest rate (or price) risk and reinvestment rate risk. Which of the following bonds has the most interest rate risk? A 5-year bond with a 9 percent annual coupon. A 5-year bond with a zero coupon. A 10-year bond with a 9 percent annual coupon. A 10-year bond with a zero coupon. g. Only do this part if you are using a spreadsheet. Calculate the price of each bond (A, B, and C) at the end of each year until maturity, assuming interest rates remain constant. Create a graph showing the time path of each bond's value similar to Figure 7-2. (1) What is the expected interest yield for each bond in each year? (2) What is the expected capital gains yield for each bond in each year? (3) What is the total return for each bond in each year? Chapter 7 Bonds and Their Valuation 243 Integrated Case Western Money Management Inc. 7-22 Bond valuation Robert Black and Carol Alvarez are vice presidents of Western Money Management and co-directors of the company's pension fund management division. A major new client, the California League of Cities, has requested that Western present an investment seminar to the mayors of the represented cities, and Black and Alvarez, who will make the actual presentation, have asked you to help them by answering the following questions. a. What are a bond's key features? b. What are call provisions and sinking fund provisions? Do these provisions make bonds more or less risky? c. How is the value of any asset whose value is based on expected future cash flows determined? d. How is a bond's value determined? What is the value of a 10-year, $1,000 par value bond with a 10 percent annual coupon if its required return is 10 percent? e. (1) What is the value of a 13 percent coupon bond that is otherwise identical to the bond described in part d? Would we now have a discount or a premium bond? (2) What is the value of a 7 percent coupon bond with these characteristics? Would we now have a discount or a premium bond? (3) What would happen to the values of the 7 percent, 10 percent, and 13 percent coupon bonds over time if the required return remained at 10 percent? [Hint: With a financial calculator, enter PMT, I/YR, FV, and N, and then change (override) N to see what happens to the PV as it approaches maturity.] f. (1) What is the yield to maturity on a 10-year, 9 percent, annual coupon, $1,000 par value bond that sells for $887.00? That sells for $1,134.20? What does the fact that it sells at a discount or at a premium tell you about the relationship between rd and the coupon rate? (2) What are the total return, the current yield, and the capital gains yield for the discount bond? (Assume it is held to maturity and the company does not default on it.) g. What is interest rate (or price) risk? Which has more interest rate risk, an annual payment 1-year bond or a 10-year bond? Why? h. What is reinvestment rate risk? Which has more reinvestment rate risk, a 1-year bond or a 10-year bond? i. How does the equation for valuing a bond change if semiannual payments are made? Find the value of a 10-year, semiannual payment, 10 percent coupon bond if nominal rd 13 percent. j. Suppose you could buy, for $1,000, either a 10 percent, 10-year, annual payment bond or a 10 percent, 10-year, semiannual payment bond. They are equally risky. Which would you prefer? If $1,000 is the proper price for the semiannual bond, what is the equilibrium price for the annual payment bond? k. Suppose a 10-year, 10 percent, semiannual coupon bond with a par value of $1,000 is currently selling for $1,135.90, producing a nominal yield to maturity of 8 percent. However, it can be called after 4 years for $1,050. (1) What is the bond's nominal yield to call (YTC)? (2) If you bought this bond, do you think you would be more likely to earn the YTM or the YTC? Why? l. Does the yield to maturity represent the promised or expected return on the bond? Explain. m. These bonds were rated AA by S&P. Would you consider them investment-grade or junk bonds? n. What factors determine a company's bond rating? o. If this firm were to default on the bonds, would the company be immediately liquidated? Would the bondholders be assured of receiving all of their promised payments? Explain. Please go to the ThomsonNOW Web site to access the Cyberproblems. C H APTE R DYNAMIC GRAPHICS/COMSTOCK/PICTUREQUEST 8 RISK AND RATES OF RETURN No Pain No Gain Throughout the 1990s, the market soared, and investors became accustomed to great stock market returns. In 2000, though, stocks began a sharp decline, leading to a reassessment of the risks inherent in the stock market. This point was underscored by a Wall Street Journal article shortly after the terrorist attacks of September 2001: Investing in the stock market can be risky, sometimes very risky. While that may seem obvious after the Dow Jones Industrial Average posted its worst weekly percentage loss in 61 years and its worstever weekly point loss, it wasn't something that most investors spent much time thinking about during the bull market of the 1990s. Now, with the Bush administration warning of a lengthy battle against terrorism, investment advisors say that the risks associated with owning stocks--as opposed to safer securities with more predictable returns, such as bonds--are poised to rise. This is leading to an increase in what analysts call a "risk premium," and as it gets higher, investors require a greater return from stocks compared to bonds. For most analysts, it is not a question of whether stocks are riskier today than they have been in recent years. Rather, they are asking how much riskier? And for how long will this period of heightened risk continue? It is also important to understand that some stocks are riskier than others. Moreover, even in years when the overall stock market goes up, many individual stocks go down, so there's less risk to holding a "basket" of stocks than just one stock. Indeed, according to a BusinessWeek article, the single best weapon against risk is diversification into stocks that are not highly correlated with one another: "By spreading your money around, you're not tied to the fickleness of a given market, stock, or industry. . . . Correlation, in portfolio-manager speak, helps you diversify properly because it describes how closely two investments Chapter 8 Risk and Rates of Return 245 track each other. If they move in tandem, they're likely to suffer from the same bad news. So, you should combine assets with low correlations." U.S. investors tend to think of "the stock market" as the U.S. stock market. However, U.S. stocks amount to only 35 percent of the value of all stocks. Foreign markets have been quite profitable, and they are not perfectly correlated with U.S. markets. Therefore, global diversification offers U.S. investors an opportunity to raise returns and at the same time reduce risk. However, foreign investing brings some risks of its own, most notably "exchange rate risk," which is the danger that exchange rate shifts will decrease the number of dollars a foreign currency will buy. Although the central thrust of the BusinessWeek article was on measuring and then reducing risk, it also pointed out that some extremely risky instruments have been marketed to naive investors as having very little risk. For example, several mutual funds advertise that their portfolios "contain only securities backed by the U.S. government," but they failed to highlight that the funds themselves were using financial leverage, were investing in "derivatives," or were taking some other action that exposed investors to huge risks. When you finish this chapter, you should understand what risk is, how it can be measured, and how to minimize it or at least be adequately compensated for bearing it. Sources: "Figuring Risk: It's Not So Scary," BusinessWeek, November 1, 1993, pp. 154155; "T-Bill Trauma and the Meaning of Risk," The Wall Street Journal, February 12, 1993, p. C1; and "Stock Risks Poised to Rise in Changed Postattack World," The Wall Street Journal, September 24, 2001, p. C1. Putting Things In Perspective We start this chapter from the basic premise that investors like returns and dislike risk and therefore will invest in risky assets only if those assets offer higher expected returns. We define precisely what the term risk means as it relates to investments, examine procedures that are used to measure risk, and discuss the relationship between risk and return. Investors should understand these concepts, as should managers as they develop the plans that will shape their firms' futures. Risk can be measured in different ways, and different conclusions about an asset's riskiness can be reached depending on the measure used. Risk analysis can be confusing, but it will help if you keep the following points in mind: 1. All financial assets are expected to produce cash flows, and the riskiness of an asset is based on the riskiness of its cash flows. 2. An asset's risk can be considered in two ways: (a) on a stand-alone basis, where the asset's cash flows are analyzed by themselves, or (b) in a portfolio context, where the cash flows from a number of assets are combined and then the consolidated cash flows are analyzed.1 There is an important difference between stand-alone and portfolio risk, and an 1 A portfolio is a collection of investment securities. If you owned some General Motors stock, some ExxonMobil stock, and some IBM stock, you would be holding a three-stock portfolio. Because diversification lowers risk without sacrificing much if any expected return, most stocks are held in portfolios. 246 Part 3 Financial Assets 3. 4. 5. 6. asset that has a great deal of risk if held by itself may be less risky if it is held as part of a larger portfolio. In a portfolio context, an asset's risk can be divided into two components: (a) diversifiable risk, which can be diversified away and is thus of little concern to diversified investors, and (b) market risk, which reflects the risk of a general stock market decline and which cannot be eliminated by diversification, hence does concern investors. Only market risk is relevant to rational investors--diversifiable risk is irrelevant because it can and will be eliminated. An asset with a high degree of relevant (market) risk must offer a relatively high expected rate of return to attract investors. Investors in general are averse to risk, so they will not buy risky assets unless those assets have high expected returns. If investors on average think a security's expected return is too low to compensate for its risk, then the price of the security will decline, which will boost the expected return. Conversely, if the expected return is more than enough to compensate for the risk, then the security's market price will increase, thus lowering the expected return. The security will be in equilibrium when its expected return is just sufficient to compensate for its risk. In this chapter, we focus on financial assets such as stocks and bonds, but the concepts discussed here also apply to physical assets such as computers, trucks, or even whole plants. 8.1 STAND-ALONE RISK Risk The chance that some unfavorable event will occur. Stand-Alone Risk The risk an investor would face if he or she held only one asset. Risk is defined in Webster's as "a hazard; a peril; exposure to loss or injury." Thus, risk refers to the chance that some unfavorable event will occur. If you engage in skydiving, you are taking a chance with your life--skydiving is risky. If you bet on the horses, you are risking your money. As we saw in previous chapters, both individuals and firms invest funds today with the expectation of receiving additional funds in the future. Bonds offer relatively low returns, but with relatively little risk--at least if you stick to Treasury bonds and high-grade corporates. Stocks offer the chance of higher returns, but, as we saw in Chapter 5, stocks are generally riskier than bonds. If you invest in speculative stocks (or, really, any stock), you are taking a significant risk in the hope of making an appreciable return. An asset's risk can be analyzed in two ways: (1) on a stand-alone basis, where the asset is considered in isolation; and (2) on a portfolio basis, where the asset is held as one of a number of assets in a portfolio. Thus, an asset's standalone risk is the risk an investor would face if he or she held only this one asset. Obviously, most assets are held in portfolios, but it is necessary to understand stand-alone risk in order to understand risk in a portfolio context. To illustrate stand-alone risk, suppose an investor buys $100,000 of shortterm Treasury bills with an expected return of 5 percent. In this case, the invest- Chapter 8 Risk and Rates of Return 247 ment's return, 5 percent, can be estimated quite precisely, and the investment is defined as being essentially risk free. This same investor could also invest the $100,000 in the stock of a company just being organized to prospect for oil in the mid-Atlantic. The returns on the stock would be much harder to predict. In the worst case the company would go bankrupt and the investor would lose all of her money, in which case the return would be 100 percent. In the best-case scenario, the company would discover large amounts of oil and the investor would receive huge positive returns. When evaluating this investment, the investor might analyze the situation and conclude that the expected rate of return, in a statistical sense, is 20 percent, but it should also be recognized that the actual rate of return could range from, say, 1,000 to 100 percent. Because there is a significant danger of actually earning much less than the expected return, such a stock would be relatively risky. No investment would be undertaken unless the expected rate of return was high enough to compensate the investor for the perceived risk. In our example, it is clear that few, if any, investors would be willing to buy the oil exploration company's stock if its expected return were the same as that of the T-bill. Risky assets rarely produce their expected rates of return--generally, risky assets earn either more or less than was originally expected. Indeed, if assets always produced their expected returns, they would not be risky. Investment risk, then, is related to the probability of actually earning a low or negative return--the greater the chance of a low or negative return, the riskier the investment. However, risk can be defined more precisely, as we demonstrate in the next section. Probability Distributions An event's probability is defined as the chance that the event will occur. For example, a weather forecaster might state, "There is a 40 percent chance of rain today and a 60 percent chance of no rain." If all possible events, or outcomes, are listed, and if a probability is assigned to each event, the listing is called a probability distribution. For our weather forecast, we could set up the following probability distribution: Outcome (1) Rain No rain Probability (2) 0.4 0.6 1.0 40% 60 100% Probability Distribution A listing of all possible outcomes, or events, with a probability (chance of occurrence) assigned to each outcome. The possible outcomes are listed in Column 1, while the probabilities of these outcomes, expressed both as decimals and as percentages, are given in Column 2. Notice that the probabilities must sum to 1.0, or 100 percent. Probabilities can also be assigned to the possible outcomes--in this case returns--from an investment. If you plan to buy a one-year bond and hold it for a year, you would expect to receive interest on the bond plus a return of your original investment, and those payments would provide you with a rate of return on your investment. The possible outcomes from this investment are (1) that the issuer will make the required payments or (2) that the issuer will default on the payments. The higher the probability of default, the riskier the bond, and the higher the risk, the higher the required rate of return. If you invest in a stock instead of buying a bond, you would again expect to earn a return on your money. A stock's return would come from dividends plus capital gains. Again, the riskier the stock--which means the higher the probability that the firm will fail to provide the dividends and capital gains you expect--the higher the expected return must be to induce you to invest in the stock. 248 Part 3 Financial Assets With this in mind, consider the possible rates of return (dividend yield plus capital gain or loss) that you might earn next year on a $10,000 investment in the stock of either Martin Products Inc. or U.S. Water Company. Martin manufactures and distributes computer terminals and equipment for the rapidly growing data transmission industry. Because it faces intense competition, its new products may or may not be competitive in the marketplace, so its future earnings cannot be predicted very well. Indeed, some new company could develop better products and quickly bankrupt Martin. U.S. Water, on the other hand, supplies an essential service, and it has city franchises that protect it from competition. Therefore, its sales and profits are relatively stable and predictable. The rate-of-return probability distributions for the two companies are shown in Table 8-1. There is a 30 percent chance of a strong economy and thus strong demand, in which case both companies will have high earnings, pay high dividends, and enjoy capital gains. There is a 40 percent probability of normal demand and moderate returns, and there is a 30 percent probability of weak demand, which will mean low earnings and dividends as well as capital losses. Notice, however, that Martin Products' rate of return could vary far more widely than that of U.S. Water. There is a fairly high probability that the value of Martin's stock will drop substantially, resulting in a 70 percent loss, while the worst that could happen to U.S. Water is a 10 percent return.2 Expected Rate of Return Expected Rate of Return, r ^ The rate of return expected to be realized from an investment; the weighted average of the probability distribution of possible results. If we multiply each possible outcome by its probability of occurrence and then sum these products, as in Table 8-2, we obtain a weighted average of outcomes. The weights are the probabilities, and the weighted average is the expected rate of return, r, called "r-hat."3 The expected rates of return for both Martin Prod^ ucts and U.S. Water are shown in Table 8-2 to be 15 percent. This type of table is known as a payoff matrix. TA B L E 8 - 1 Probability Distributions for Martin Products and U.S. Water RATE OF RETURN ON STOCK IF THIS DEMAND OCCURS Demand for the Company's Products Strong Normal Weak Probability of this Demand Occurring 0.3 0.4 0.3 1.0 Martin Products 100% 15 (70) U.S. Water 20% 15 10 2 It is, of course, completely unrealistic to think that any stock has no chance of a loss. Only in hypothetical examples could this occur. To illustrate, the price of Columbia Gas's stock dropped from $34.50 to $20.00 in just three hours a few years ago. All investors were reminded that any stock is exposed to some risk of loss, and those investors who bought Columbia Gas learned that the hard way. 3 In Chapters 7 and 9, we use r and r to signify the returns on bonds and stocks, respectively. d s However, this distinction is unnecessary in this chapter, so we just use the general term, r, to signify the expected return on an investment. Chapter 8 Risk and Rates of Return 249 TA B L E 8 - 2 Calculation of Expected Rates of Return: Payoff Matrix MARTIN PRODUCTS Rate of Return If This Demand Occurs (3) 100% 15 (70) r ^ U.S. WATER Rate of Return If This Demand Occurs (5) 20% 15 10 r ^ Demand for the Company's Products (1) Strong Normal Weak Probability of This Demand Occurring (2) 0.3 0.4 0.3 1.0 Product: (2) (3) (4) 30% 6 (21) 15% Product: (2) (5) (6) 6% 6 3 15% The expected rate of return can also be expressed as an equation that does the same thing as the payoff matrix table:4 Expected rate of return r ^ P1r1 N i P2r2 ... PNrN (8-1) a Pi ri 1 Here ri is the ith possible outcome, Pi is the probability of the ith outcome, and N is the number of possible outcomes. Thus, r is a weighted average of the possi^ ble outcomes (the ri values), with each outcome's weight being its probability of occurrence. Using the data for Martin Products, we obtain its expected rate of return as follows: r ^ P1(r1) 15% P2(r2) P3(r3) 0.3( 70%) 0.3(100%) 0.4(15%) U.S. Water's expected rate of return is also 15 percent: r ^ 0.3(20%) 15% 0.4(15%) 0.3(10%) We can graph the rates of return to obtain a picture of the variability of possible outcomes; this is shown in the Figure 8-1 bar charts. The height of each bar signifies the probability that a given outcome will occur. The range of probable returns for Martin Products is from 70 to 100 percent, and the expected return is 15 percent. The expected return for U.S. Water is also 15 percent, but its possible range is much narrower. The second form of the equation is simply a shorthand expression in which sigma (a ) means "sum up," or add the values of n factors. If i 1, then Piri P1r1; if i 2, then Piri P2r2; and so on 4 N until i N, the last possible outcome. The symbol a simply says, "Go through the following i 1 process: First, let i 1 and find the first product; then i 2 and find the second product; then continue until each individual product up to 1 N has been found, and then add these individual products to find the expected rate of return." 250 Part 3 Financial Assets FIGURE 8-1 Probability Distributions of Martin Products' and U.S. Water's Rates of Return b. U.S. Water Probability of Occurrence 0.4 a. Martin Products Probability of Occurrence 0.4 0.3 0.3 0.2 0.2 0.1 0.1 70 0 15 100 Rate of Return (%) 0 10 15 20 Rate of Return (%) Expected Rate of Return Expected Rate of Return Thus far, we have assumed that only three outcomes could occur: strong, normal, and weak demand. Actually, of course, demand could range from a deep depression to a fantastic boom, and there are an unlimited number of possibilities in between. Suppose we had the time and patience to assign a probability to each possible level of demand (with the sum of the probabilities still equaling 1.0) and to assign a rate of return to each stock for each level of demand. We would have a table similar to Table 8-1, except that it would have many more entries in each column. This table could be used to calculate expected rates of return as shown previously, and the probabilities and outcomes could be represented by continuous curves such as those presented in Figure 8-2. Here we have changed the assumptions so that there is essentially a zero probability that Martin Products' return will be less than 70 percent or more than 100 percent, or that U.S. Water's return will be less than 10 percent or more than 20 percent. However, virtually any return within these limits is possible. The tighter (or more peaked) the probability distribution, the more likely it is that the actual outcome will be close to the expected value, and, consequently, the less likely it is that the actual return will end up far below the expected return. Thus, the tighter the probability distribution, the lower the risk faced by the owners of a stock. Since U.S. Water has a relatively tight probability distribution, its actual return is likely to be closer to its 15 percent expected return than is that of Martin Products. Measuring Stand-Alone Risk: The Standard Deviation Risk is a difficult concept to grasp, and a great deal of controversy has surrounded attempts to define and measure it. However, a common definition, and one that is satisfactory for many purposes, is stated in terms of probability distributions such as those presented in Figure 8-2: The tighter the probability distribution of expected future returns, the smaller the risk of a given investment. According to this Chapter 8 Risk and Rates of Return 251 FIGURE 8-2 Continuous Probability Distributions of Martin Products' and U.S. Water's Rates of Returns Probability Density U.S. Water Martin Products 70 0 15 100 Rate of Return (%) Expected Rate of Return Note: The assumptions regarding the probabilities of various outcomes have been changed from those in Figure 8-1. There the probability of obtaining exactly 15 percent was 40 percent; here it is much smaller because there are many possible outcomes instead of just three. With continuous distributions, it is more appropriate to ask what the probability is of obtaining at least some specified rate of return than to ask what the probability is of obtaining exactly that rate. This topic is covered in detail in statistics courses. definition, U.S. Water is less risky than Martin Products because there is a smaller chance that its actual return will end up far below its expected return. To be most useful, our risk measure should have a definite value--we need to quantify the tightness of the probability distribution. One such measure is the standard deviation, whose symbol is , pronounced "sigma." The smaller the standard deviation, the tighter the probability distribution, and, accordingly, the lower the riskiness of the stock. To calculate the standard deviation, we proceed as shown in Table 8-3, taking the following steps: 1. Calculate the expected rate of return: N Standard Deviation, A statistical measure of the variability of a set of observations. Expected rate of return r ^ i a Pi ri 1 For Martin, we previously found r 15%. ^ 2. Subtract the expected rate of return (r) from each possible outcome (ri) to ^ obtain a set of deviations about r as shown in Column 1 of Table 8-3: ^ Deviationi ri r ^ Variance, 2 The square of the standard deviation. 3. Square each deviation, then multiply the result by its probability of occurrence, and then sum those products to obtain the variance of the probability distribution as shown in Columns 2 and 3 of the table: N Variance 2 i a (ri 1 r)2Pi ^ (8-2) 252 Part 3 Financial Assets TA B L E 8 - 3 ri (1) r ^ Calculating Martin Products' Standard Deviation (ri r )2 ^ (2) (ri r )2Pi ^ (3) 100 15 70 15 15 15 85 0 85 7,225 0 7,225 2s (7,225)(0.3) (0)(0.4) (7,225)(0.3) 24,335 s2 2,167.5 0.0 2,167.5 4,335.0 65.84% Variance 2 Standard deviation s 4. Finally, find the square root of the variance to obtain the standard deviation: N Standard deviation 1r Ba i i 1 ^ r 2 2Pi (8-3) Thus, the standard deviation is a weighted average of the deviations from the expected value, and it provides an idea of how far above or below the expected return the actual return is likely to be. Martin's standard deviation is seen in Table 8-3 to be 65.84%. Using these same procedures, we find U.S. Water's standard deviation to be 3.87 percent. Martin Products has a much larger standard deviation, which indicates a much greater variation of returns and thus a greater chance that the expected return will not be realized. Therefore, Martin Products is a riskier investment than U.S. Water when held alone. If a probability distribution is "normal," the actual return will be within 1 standard deviation around the expected return 68.26 percent of the time. Figure 8-3 illustrates this point, and it also shows the situation for 2 and 3 . For Martin Products, r 15% and ^ 65.84%, whereas r 15% and ^ 3.87% for U.S. Water. Thus, if the two distributions were normal, there would be a 68.26% probability that Martin's actual return would be in the range of 15 65.84%, or from 50.84 to 80.84 percent. For U.S. Water, the 68.26 percent range is 15 3.87%, or from 11.13 to 18.87 percent. With such a small , there is only a small probability that U.S. Water's return would be much less than expected, so the stock is not very risky. For the average firm listed on the New York Stock Exchange, has generally been in the range of 35 to 40 percent in recent years. Using Historical Data to Measure Risk In the example just given, we described the procedure for finding the mean and standard deviation when the data are in the form of a probability distribution. If only sample returns data over some past period are available, the standard deviation of returns should be estimated using this formula: Estimated S R a 1rt t 1 N rAvg 2 2 1 N (8-3a) Here rt ("r bar t") denotes the past realized rate of return in Period t and rAvg is the average annual return earned during the last N years. Here is an example: Year r t 2003 2004 2005 15% 5 20 Chapter 8 Risk and Rates of Return 253 FIGURE 8-3 Probability Ranges for a Normal Distribution 68.26% 95.46% 99.74% 3 2 1 ^ r +1 +2 +3 Notes: a. The area under the normal curve always equals 1.0, or 100 percent. Thus, the areas under any pair of normal curves drawn on the same scale, whether they are peaked or flat, must be equal. b. Half of the area under a normal curve is to the left of the mean, indicating that there is a 50 percent probability that the actual outcome will be less than the mean, and half is to the right of r, indicating a 50 percent probability that it will be greater than the mean. ^ c. Of the area under the curve, 68.26 percent is within 1s of the mean, indicating that the probability is 68.26 percent that the actual outcome will be within the range r 1s to r 1s. ^ ^ d. Procedures exist for finding the probability of other ranges. These procedures are covered in statistics courses. e. For a normal distribution, the larger the value of s, the greater the probability that the actual outcome will vary widely from, and hence perhaps be far below, the expected, or most likely, outcome. Since the probability of having the actual result turn out to be far below the expected result is one definition of risk, and since s measures this probability, we can use s as a measure of risk. This definition may not be a good one, however, if we are dealing with an asset held in a diversified portfolio. This point is covered later in the chapter. rAvg Estimated s 1or S2 350% B 2 B 115% 115% 5% 3 20% 2 10.0% 10% 2 2 1 120% 10% 2 2 10% 2 2 1 5% 3 13.2% The historical is often used as an estimate of the future . Much less often, and generally incorrectly, rAvg for some past period is used as an estimate of r, the ^ expected future return. Because past variability is likely to be repeated, may be a good estimate of future risk. However, it is much less reasonable to expect that the average return during any particular past period is the best estimate of what investors think will happen in the future. For instance, from 2000 through 2002 the historical average return on the S&P 500 index was negative, but it is not reasonable to assume that investors expect returns to continue to be negative in the future. If they expected negative returns, they would obviously not have been willing to buy or hold stocks. 254 Part 3 Financial Assets Equation 8-3a is built into all financial calculators, and it is easy to use.5 We simply enter the rates of return and press the key marked S (or Sx) to obtain the standard deviation. However, calculators have no built-in formula for finding where probabilistic data are involved. There you must go through the process outlined in Table 8-3 and Equation 8-3. The same situation holds for Excel and other computer spreadsheet programs. Both versions of the standard deviation are interpreted and used in the same manner--the only difference is in the way they are calculated. Measuring Stand-Alone Risk: The Coefficient of Variation If a choice has to be made between two investments that have the same expected returns but different standard deviations, most people would choose the one with the lower standard deviation and, therefore, the lower risk. Similarly, given a choice between two investments with the same risk (standard deviation) but different expected returns, investors would generally prefer the investment with the higher expected return. To most people, this is common sense--return is "good," risk is "bad," and, consequently, investors want as much return and as little risk as possible. But how do we choose between two investments if one has the higher expected return but the other the lower standard deviation? To help answer this question, we use another measure of risk, the coefficient of variation (CV), which is the standard deviation divided by the expected return: Coefficient of Variation (CV) Standardized measure of the risk per unit of return; calculated as the standard deviation divided by the expected return. Coefficient of variation CV r ^ (8-4) The coefficient of variation shows the risk per unit of return, and it provides a more meaningful risk measure when the expected returns on two alternatives are not the same. Since U.S. Water and Martin Products have the same expected return, the coefficient of variation is not necessary in this case. Here the firm with the larger standard deviation, Martin, must have the larger coefficient of variation. In fact, the coefficient of variation for Martin is 65.84/15 4.39 and that for U.S. Water is 3.87/15 0.26. Thus, Martin is almost 17 times riskier than U.S. Water on the basis of this criterion. For a case where the coefficient of variation is actually necessary, consider Projects X and Y in Figure 8-4. These projects have different expected rates of return and different standard deviations. Project X has a 60 percent expected rate of return and a 15 percent standard deviation, while Y has an 8 percent expected return but only a 3 percent standard deviation. Is Project X riskier, on a relative basis, because it has the larger standard deviation? If we calculate the coefficients of variation for these two projects, we find that Project X has a coefficient of variation of 15/60 0.25, and Project Y has a coefficient of variation of 3/8 0.375. Thus, Project Y actually has more risk per unit of return than Project X, in spite of the fact that X's standard deviation is larger. Therefore, even though Project Y has the lower standard deviation, according to the coefficient of variation it is riskier than Project X. Project Y has the smaller standard deviation, hence the more peaked probability distribution, but it is clear from the graph that the chances of a really low return are higher for Y than for X because X's expected return is so high. Because 5 See our tutorials or your calculator manual for instructions on calculating historical standard deviations. Chapter 8 Risk and Rates of Return 255 FIGURE 8-4 Comparison of Probability Distributions and Rates of Return for Projects X and Y Probability Density Project Y Project X 0 8 60 Expected Rate of Return (%) the coefficient of variation captures the effects of both risk and return, it is a better measure for evaluating risk in situations where investments have substantially different expected returns. Risk Aversion and Required Returns Suppose you have worked hard and saved $1 million, and you now plan to invest it and retire on the income it produces. You can buy a 5 percent U.S. Treasury bill, and at the end of one year you will have a sure $1.05 million, which is your original investment plus $50,000 in interest. Alternatively, you can buy stock in R&D Enterprises. If R&D's research programs are successful, your stock will increase in value to $2.1 million. However, if the research is a failure, the value of your stock will be zero, and you will be penniless. You regard R&D's chances of success or failure as being 5050, so the expected value of the stock investment is 0.5($0) 0.5($2,100,000) $1,050,000. Subtracting the $1 million cost of the stock leaves an expected profit of $50,000, or an expected (but risky) 5 percent rate of return, the same as for the T-bill: Expected rate of return Expected ending value Cost $1,050,000 $1,000,000 $1,000,000 $50,000 $1,000,000 5% Cost Thus, you have a choice between a sure $50,000 profit (representing a 5 percent rate of return) on the Treasury bill and a risky expected $50,000 profit (also representing a 5 percent expected rate of return) on the R&D Enterprises stock. Which one would you choose? If you choose the less risky investment, you are risk averse. Most investors are indeed risk averse, and certainly the average investor is risk averse with regard to his or her "serious money." Because this is a well-documented fact, we assume risk aversion in our discussions throughout the remainder of the book. Risk Aversion Risk-averse investors dislike risk and require higher rates of return as an inducement to buy riskier securities. 256 Part 3 Financial Assets The Trade-Off between Risk and Return The table accompanying this box summarizes the historical trade-off between risk and return for different classes of investments from 1926 through 2004. As the table shows, those assets that produced the highest average returns also had the highest standard deviations and the widest ranges of returns. For example, small-company stocks had the highest average annual return, 17.5 percent, but the standard deviation of their returns, 33.1 percent, was also the highest. By contrast, U.S. Treasury bills had the lowest standard deviation, 3.1 percent, but they also had the lowest average return, 3.8 percent. While there is no guarantee that history will repeat itself, the returns and standard deviations observed in the past are a good starting point for estimating investments' future returns. Risk Premium, RP The difference between the expected rate of return on a given risky asset and that on a less risky asset. What are the implications of risk aversion for security prices and rates of return? The answer is that, other things held constant, the higher a security's risk the lower its price and the higher its required return. To see how risk aversion affects security prices, look back at Figure 8-2 and consider again U.S. Water's and Martin Products' stocks. Suppose each stock sold for $100 per share and each had an expected rate of return of 15 percent. Investors are averse to risk, so under those conditions there would be a general preference for U.S. Water. People with money to invest would bid for U.S. Water rather than Martin stock, and Martin's stockholders would start selling their stock and using the money to buy U.S. Water. Buying pressure would drive up U.S. Water's stock, and selling pressure would simultaneously cause Martin's price to decline. These price changes, in turn, would cause changes in the expected returns of the two securities. In general, if expected future cash flows remain the same, your expected return would be higher if you were able to purchase the stock at a lower price. Suppose, for example, that U.S. Water's stock price were bid up from $100 to $150, whereas Martin's stock price declined from $100 to $75. These price changes would cause U.S. Water's expected return to fall to 10 percent, and Martin's expected return to rise to 20 percent.6 The difference in returns, 20% 10% 10%, would be a risk premium, RP, which represents the additional compensation investors require for bearing Martin's higher risk. This example demonstrates a very important principle: In a market dominated by risk-averse investors, riskier securities must have higher expected returns as estimated by investors at the margin than less risky securities. If this situation does not exist, buying and selling will occur in the market until it does exist. We will consider the question of how much higher the returns on risky securities must be later in the chapter, after we see how diversification affects the way risk should be measured. 6 To understand how we might arrive at these numbers, assume that each stock is expected to pay shareholders $15 a year in perpetuity. The price of this perpetuity can be found by dividing the annual cash flow by the stock's return. Thus, in this example, if the stock's expected return is 15 percent, the price of the stock would be $15/0.15 $100. Likewise, a 10 percent expected return would be consistent with a $150 stock price ($15/0.10), and a 20 percent expected return would be consistent with a $75 stock price ($15/0.20). Chapter 8 Risk and Rates of Return 257 Selected Realized Returns, 19262004 Average Return Small-company stocks Large-company stocks Long-term corporate bonds Long-term government bonds U.S. Treasury bills 17.5% 12.4 6.2 5.8 3.8 Standard Deviation 33.1% 20.3 8.6 9.3 3.1 Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2005 Yearbook (Chicago: Ibbotson Associates, 2005), p. 28. What does "investment risk" mean? Set up an illustrative probability distribution table, or "payoff matrix," for an investment with probabilities for different conditions, returns under those conditions, and the expected return. Which of the two stocks graphed in Figure 8-2 is less risky? Why? How is the standard deviation calculated based on (1) a probability distribution of returns and (b) historical returns? Which is a better measure of risk if assets have different expected returns: (1) the standard deviation or (2) the coefficient of variation? Why? Explain why you agree or disagree with the following statement: "Most investors are risk averse." How does risk aversion affect rates of return? An investment has a 50 percent chance of producing a 20 percent return, a 25 percent chance of producing an 8 percent return, and a 25 percent chance of producing a 12 percent return. What is its expected return? (9%) An investment has an expected return of 10 percent and a standard deviation of 30 percent. What is its coefficient of variation? (3.0) 8.2 RISK IN A PORTFOLIO CONTEXT Thus far we have considered the riskiness of assets when they are held in isolation. Now we analyze the riskiness of assets held as a part of a portfolio. As we shall see, an asset held in a portfolio is less risky than the same asset held in isolation. Since investors dislike risk, and since risk can be reduced by holding 258 Part 3 Financial Assets portfolios--that is, by diversifying--most financial assets are indeed held in portfolios. Banks, pension funds, insurance companies, mutual funds, and other financial institutions are required by law to hold diversified portfolios. Even individual investors--at least those whose security holdings constitute a significant part of their total wealth--generally hold portfolios, not the stock of a single firm. Therefore, the fact that a particular stock goes up or down is not very important--what is important is the return on the investor's portfolio, and the risk of that portfolio. Logically, then, the risk and return of an individual security should be analyzed in terms of how the security affects the risk and return of the portfolio in which it is held. To illustrate, Pay Up Inc. is a collection agency company that operates nationwide through 37 offices. The company is not well known, its stock is not very liquid, and its earnings have fluctuated quite a bit in the past. This suggests that Pay Up is risky and that its required rate of return, r, should be relatively high. However, Pay Up's required rate of return in 2005 (and all other years) was actually quite low in comparison to that of most other companies. This indicates that investors regard Pay Up as being a low-risk company in spite of its uncertain profits. The reason for this counterintuitive finding has to do with diversification and its effect on risk. Pay Up's earnings rise during recessions, whereas most other companies' earnings tend to decline when the economy slumps. Thus, Pay Up's stock is like fire insurance--it pays off when other things go bad. Therefore, adding Pay Up to a portfolio of "normal" stocks stabilizes returns on the portfolio, thus making the portfolio less risky. Expected Portfolio Returns, ^p r Expected Return on a Portfolio, rp ^ The weighted average of the expected returns on the assets held in the portfolio. The expected return on a portfolio, r p, is simply the weighted average of the ^ expected returns on the individual assets in the portfolio, with the weights being the percentage of the total portfolio invested in each asset: r ^p w1^1 r N i ^ a wiri 1 w2^2 r ### wN^N r (8-5) Here the ri's are the expected returns on the individual stocks, the wi's are the ^ weights, and there are N stocks in the portfolio. Note that (1) wi is the fraction of the portfolio's dollar value invested in Stock i (that is, the value of the investment in Stock i divided by the total value of the portfolio) and (2) the wi's must sum to 1.0. Assume that in March 2005, a security analyst estimated that the following returns could be expected on the stocks of four large companies: Expected Return, r ^ Microsoft General Electric Pfizer Coca-Cola 12.0% 11.5 10.0 9.5 Realized Rate of Return, r The return that was actually earned during some past period. The actual return ( r ) usually turns out to be different from the expected return (r ^) except for riskless assets. If we formed a $100,000 portfolio, investing $25,000 in each stock, the portfolio's expected return would be 10.75 percent: rp ^ 0.25 112% 2 10.75% w1r1 ^ w2r2 ^ 0.25 111.5% 2 w3r3 ^ w4r4 ^ 0.25 110% 2 0.25 19.5% 2 Of course, after the fact and a year later, the actual realized rates of return, r i , on - , or "r-bar," values--will almost certainly be difthe individual stocks--the ri Chapter 8 Risk and Rates of Return 259 ferent from their expected values, so rp will be different from rp ^ 10.75%. For example, Coca-Cola's price might double and thus provide a return of 100 percent, whereas Microsoft might have a terrible year, fall sharply, and have a return of 75 percent. Note, though, that those two events would be offsetting, so the portfolio's return might still be close to its expected return, even though the individual stocks' returns were far from their expected values. Portfolio Risk Although the expected return on a portfolio is simply the weighted average of the expected returns of the individual assets in the portfolio, the riskiness of the portfolio, p, is not the weighted average of the individual assets' standard deviations. The portfolio's risk is generally smaller than the average of the assets' 's. To illustrate the effect of combining assets, consider the situation in Figure 8-5. The bottom section gives data on rates of return for Stocks W and M individually, and also for a portfolio invested 50 percent in each stock. The three top graphs show plots of the data in a time series format, and the lower graphs show the probability distributions of returns, assuming that the future is expected to be like the past. The two stocks would be quite risky if they were held in isolation, but when they are combined to form Portfolio WM, they are not risky at all. (Note: These stocks are called W and M because the graphs of their returns in Figure 8-5 resemble a W and an M.) Stocks W and M can be combined to form a riskless portfolio because their returns move countercyclically to each other--when W's returns fall, those of M rise, and vice versa. The tendency of two variables to move together is called correlation, and the correlation coefficient, r (pronounced "rho"), measures this tendency.7 In statistical terms, we say that the returns on Stocks W and M are perfectly negatively correlated, with r 1.0. The opposite of perfect negative correlation, with r 1.0, is perfect positive correlation, with r 1.0. Returns on two perfectly positively correlated stocks (M and M ) would move up and down together, and a portfolio consisting of two such stocks would be exactly as risky as the individual stocks. This point is illustrated in Figure 8-6, where we see that the portfolio's standard deviation is equal to that of the individual stocks. Thus, diversification does nothing to reduce risk if the portfolio consists of perfectly positively correlated stocks. Figures 8-5 and 8-6 demonstrate that when stocks are perfectly negatively correlated (r 1.0), all risk can be diversified away, but when stocks are perfectly positively correlated (r 1.0), diversification does no good whatever. In reality, virtually all stocks are positively correlated, but not perfectly so. Past studies have estimated that on average the correlation coefficient for the monthly returns on two randomly selected stocks is about 0.3.8 Under this condition, combining Correlation The tendency of two variables to move together. Correlation Coefficient, r A measure of the degree of relationship between two variables. 7 The correlation coefficient, r, can range from 1.0, denoting that the two variables move up and down in perfect synchronization, to 1.0, denoting that the variables always move in exactly opposite directions. A correlation coefficient of zero indicates that the two variables are not related to each other--that is, changes in one variable are independent of changes in the other. It is easy to calculate correlation coefficients with a financial calculator. Simply enter the returns on the two stocks and then press a key labeled "r." For W and M, r 1.0. See our tutorial or your calculator manual for the exact steps. Also, note that the correlation coefficient is often denoted by the term "r." We use r here to avoid confusion with r as used to denote the rate of return. 8 A recent study by Chan, Karceski, and Lakonishok (1999) estimated that the average correlation coefficient between two randomly selected stocks was 0.28, while the average correlation coefficient between two large-company stocks was 0.33. The time period of their sample was 1968 to 1998. See Louis K. C. Chan, Jason Karceski, and Josef Lakonishok, "On Portfolio Optimization: Forecasting Covariance and Choosing the Risk Model," The Review of Financial Studies, Vol. 12, no. 5 (Winter 1999), pp. 937974. 260 Part 3 Financial Assets FIGURE 8-5 a. Rates of Return _ Rate of Return Distributions for Two Perfectly Negatively Correlated Stocks (r 1.0) and for Portfolio WM _ rW(%) Stock W r M(%) Stock M _ r p (%) Portfolio WM 25 25 25 15 15 15 0 2005 0 2005 0 2005 10 b. Probability Distributions of Returns Probability Density Stock W 10 10 Probability Density Stock M Probability Density Portfolio WM 0 15 ^ (= r W ) Percent 0 15 ^ (= r M ) Percent 0 15 ^ (= rp ) Percent Year 2001 2002 2003 2004 2005 Average return Standard deviation Stock W ( r w) 40.0% (10.0) 35.0 (5.0) 15.0 15.0% 22.6% Stock M ( r M) (10.0%) 40.0 (5.0) 35.0 15.0 15.0% 22.6% Portfolio WM ( r p) 15.0% 15.0 15.0 15.0 15.0 15.0% 0.0% stocks into portfolios reduces risk but does not completely eliminate it. Figure 8-7 illustrates this point with two stocks whose correlation coefficient is r 0.35. The portfolio's average return is 15 percent, which is exactly the same as the average return for our other two illustrative portfolios, but its standard deviation is 18.6 percent, which is between the other two portfolios' standard deviations. Chapter 8 Risk and Rates of Return 261 FIGURE 8-6 a. Rates of Return _ Rate of Return Distributions for Two Perfectly Correlated Stocks (r 1.0) and for Portfolio MM' _ r M (%) Stock M rM (%) Stock M _ r p (%) Portfolio MM 25 25 25 15 15 15 0 2005 0 2005 0 2005 10 b. Probability Distributions of Returns Probability Density 10 10 Probability Density Probability Density 0 15 ^ (= r M ) Percent 0 15 ^ (= r M ) Percent 0 15 ^ (= rp ) Percent Year 2001 2002 2003 2004 2005 Average return Standard deviation Stock M ( rM ) (10.0%) 40.0 (5.0) 35.0 15.0 15.0% 22.6% Stock M' ( r M') (10.0%) 40.0 (5.0) 35.0 15.0 15.0% 22.6% Portfolio MM' ( r p) (10.0%) 40.0 (5.0) 35.0 15.0 15.0% 22.6% These examples demonstrate that in one extreme case (r 1.0), risk can be completely eliminated, while in the other extreme case (r 1.0), diversification does no good whatever. The real world lies between these extremes, so combining stocks into portfolios reduces, but does not eliminate, the risk inherent in the individual stocks. Also, we should note that in the real world, it is impossible to 262 Part 3 Financial Assets FIGURE 8-7 Rate of Return Distributions for Two Partially Correlated Stocks (r 0.35) and for Portfolio WV Stock W r v (%) 60 _ a. Rates of Return r W (%) 60 _ Stock V r p (%) 60 _ Stock WV 45 45 45 30 30 30 15 15 15 0 2005 0 2005 0 2005 15 15 15 b. Probability Distributions of Returns Probability Density Portfolio WV Stocks W and V 0 15 ^ (= r p ) Stock W ( r w) 40.0% (10.0) 35.0 (5.0) 15.0 15.0% 22.6% Stock V ( r v) 40.0% 15.0 (5.0) (10.0) 35.0 15.0% 22.6% Percent Year 2001 2002 2003 2004 2005 Average return Standard deviation Portfolio WV ( r p) 40.0% 2.5 15.0 (7.5) 25.0 15.0% 18.6% find stocks like W and M, whose returns are expected to be perfectly negatively correlated. Therefore, it is impossible to form completely riskless stock portfolios. Diversification can reduce risk but not eliminate it, so the real world is similar to the situation depicted in Figure 8-7. What would happen if we included more than two stocks in the portfolio? As a rule, portfolio risk declines as the number of stocks in the portfolio increases. If we Chapter 8 Risk and Rates of Return 263 The Benefits of Diversification Are More Important Than Ever Have stocks become riskier in recent years? Looking at what's happened to their individual portfolios, many investors may answer that question with a resounding yes. Furthermore, academic studies confirm this intuition--the average volatility of individual stocks has increased over time. However, studies have also found that volatility in the overall stock market has not increased. The reason for this apparent discrepancy is that the correlation between individual stocks has fallen in recent years, so declines in one stock are offset by gains in others, and this reduces overall market volatility. A study by Campbell, Lettau, Malkiel, and Xu found that the average correlation fell from around 0.35 in the late 1970s to less than 0.10 by the late 1990s. What does this mean for the average investor? Individual stocks have become riskier, increasing the danger of putting all of your eggs in one basket, but at the same time, lower correlations between individual stocks mean that diversification is more useful than ever for reducing portfolio risk. Diversify, diversify, diversify! Source: John Y. Campbell, Martin Lettau, Burton G. Malkiel, and Yexiao Xu, "Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk," Journal of Finance, Vol. 56, no. 1 (February 2001), pp.143. added enough partially correlated stocks, could we completely eliminate risk? In general, the answer is no, but here are two points worth noting: 1. The extent to which adding stocks to a portfolio reduces its risk depends on the degree of correlation among the stocks: The smaller the correlation coefficients, the lower the risk in a large portfolio. If we could find a set of stocks whose correlations were zero or negative, all risk could be eliminated. However, in the real world, the correlations among the individual stocks are generally positive but less than 1.0, so some but not all risk can be eliminated. 2. Some individual stocks are riskier than others, so some stocks will help more than others in terms of reducing the portfolio's risk. This point will be explored further in the next section, where we measure stocks' risks in a portfolio context. To test your understanding up to this point, would you expect to find higher correlations between the returns on two companies in the same or in different industries? For example, is it likely that the correlation between Ford's and General Motors' stocks would be higher, or would the correlation be higher between either Ford or GM and Coke, and how would those correlations affect the risk of portfolios containing them? Answer: Ford's and GM's returns are highly correlated with one another because both are affected by similar forces. These stocks are positively correlated with Coke, but the correlation is lower because stocks in different industries are subject to different factors. For example, people reduce auto purchases more than Coke consumption when interest rates rise. Implications: A two-stock portfolio consisting of Ford and GM would be less well diversified than a two-stock portfolio consisting of Ford or GM, plus Coke. Thus, to minimize risk, portfolios should be diversified across industries. Diversifiable Risk versus Market Risk As noted earlier, it is difficult if not impossible to find stocks whose expected returns are negatively correlated to one another--most stocks tend to do well 264 Part 3 Financial Assets Market Portfolio A portfolio consisting of all stocks. Diversifiable Risk That part of a security's risk associated with random events; it can be eliminated by proper diversification. Market Risk That part of a security's risk that cannot be eliminated by diversification. Capital Asset Pricing Model (CAPM) A model based on the proposition that any stock's required rate of return is equal to the risk-free rate of return plus a risk premium that reflects only the risk remaining after diversification. when the national economy is strong and badly when it is weak.9 Thus, even very large portfolios end up with a substantial amount of risk, but not as much as if all the money were invested in only one stock. To see more precisely how portfolio size affects portfolio risk, consider Figure 8-8, which shows how a portfolio's risk is affected by adding more and more randomly selected New York Stock Exchange (NYSE) stocks. Standard deviations are plotted for an average one-stock portfolio, a two-stock portfolio, and so on, up to a portfolio consisting of all 2,000-plus common stocks that were listed on the NYSE at the time the data were graphed. The graph illustrates that, in general, the riskiness of a portfolio consisting of large-company stocks tends to decline and to approach a minimum level as the size of the portfolio increases. According to data accumulated in recent years, 1, the standard deviation of a one-stock portfolio (or an average stock) is approximately 35 percent. A portfolio consisting of all stocks, which is called the market portfolio, would have a much lower standard deviation, M, about 20 percent, as represented by the horizontal dashed line in Figure 8-8. Thus, almost half of the riskiness inherent in an average individual stock can be eliminated if the stock is held in a reasonably well-diversified portfolio, which is one containing 40 or more stocks. Some risk will always remain, however, so it is virtually impossible to diversify away the effects of broad stock market movements that affect almost all stocks. The part of a stock's risk that can be eliminated is called diversifiable risk, while the part that cannot be eliminated is called market risk.10 Diversifiable risk is caused by such random events as lawsuits, strikes, successful and unsuccessful marketing programs, winning or losing a major contract, and other events that are unique to a particular firm. Because these events are random, their effects on a portfolio can be eliminated by diversification--bad events in one firm will be offset by good events in another. Market risk, on the other hand, stems from factors that systematically affect most firms: war, inflation, recessions, and high interest rates. Because most stocks are negatively affected by these factors, market risk cannot be eliminated by diversification. We know that investors demand a premium for bearing risk; that is, the higher the riskiness of a security, the higher its expected return must be to induce investors to buy (or to hold) it. However, rational investors are primarily concerned with the riskiness of their portfolios rather than the riskiness of the individual securities in the portfolio, so the riskiness of an individual stock should be judged by its effect on the riskiness of the portfolio in which it is held. This type of risk is addressed by the Capital Asset Pricing Model (CAPM), which describes the relationship between risk and rates of return.11 According to the CAPM, the relevant riskiness of an individual stock is its contribution to the riski- It is not too hard to find a few stocks that happened to have risen because of a particular set of circumstances in the past while most other stocks were declining, but it is much harder to find stocks that could logically be expected to increase in the future when other stocks are falling. 10 Diversifiable risk is also known as company-specific, or unsystematic, risk. Market risk is also known as nondiversifiable, or systematic, or beta, risk; it is the risk that remains after diversification. 11 Indeed, the 1990 Nobel Prize was awarded to the developers of the CAPM, Professors Harry Markowitz and William F. Sharpe. The CAPM is a relatively complex subject, and only its basic elements are presented in this text. For a more detailed discussion, see any standard investments textbook. The basic concepts of the CAPM were developed specifically for common stocks, and, therefore, the theory is examined first in this context. However, it has become common practice to extend CAPM concepts to capital budgeting and to speak of firms having "portfolios of tangible assets and projects." Capital budgeting is discussed in Part 4. 9 Chapter 8 Risk and Rates of Return 265 FIGURE 8-8 Effects of Portfolio Size on Portfolio Risk for Average Stocks Portfolio Risk, p (%) 35 30 Diversifiable Risk 25 M = 20.4 15 Portfolio's StandAlone Risk: Declines 10 as Stocks Are Added Minimum Attainable Risk in a Portfolio of Average Stocks Portfolio's Market Risk: Remains Constant 5 01 10 20 30 40 2,000+ Number of Stocks in the Portfolio ness of a well-diversified portfolio. In other words, the riskiness of General Electric's stock to a doctor who has a portfolio of 40 stocks or to a trust officer managing a 150-stock portfolio is the contribution GE's stock makes to the portfolio's riskiness. The stock might be quite risky if held by itself, but if half of its risk can be eliminated by diversification, then its relevant risk, which is its contribution to the portfolio's risk, is much smaller than its stand-alone risk. A simple example will help make this point clear. Suppose you are offered the chance to flip a coin once. If a head comes up, you win $20,000, but if a tail comes up, you lose $16,000. This is a good bet--the expected return is 0.5($20,000) 0.5( $16,000) $2,000. However, it is a highly risky proposition, because you have a 50 percent chance of losing $16,000. Thus, you might well refuse to make the bet. Alternatively, suppose you were offered the chance to flip a coin 100 times, and you would win $200 for each head but lose $160 for each tail. It is possible that you would flip all heads and win $20,000, and it is also possible that you would flip all tails and lose $16,000, but the chances are very high that you would actually flip about 50 heads and about 50 tails, winning a net of about $2,000. Although each individual flip is a risky bet, collectively you have a low-risk proposition because multiple flipping diversifies away most of the risk. This is the idea behind holding portfolios of stocks rather Relevant Risk The risk of a security that cannot be diversified away. This is the risk that affects portfolio risk and thus is relevant to a rational investor. 266 Part 3 Financial Assets than just one stock, except that with stocks all of the risk cannot be eliminated by diversification--those risks that are related to broad, systematic changes in the stock market will remain even in a highly diversified portfolio. Are all stocks equally risky in the sense that adding them to a well-diversified portfolio would have the same effect on the portfolio's riskiness? The answer is no. Different stocks will affect the portfolio differently, so different securities have different degrees of relevant risk. How can the relevant risk of an individual stock be measured? As we have seen, all risk except that related to broad market movements can, and presumably will, be diversified away by most investors. After all, why accept a risk that can easily be eliminated? The risk that remains after diversifying is market risk, or the risk that is inherent in the market, and it can be measured by the degree to which a given stock tends to move up or down with the market. In the next section, we explain how to measure a stock's market risk, and then, in a later section, we introduce an equation for determining a stock's required rate of return, given its market risk. The Concept of Beta Beta Coefficient, b A metric that shows the extent to which a given stock's returns move up and down with the stock market. Beta thus measures market risk. The tendency of a stock to move up and down with the market, and thus its market risk, is reflected in its beta coefficient, b. Beta is a key element of the CAPM. An average-risk stock is defined as one that tends to move up and down in step with the general market as measured by some index such as the Dow Jones Industrials, the S&P 500, or the New York Stock Exchange Index. Such a stock is, by definition, assigned a beta of b 1.0. Thus, a stock with b 1.0 will, in general, move up by 10 percent if the market moves up by 10 percent, while if the market falls by 10 percent, the stock will likewise fall by 10 percent. A portfolio of such b 1.0 stocks will thus move up and down with the broad market averages, and it will be just as risky as the averages. If b 0.5, the stock would be only half as volatile as the market--it would rise and fall only half as much-- and a portfolio of such stocks would be only half as risky as a portfolio of b 1.0 stocks. On the other hand, if b 2.0, the stock would be twice as volatile as an average stock, so a portfolio of such stocks would be twice as risky as an average portfolio. The value of such a portfolio could double--or halve--in a short time, and if you held such a portfolio, you could quickly go from millionaire to pauper. Figure 8-9 graphs the three stocks' returns to show their relative volatility. The illustrative data below the graph show that in Year 1, the "market," as defined by a portfolio containing all stocks, had a total return (dividend yield plus capital gains yield) of rM 10%, and Stocks H, A, and L (for High, Average, and Low risk) also all had returns of 10 percent. In Year 2, the market went up sharply, and its return was rM 20%. Returns on the three stocks were also high: H soared by 30 percent; A returned 20 percent, the same as the market; and L returned only 15 percent. In Year 3 the market dropped sharply, and its return was rM 10%. The three stocks' returns also fell, H plunging by 30 percent, A falling by 10 percent, and L returning rL 0%. Thus, the three stocks all moved in the same direction as the market, but H was by far the most volatile, A was exactly as volatile as the market, and L was less volatile. Beta measures a given stock's volatility relative to an average stock, which by definition has b 1.0, and the stock's beta can be calculated by plotting a line like those in Figure 8-9. The slopes of the lines show how each stock moves in response to a movement in the general market--indeed, the slope coefficient of such a "regression line" is defined as the stock's beta coefficient. (Procedures for calculating betas are described in Web Appendix 8A, which can be accessed through the ThomsonNOW Web site. Betas for literally thousands of companies are calculated and published by Merrill Lynch, Value Line, and numerous other organiza- Chapter 8 Risk and Rates of Return 267 FIGURE 8-9 Relative Volatility of Stocks H, A, and L Return on Stock i, r i (%) _ Stock H, High Risk: b = 2.0 30 Stock A, Average Risk: b = 1.0 20 Stock L, Low Risk: b = 0.5 10 X 20 10 0 10 20 30 _ Return on the Market, rM(%) 10 20 30 Year 1 2 3 rH rA rL rM 10% 30 (30) 10% 20 (10) 10% 15 0 10% 20 (10) Note: These three stocks plot exactly on their regression lines. This indicates that they are exposed only to market risk. Mutual funds that concentrate on stocks with betas of 2, 1, and 0.5 would have patterns similar to those shown in the graph. tions, and the beta coefficients of some well-known companies are shown in Table 8-4. Most stocks have betas in the range of 0.50 to 1.50, and the average for all stocks is 1.0 by definition. Theoretically, it would be possible for a stock to have a negative beta. In this case, the stock's returns would tend to rise whenever the returns on other stocks fall. However, we have never seen a negative beta as reported by one of the many organizations that publish betas for publicly held firms. Moreover, even though a stock may have a positive long-run beta, company-specific problems might cause its realized return to decline even when the general market is strong. If a stock whose beta is greater than 1.0 is added to a bp 1.0 portfolio, then the portfolio's beta, and consequently its risk, will increase. Conversely, if 268 Part 3 Financial Assets TA B L E 8 - 4 Illustrative List of Beta Coefficients Stock Merrill Lynch eBay General Electric Best Buy Microsoft ExxonMobil FPL Group Coca-Cola Procter & Gamble Heinz Beta 1.50 1.45 1.30 1.25 1.15 0.80 0.70 0.60 0.60 0.55 Source: Adapted from Value Line, March 2005. a stock whose beta is less than 1.0 is added to a bp 1.0 portfolio, the portfolio's beta and risk will decline. Thus, because a stock's beta measures its contribution to the riskiness of a portfolio, beta is theoretically the correct measure of the stock's riskiness. The preceding analysis of risk in a portfolio context is part of the Capital Asset Pricing Model (CAPM), and we can summarize our discussion up to this point as follows: 1. A stock's risk consists of two components, market risk and diversifiable risk. 2. Diversifiable risk can be eliminated by diversification, and most investors do indeed diversify, either by holding large portfolios or by purchasing shares in a mutual fund. We are left, then, with market risk, which is caused by general movements in the stock market and which reflects the fact that most stocks are systematically affected by events like wars, recessions, and inflation. Market risk is the only relevant risk to a rational, diversified investor because such an investor would eliminate diversifiable risk. 3. Investors must be compensated for bearing risk--the greater the riskiness of a stock, the higher its required return. However, compensation is required only for risk that cannot be eliminated by diversification. If risk premiums existed on a stock due to its diversifiable risk, then that stock would be a bargain to well-diversified investors. They would start buying it and bidding up its price, and the stock's final (equilibrium) price would result in an expected return that reflected only its non-diversifiable market risk. If this point is not clear, an example may help clarify it. Suppose half of Stock A's risk is market risk (it occurs because Stock A moves up and down with the market), while the other half of A's risk is diversifiable. You are thinking of buying Stock A and holding it as a one-stock portfolio, so if you buy it you will be exposed to all of its risk. As compensation for bearing so much risk, you want a risk premium of 8 percent over the 6 percent T-bond rate, so your required return is rA 6% 8% 14%. But suppose other investors, including your professor, are well diversified; they are also looking at Stock A, but they would hold it in diversified portfolios, eliminate its diversifiable risk, and thus be exposed to only half as much risk as you. Therefore, their risk premium would be only half as large as yours, and their required rate of return would be rA 6% 4% 10%. Chapter 8 Risk and Rates of Return 269 If the stock were priced to yield the 14 percent you require, then diversified investors, including your professor, would rush to buy it. That would push its price up and its yield down; hence, you could not buy it at a price low enough to provide you with the 14 percent return. In the end, you would have to accept a 10 percent return or else keep your money in the bank. Thus, risk premiums in a market populated by rational, diversified investors can reflect only market risk. 4. The market risk of a stock is measured by its beta coefficient, which is an index of the stock's relative volatility. Some benchmark betas follow: b 0.5: Stock is only half as volatile, or risky, as an average stock. b 1.0: Stock is of average risk. b 2.0: Stock is twice as risky as an average stock. 5. A portfolio consisting of low-beta securities will itself have a low beta, because the beta of a portfolio is a weighted average of its individual securities' betas: bp w1b1 N i w2b2 ### wNbN (8-6) a wibi 1 Here bp is the beta of the portfolio, and it shows how volatile the portfolio is relative to the market; wi is the fraction of the portfolio invested in the ith stock; and bi is the beta coefficient of the ith stock. For example, if an investor holds a $100,000 portfolio consisting of $33,333.33 invested in each of three stocks, and if each of the stocks has a beta of 0.7, then the portfolio's beta will be bp 0.7: bp 0.3333(0.7) 0.3333(0.7) 0.3333(0.7) 0.7 Such a portfolio will be less risky than the market, so it should experience relatively narrow price swings and have relatively small rate-of-return fluctuations. In terms of Figure 8-9, the slope of its regression line would be 0.7, which is less than that for a portfolio of average stocks. Now suppose one of the existing stocks is sold and replaced by a stock with bi 2.0. This action will increase the beta of the portfolio from bp1 0.7 to bp2 1.13: bp2 0.333 10.72 0.3333 10.72 0.3333 12.0 2 1.13 0.2 been added, the portfolio's beta would have Had a stock with bi declined from 0.7 to 0.53. Adding a low-beta stock would therefore reduce the portfolio's riskiness. Consequently, changing the stocks in a portfolio can change the riskiness of that portfolio. 6. Because a stock's beta coefficient determines how the stock affects the riskiness of a diversified portfolio, beta is the most relevant measure of any stock's risk. Explain the following statement: "An asset held as part of a portfolio is generally less risky than the same asset held in isolation." What is meant by perfect positive correlation, perfect negative correlation, and zero correlation? In general, can the riskiness of a portfolio be reduced to zero by increasing the number of stocks in the portfolio? Explain. 270 Part 3 Financial Assets G L O B A L P E R S P E C T I V E S The Benefits of Diversifying Overseas The increasing availability of international securities is making it possible to achieve a better risk-return trade-off than could be obtained by investing only in U.S. securities. So, investing overseas might result in a portfolio with less risk but a higher expected return. This result occurs because of low correlations between the returns on U.S. and international securities, along with potentially high returns on overseas stocks. Figure 8-8, presented earlier, demonstrated that an investor can reduce the risk of his or her portfolio by holding a number of stocks. The figure accompanying this box suggests that investors may be able to reduce risk even further by holding a portfolio of stocks from all around the world, given the fact that the returns on domestic and international stocks are not perfectly correlated. Even though foreign stocks represent roughly 60 percent of the worldwide equity market, and despite the apparent benefits from investing overseas, the typical U.S. investor still puts less than 10 percent of his or her money in foreign stocks. One possible explanation for this reluctance to invest overseas is that investors prefer domestic stocks because of lower transactions costs. However, this explanation is questionable because recent studies reveal that investors buy and sell overseas stocks more frequently than they trade their domestic stocks. Other explanations for the domestic bias include the additional risks from investing overseas (for example, exchange rate risk) and the fact that the typical U.S. investor is uninformed about international investments and/or thinks that international investments are extremely risky. It has been argued that world capital markets have become more integrated, causing the correlation of returns between different countries to increase, which reduces the benefits from international diversification. In addition U.S. corporations are investing more internationally, providing U.S. investors with international diversification even if they buy only U.S. stocks. Whatever the reason for their relatively small holdings of international assets, our guess is that in the future U.S. investors will shift more of their assets to overseas investments. Source: For further reading, see also Kenneth Kasa, "Measuring the Gains from International Portfolio Diversification," Federal Reserve Bank of San Francisco Weekly Letter, Number 9414, April 8, 1994. Portfolio Risk, p (%) U.S. Stocks U.S. and International Stocks Number of Stocks in the Portfolio Chapter 8 Risk and Rates of Return 271 What is an average-risk stock? What is the beta of such a stock? Why is it argued that beta is the best measure of a stock's risk? If you plotted a particular stock's returns versus those on the Dow Jones Index over the past five years, what would the slope of the regression line indicate about the stock's risk? An investor has a two-stock portfolio with $25,000 invested in Merrill Lynch and $50,000 invested in Coca-Cola. Merrill Lynch's beta is estimated to be 1.50 and Coca-Cola's beta is estimated to be 0.60. What is the estimated beta of the investor's portfolio? (0.90) 8.3 THE RELATIONSHIP BETWEEN RISK AND RATES OF RETURN The preceding section demonstrated that under the CAPM theory, beta is the most appropriate measure of a stock's relevant risk. The next issue is this: For a given level of risk as measured by beta, what rate of return is required to compensate investors for bearing that risk? To begin, let us define the following terms: ri ^ ri expected rate of return on the ith stock. required rate of return on the ith stock. Note that if ri is less than ri, the ^ typical investor would not purchase this stock or would sell it if he or she owned it. If ri were greater than ri, the investor would buy ^ the stock because it would look like a bargain. Investors would be indifferent if ri ri. ^ realized, after-the-fact return. One obviously does not know r at the time he or she is considering the purchase of a stock. risk-free rate of return. In this context, rRF is generally measured by the return on long-term U.S. Treasury bonds. beta coefficient of the ith stock. The beta of an average stock is bA 1.0. required rate of return on a portfolio consisting of all stocks, which is called the market portfolio. rM is also the required rate of return on an average (bA 1.0) stock. (rM rRF) risk premium on "the market," and also the premium on an average stock. This is the additional return over the risk-free rate required to compensate an average investor for assuming an average amount of risk. Average risk means a stock where bi bA 1.0. (rM rRF)bi (RPM)bi risk premium on the ith stock. A stock's risk premium will be less than, equal to, or greater than the premium on an average stock, RPM, depending on whether its beta is less than, equal to, or greater than 1.0. If bi bA 1.0, then RPi RPM. Market Risk Premium, RPM The additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. r rRF bi rM RPM RPi The market risk premium, RPM, shows the premium investors require for bearing the risk of an average stock. The size of this premium depends on how risky investors think the stock market is and on their degree of risk aversion. Let us assume that at the current time Treasury bonds yield rRF 6% and an average share of stock has a required rate of return of rM 11%. Therefore, the market risk premium is 5 percent, calculated as follows: RPM rM rRF 11% 6% 5% 272 Part 3 Financial Assets Estimating the Market Risk Premium The Capital Asset Pricing Model (CAPM) is more than a theory describing the trade-off between risk and return--it is also widely used in practice. As we will see later, investors use the CAPM to determine the discount rate for valuing stocks, and corporate managers use it to estimate the cost of equity capital. The market risk premium is a key component of the CAPM, and it should be the difference between the expected future return on the overall stock market and the expected future return on a riskless investment. However, we cannot obtain investors' expectations, so instead academicians and practitioners often use a historical risk premium as a proxy for the expected risk premium. The historical premium is found by first taking the difference between the actual return on the overall stock market and the risk-free rate in a number of different years and then averaging the annual results. Ibbotson Associates, which provides perhaps the most comprehensive estimates of historical risk premiums, reports that the annual premiums have averaged 7.2 percent over the past 79 years. However, there are three potential problems with historical risk premiums. First, what is the proper number of years over which to compute the average? Ibbotson goes back to 1926, when good data first became available, but that is a rather arbitrary choice, and the starting and ending points make a major difference in the calculated premium. Second, historical premiums are likely to be misleading at times when the market risk premium is changing. To illustrate, the stock market was very strong from 1995 through 1999, in part because investors were becoming less risk averse, which means that they applied a lower risk premium when they valued stocks. The strong market resulted in stock returns of about 30 percent per year, and when bond yields were subtracted the resulting annual risk premiums averaged 22.3 percent a year. When those high numbers were added to data from prior years, they caused the long-run historical risk premium as reported by Ibbotson to increase. Thus, a declining "true" risk premium led to very high stock returns, which, in turn, led to an increase in the calculated historical risk premium. That's a worrisome result, to say the least. The third concern is that historical estimates may be biased upward because they only include the returns of firms that have survived--they do not reflect the losses incurred on investments in failed firms. Stephen Brown, William Goetzmann, and Stephen Ross discussed the implications of this "survivorship bias" in a 1995 Journal of Finance article. Putting these ideas into practice, Tim Koller, Marc Goedhart, and David Wessels recently suggested that "survivorship bias" increases historical returns by 1 to 2 percent a year. Therefore, they suggest that practitioners subtract 1 to 2 percent from the historical estimates to obtain a risk premium for use in the CAPM. Sources: Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2005 Yearbook (Chicago: Ibbotson Associates, 2005); Stephen J. Brown, William N. Goetzmann, and Stephen A. Ross, "Survival," Journal of Finance, Vol. 50, no. 3 (July 1995), pp. 853873; and Tim Koller, Marc Goedhart, and David Wessels, Valuation: Measuring and Managing the Value of Companies, 4th edition (New York: McKinsey & Company, 2005). It should be noted that the risk premium of an average stock, rM rRF, is actually hard to measure because it is impossible to obtain a precise estimate of the expected future return of the market, rM.12 Given the difficulty of estimating future market returns, analysts often look to historical data to estimate the market risk premium. Historical data suggest that the market risk premium varies somewhat from year to year due to changes in investors' risk aversion, but that it has generally ranged from 4 to 8 percent. 12 This concept, as well as other aspects of the CAPM, is discussed in more detail in Chapter 3 of Eugene F. Brigham and Philip R. Daves, Intermediate Financial Management, 8th ed. (Mason, OH: Thomson/South-Western, 2004). That chapter also discusses the assumptions embodied in the CAPM framework. Some of those assumptions are unrealistic, and because of this the theory does not hold exactly. Chapter 8 Risk and Rates of Return 273 While historical estimates might be a good starting point for estimating the market risk premium, those estimates would be misleading if investors' attitudes toward risk change considerably over time. (See the box entitled "Estimating the Market Risk Premium.") Indeed, many analysts have argued that the market risk premium has fallen in recent years. If this claim is correct, the market risk premium is considerably lower than one based on historical data. The risk premium on individual stocks varies in a systematic manner from the market risk premium. For example, if one stock were twice as risky as another, its risk premium would be twice as high, while if its risk were only half as much, its risk premium would be half as large. Further, we can measure a stock's relative riskiness by its beta coefficient. If we know the market risk premium, RPM, and the stock's risk as measured by its beta coefficient, bi, we can find the stock's risk premium as the product (RPM)bi. For example, if bi 0.5 and RPM 5%, then RPi is 2.5 percent: Risk premium for Stock i RPi (RPM)bi (5%)(0.5) 2.5% (8-7) As the discussion in Chapter 6 implied, the required return for any stock can be expressed in general terms as follows: Required return on a stock Risk-free return Premium for the stock's risk Here the risk-free return includes a premium for expected inflation, and if we assume that the stocks under consideration have similar maturities and liquidity, then the required return on Stock i can be expressed by the Security Market Line (SML) equation: SML Equation: Required return on Stock i ri Risk-free rate rRF rRF 6% 6% 8.5% If some other Stock j had bj 2.0 and thus was riskier than Stock i, then its required rate of return would be 16 percent: a Market risk Stock i's ba b premium beta (8-8) (rM (11% rRF)bi 6%)(0.5) Security Market Line (SML) Equation An equation that shows the relationship between risk as measured by beta and the required rates of return on individual securities. (RPM)bi 5%(0.5) rj 6% (5%)2.0 16% An average stock, with b 1.0, would have a required return of 11 percent, the same as the market return: rA 6% (5%)1.0 11% rM 274 Part 3 Financial Assets Security Market Line (SML) The line on a graph that shows the relationship between risk as measured by beta and the required rate of return for individual securities. When the SML equation is plotted on a graph, the resulting line is called the Security Market Line (SML). Figure 8-10 shows the SML situation when rRF 6% and rM 11%. Note the following points: 1. Required rates of return are shown on the vertical axis, while risk as measured by beta is shown on the horizontal axis. This graph is quite different from the one shown in Figure 8-9, where the returns on individual stocks were plotted on the vertical axis and returns on the market index were shown on the horizontal axis. The slopes of the three lines in Figure 89 were used to calculate the three stocks' betas, and those betas were then plotted as points on the horizontal axis of Figure 8-10. 2. Riskless securities have bi 0; therefore, rRF appears as the vertical axis intercept in Figure 8-10. If we could construct a portfolio that had a beta of zero, it would have an expected return equal to the risk-free rate. 3. The slope of the SML (5 percent in Figure 8-10) reflects the degree of risk aversion in the economy--the greater the average investor's risk aversion, then (a) the steeper the slope of the line, (b) the greater the risk premium for all stocks, and (c) the higher the required rate of return on all stocks.13 These points are discussed further in a later section. 4. The values we worked out for stocks with bi 0.5, bi 1.0, and bi 2.0 agree with the values shown on the graph for rLow, rA, and rHigh. FIGURE 8-10 Required Rate of Return (%) The Security Market Line (SML) SML: ri = r RF + (r M r RF) bi = 6% + (11% 6%) bi = 6% + (5%) bi rHigh = 16 rM = r A = 11 r Low = 8.5 r RF = 6 Safe Stock's Risk Premium: 2.5% Market Risk Premium: 5%. Applies Also to an Average Stock, and Is the Slope Coefficient in the SML Equation Relatively Risky Stock's Risk Premium: 10% Risk-Free Rate, r RF 0 0.5 1.0 1.5 2.0 Risk, b i 13 Students sometimes confuse beta with the slope of the SML. This is a mistake. Consider Figure 8-10. The slope of any straight line is equal to the "rise" divided by the "run," or (Y1 Y0)/(X1 X0). If we let Y r and X beta, and we go from the origin to b 1.0, we see that the slope is (rM rRF)/(bM bRF) (11% 6%)/(1 0) 5%. Thus, the slope of the SML is equal to (rM rRF), the market risk premium. In Figure 8-10, ri 6% 5%bi, so a doubling of beta from 1.0 to 2.0 would produce a 5 percentage point increase in ri. Chapter 8 Risk and Rates of Return 275 Both the Security Market Line and a company's position on it change over time due to changes in interest rates, investors' risk aversion, and individual companies' betas. Such changes are discussed in the following sections. The Impact of Inflation As we discussed in Chapter 6, interest amounts to "rent" on borrowed money, or the price of money. Thus, rRF is the price of money to a riskless borrower. We also saw that the risk-free rate as measured by the rate on U.S. Treasury securities is called the nominal, or quoted, rate, and it consists of two elements: (1) a real, inflation-free rate of return, r*, and (2) an inflation premium, IP, equal to the anticipated rate of inflation.14 Thus, rRF r* IP. The real rate on long-term Treasury bonds has historically ranged from 2 to 4 percent, with a mean of about 3 percent. Therefore, if no inflation were expected, long-term Treasury bonds would yield about 3 percent. However, as the expected rate of inflation increases, a premium must be added to the real risk-free rate of return to compensate investors for the loss of purchasing power that results from inflation. Therefore, the 6 percent rRF shown in Figure 8-10 might be thought of as consisting of a 3 percent real risk-free rate of return plus a 3 percent inflation premium: rRF r* IP 3% 3% 6%. If the expected inflation rate rose by 2 percent, to 3% 2% 5%, this would cause rRF to rise to 8 percent. Such a change is shown in Figure 8-11. Notice that under the CAPM, an increase in rRF leads to an equal increase in the rate of return on all risky assets, because the same inflation premium is built into required rates of return on both riskless and risky assets.15 Therefore, the rate of return on our illustrative average stock, rM, increases from 11 to 13 percent. Other risky securities' returns also rise by two percentage points. Changes in Risk Aversion The slope of the Security Market Line reflects the extent to which investors are averse to risk--the steeper the slope of the line, the more the average investor requires as compensation for bearing risk, which denotes increased risk aversion. Suppose investors were indifferent to risk; that is, they were not at all risk averse. If rRF were 6 percent, then risky assets would also have a required return of 6 percent, because if there were no risk aversion, there would be no risk premium. In that case, the SML would plot as a horizontal line. However, investors are risk averse, so there is a risk premium, and the greater the risk aversion, the steeper the slope of the SML. Figure 8-12 illustrates an increase in risk aversion. The market risk premium rises from 5 to 7.5 percent, causing rM to rise from rM1 11% to rM2 13.5%. The returns on other risky assets also rise, and the effect of this shift in risk aversion is more pronounced on riskier securities. For example, the required return on a stock with bi 0.5 increases by only 1.25 percentage points, from 8.5 to 9.75 percent, whereas that on a stock with bi 1.5 increases by 3.75 percentage points, from 13.5 to 17.25 percent. 14 Long-term Treasury bonds also contain a maturity risk premium, MRP. We include the MRP in r* to simplify the discussion. 15 Recall that the inflation premium for any asset is the average expected rate of inflation over the asset's life. Thus, in this analysis we must assume either that all securities plotted on the SML graph have the same life or else that the expected rate of future inflation is constant. It should also be noted that rRF in a CAPM analysis can be proxied by either a long-term rate (the T-bond rate) or a short-term rate (the T-bill rate). Traditionally, the T-bill rate was used, but in recent years there has been a movement toward use of the T-bond rate because there is a closer relationship between T-bond yields and stocks than between T-bill yields and stocks. See Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2005 Yearbook (Chicago: Ibbotson Associates, 2005) for a discussion. 276 Part 3 Financial Assets FIGURE 8-11 Required Rate of Return (%) Shift in the SML Caused by an Increase in Inflation SML 2 = 8% + 5%(bi) SML 1 = 6% + 5%(bi) rM2 = 13 rM1 = 11 rRF2 = 8 Increase in Anticipated Inflation, rRF1 = 6 Original IP = 3% r* = 3 Real Risk-Free Rate of Return, r* 0 0.5 1.0 1.5 2.0 Risk, b i IP = 2% FIGURE 8-12 Shift in the SML Caused by Increased Risk Aversion SML2 = 6% + 7.5%(bi) Required Rate of Return (%) 17.25 SML1 = 6% + 5%(bi) rM2 = 13.5 rM1 = 11 9.75 8.5 rRF = 6 Original Market Risk Premium, rM1 rRF = 5% New Market Risk Premium, rM2 rRF = 7.5% 0 0.5 1.0 1.5 2.0 Risk, b i Chapter 8 Risk and Rates of Return 277 Changes in a Stock's Beta Coefficient As we shall see later in the book, a firm can influence its market risk, hence its beta, through (1) changes in the composition of its assets and (2) changes in the amount of debt it uses. A company's beta can also change as a result of external factors such as increased competition in its industry, the expiration of basic patents, and the like. When such changes occur, the firm's required rate of return also changes, and, as we shall see in Chapter 9, this will affect the firm's stock price. For example, consider Allied Food Products, with a beta of 1.48. Now suppose some action occurred that caused Allied's beta to increase from 1.48 to 2.0. If the conditions depicted in Figure 8-10 held, Allied's required rate of return would increase from 13.4 to 16 percent: r1 rRF 6% (rM (11% rRF)bi 6%)1.48 13.4% to r2 6% 16% (11% 6%)2.0 As we shall see in Chapter 9, this change would have a negative effect on Allied's stock price. Differentiate among a stock's expected rate of return (r), required ^ rate of return (r), and realized, after-the-fact, historical return (r). Which would have to be larger to induce you to buy the stock, r or r? ^ At a given point in time, would r, r, and r typically be the same or ^ different? Explain. What are the differences between the relative volatility graph (Figure 8-9), where "betas are made," and the SML graph (Figure 8-10), where "betas are used"? Explain how both graphs are constructed and the information they convey. What would happen to the SML graph in Figure 8-10 if inflation increased or decreased? What happens to the SML graph when risk aversion increases or decreases? What would the SML look like if investors were indifferent to risk, that is, if they had zero risk aversion? How can a firm influence the size of its beta? A stock has a beta of 1.2. Assume that the risk-free rate is 4.5 percent and the market risk premium is 5 percent. What is the stock's required rate of return? (10.5%) Kenneth French's Web site, http://mba.tuck .dartmouth.edu/pages/ faculty/ken.french/index .html is an excellent resource for data and information regarding factors related to stock returns. 8.4 SOME CONCERNS ABOUT BETA AND THE CAPM The Capital Asset Pricing Model (CAPM) is more than just an abstract theory described in textbooks--it has great intuitive appeal, and it is widely used by analysts, investors, and corporations. However, a number of recent studies have 278 Part 3 Financial Assets raised concerns about its validity. For example, a study by Eugene Fama of the University of Chicago and Kenneth French of Dartmouth found no historical relationship between stocks' returns and their market betas, confirming a position long held by some professors and stock market analysts.16 As an alternative to the traditional CAPM, researchers and practitioners are developing models with more explanatory variables than just beta. These multivariable models represent an attractive generalization of the traditional CAPM model's insight that market risk--risk that cannot be diversified away--underlies the pricing of assets. In the multi-variable models, risk is assumed to be caused by a number of different factors, whereas the CAPM gauges risk only relative to returns on the market portfolio. These multi-variable models represent a potentially important step forward in finance theory; they also have some deficiencies when applied in practice. As a result, the basic CAPM is still the most widely used method for estimating required rates of return on stocks. Have there been any studies that question the validity of the CAPM? Explain. 8.5 SOME CONCLUDING THOUGHTS: IMPLICATIONS FOR CORPORATE MANAGERS AND INVESTORS The connection between risk and return is an important concept, and it has numerous implications for both corporate managers and investors. As we will see in later chapters, corporate managers spend a great deal of time assessing the risk and returns on individual projects. Indeed, given their concerns about the risk of individual projects, it might be fair to ask why we spend so much time discussing the riskiness of stocks. Why not begin by looking at the riskiness of such business assets as plant and equipment? The reason is that for a management whose primary goal is stock price maximization, the overriding consideration is the riskiness of the firm's stock, and the relevant risk of any physical asset must be measured in terms of its effect on the stock's risk as seen by investors. For example, suppose Goodyear, the tire company, is considering a major investment in a new product, recapped tires. Sales of recaps, hence earnings on the new operation, are highly uncertain, so on a stand-alone basis the new venture appears to be quite risky. However, suppose returns in the recap business are negatively correlated with Goodyear's other operations--when times are good and people have plenty of money, they buy new cars with new tires, but when times are bad, they tend to keep their old cars and buy recaps for them. Therefore, returns would be high on regular operations and low on the recap division during good times, but the opposite would be true during recessions. The result might be a pattern like that shown earlier in Figure 8-5 for Stocks W and M. Thus, what appears to be a risky investment when viewed on a stand-alone basis might not be very risky when viewed within the context of the company as a whole. 16 See Eugene F. Fama and Kenneth R. French, "The Cross-Section of Expected Stock Returns," Journal of Finance, Vol. 47 (1992), pp. 427465; and Eugene F. Fama and Kenneth R. French, "Common Risk Factors in the Returns on Stocks and Bonds," Journal of Financial Economics, Vol. 33 (1993), pp. 356. They found that stock returns are related to firm size and market/book ratios-- small firms, and those with low market/book ratios, had higher returns, but they found no relationship between returns and beta. Chapter 8 Risk and Rates of Return 279 This analysis can be extended to the corporation's stockholders. Because Goodyear's stock is owned by diversified stockholders, the real issue each time management makes an investment decision is this: How will this investment affect the risk of our stockholders? Again, the stand-alone risk of an individual project may look quite high, but viewed in the context of the project's effect on stockholder risk, it may not be very large. We will address this issue again in Chapter 12, where we examine the effects of capital budgeting on companies' beta coefficients and thus on stockholders' risks. While these concepts are obviously important for individual investors, they are also important for corporate managers. We summarize below some key ideas that all investors should consider. 1. There is a trade-off between risk and return. The average investor likes higher returns but dislikes risk. It follows that higher-risk investments need to offer investors higher expected returns. Put another way--if you are seeking higher returns, you must be willing to assume higher risks. 2. Diversification is crucial. By diversifying wisely, investors can dramatically reduce risk without reducing their expected returns. Don't put all of your money in one or two stocks, or one or two industries. A huge mistake many people make is to invest a high percentage of their funds in their employer's stock. If the company goes bankrupt, they not only lose their job but also their invested capital. While no stock is completely riskless, you can smooth out the bumps by holding a well-diversified portfolio. 3. Real returns are what matters. All investors should understand the difference between nominal and real returns. When assessing performance, the real return (what you have left over after inflation) is what really matters. It follows that as expected inflation increases, investors need to receive higher nominal returns. 4. The risk of an investment often depends on how long you plan to hold the investment. Common stocks, for example, can be extremely risky for shortterm investors. However, over the long haul the bumps tend to even out, and thus, stocks are less risky when held as part of a long-term portfolio. Indeed, in his best-selling book Stocks for the Long Run, Jeremy Siegel of the University of Pennsylvania concludes that "The safest long-term investment for the preservation of purchasing power has clearly been stocks, not bonds." 5. While the past gives us insights into the risk and returns on various investments, there is no guarantee that the future will repeat the past. Stocks that have performed well in recent years might tumble, while stocks that have struggled may rebound. The same thing can hold true for the stock market as a whole. Even Jeremy Siegel, who has preached that stocks have historically been good long-term investments, has also argued that there is no assurance that returns in the future will be as strong as they have been in the past. More importantly, when purchasing a stock you always need to ask, "Is this stock fairly valued, or is it currently priced too high?" We discuss this issue more completely in the next chapter. Explain the following statement: "The stand-alone risk of an individual corporate project may be quite high, but viewed in the context of its effect on stockholders' risk, the project's true risk may not be very large." How does the correlation between returns on a project and returns on the firm's other assets affect the project's risk? What are some important concepts for individual investors to consider when evaluating the risk and returns of various investments? 280 Part 3 Financial Assets Tying It All Together In this chapter, we described the relationship between risk and return. We discussed how to calculate risk and return for both individual assets and portfolios. In particular, we differentiated between stand-alone risk and risk in a portfolio context, and we explained the benefits of diversification. We also explained the CAPM, which describes how risk should be measured and how it affects rates of return. In the chapters that follow, we will give you the tools to estimate the required rates of return on a firm's common stock, and we will explain how that return and the yield on its bonds are used to develop the firm's cost of capital. As you will see, the cost of capital is a key element in the capital budgeting process. SELF-TEST QUESTIONS AND PROBLEMS (Solutions Appear in Appendix A) ST-1 Key terms Define the following terms, using graphs or equations to illustrate your answers wherever feasible: a. Risk; stand-alone risk; probability distribution b. Expected rate of return, r ^ c. Continuous probability distribution d. Standard deviation, ; variance, 2; coefficient of variation, CV e. Risk aversion; realized rate of return, r f. Risk premium for Stock i, RPi; market risk premium, RPM g. Expected return on a portfolio, rp; market portfolio ^ h. Correlation; correlation coefficient, r i. Market risk; diversifiable risk; relevant risk j. Capital Asset Pricing Model (CAPM) k. Beta coefficient, b; average stock's beta, bA l. SML equation; Security Market Line (SML) Realized rates of return Stocks A and B have the following historical returns: Year 2001 2002 2003 2004 2005 Stock A's Returns, rA (24.25%) 18.50 38.67 14.33 39.13 Stock B's Returns, rB 5.50% 26.73 48.25 (4.50) 43.86 ST-2 a. b. c. d. Calculate the average rate of return for each stock during the period 2001 through 2005. Assume that someone held a portfolio consisting of 50 percent of Stock A and 50 percent of Stock B. What would the realized rate of return on the portfolio have been in each year from 2001 through 2005? What would the average return on the portfolio have been during that period? Now calculate the standard deviation of returns for each stock and for the portfolio. Use Equation 8-3a. Looking at the annual returns on the two stocks, would you guess that the correlation coefficient between the two stocks is closer to 0.8 or to 0.8? If more randomly selected stocks had been included in the portfolio, which of the following is the most accurate statement of what would have happened to p? (1) p would have remained constant. (2) p would have been in the vicinity of 20 percent. (3) p would have declined to zero if enough stocks had been included. Chapter 8 Risk and Rates of Return 281 ST-3 Beta and the required rate of return ECRI Corporation is a holding company with four main subsidiaries. The percentage of its capital invested in each of the subsidiaries, and their respective betas, are as follows: Subsidiary Electric utility Cable company Real estate development International/special projects Percentage of Capital 60% 25 10 5 Beta 0.70 0.90 1.30 1.50 a. b. c. What is the holding company's beta? If the risk-free rate is 6 percent and the market risk premium is 5 percent, what is the holding company's required rate of return? ECRI is considering a change in its strategic focus; it will reduce its reliance on the electric utility subsidiary, so the percentage of its capital in this subsidiary will be reduced to 50 percent. At the same time, it will increase its reliance on the international/special projects division, so the percentage of its capital in that subsidiary will rise to 15 percent. What will the company's required rate of return be after these changes? QUESTIONS 8-1 Suppose you owned a portfolio consisting of $250,000 of long-term U.S. government bonds. a. Would your portfolio be riskless? Explain. b. Now suppose the portfolio consists of $250,000 of 30-day Treasury bills. Every 30 days your bills mature, and you will reinvest the principal ($250,000) in a new batch of bills. You plan to live on the investment income from your portfolio, and you want to maintain a constant standard of living. Is the T-bill portfolio truly riskless? Explain. c. What is the least risky security you can think of? Explain. The probability distribution of a less risky expected return is more peaked than that of a riskier return. What shape would the probability distribution have for (a) completely certain returns and (b) completely uncertain returns? A life insurance policy is a financial asset, with the premiums paid representing the investment's cost. a. How would you calculate the expected return on a 1-year life insurance policy? b. Suppose the owner of a life insurance policy has no other financial assets--the person's only other asset is "human capital," or earnings capacity. What is the correlation coefficient between the return on the insurance policy and that on the human capital? c. Life insurance companies must pay administrative costs and sales representatives' commissions, hence the expected rate of return on insurance premiums is generally low or even negative. Use portfolio concepts to explain why people buy life insurance in spite of low expected returns. Is it possible to construct a portfolio of real-world stocks that has an expected return equal to the risk-free rate? Stock A has an expected return of 7 percent, a standard deviation of expected returns of 35 percent, a correlation coefficient with the market of 0.3, and a beta coefficient of 0.5. Stock B has an expected return of 12 percent, a standard deviation of returns of 10 percent, a 0.7 correlation with the market, and a beta coefficient of 1.0. Which security is riskier? Why? A stock had a 12 percent return last year, a year when the overall stock market declined. Does this mean that the stock has a negative beta and thus very little risk if held in a portfolio? Explain. If investors' aversion to risk increased, would the risk premium on a high-beta stock increase by more or less than that on a low-beta stock? Explain. If a company's beta were to double, would its required return also double? In Chapter 7 we saw that if the market interest rate, rd, for a given bond increased, then the price of the bond would decline. Applying this same logic to stocks, explain (a) how a decrease in risk aversion would affect stocks' prices and earned rates of return, (b) how this would affect risk premiums as measured by the historical difference between returns on stocks and returns on bonds, and (c) the implications of this for the use of historical risk premiums when applying the SML equation. 8-2 8-3 8-4 8-5 8-6 8-7 8-8 8-9 282 Part 3 Financial Assets PROBLEMS Easy Problems 15 8-1 Expected return A stock's returns have the following distribution: Demand for the Company's Products Weak Below average Average Above average Strong Probability of This Demand Occurring 0.1 0.2 0.4 0.2 0.1 1.0 Rate of Return If This Demand Occurs (50%) (5) 16 25 60 Calculate the stock's expected return, standard deviation, and coefficient of variation. 8-2 Portfolio beta An individual has $35,000 invested in a stock with a beta of 0.8 and another $40,000 invested in a stock with a beta of 1.4. If these are the only two investments in her portfolio, what is her portfolio's beta? Required rate of return Assume that the risk-free rate is 6 percent and the expected return on the market is 13 percent. What is the required rate of return on a stock with a beta of 0.7? Expected and required rates of return Assume that the risk-free rate is 5 percent and the market risk premium is 6 percent. What is the expected return for the overall stock market? What is the required rate of return on a stock with a beta of 1.2? Beta and required rate of return A stock has a required return of 11 percent; the riskfree rate is 7 percent; and the market risk premium is 4 percent. a. What is the stock's beta? b. If the market risk premium increased to 6 percent, what would happen to the stock's required rate of return? Assume the risk-free rate and the beta remain unchanged. Expected returns Stocks X and Y have the following probability distributions of expected future returns: Probability 0.1 0.2 0.4 0.2 0.1 X (10%) 2 12 20 38 Y (35%) 0 20 25 45 8-3 8-4 8-5 Intermediate Problems 613 8-6 a. b. Calculate the expected rate of return, rY, for Stock Y. (rX 12%.) ^ ^ Calculate the standard deviation of expected returns, X , for Stock X. ( Y 20.35%.) Now calculate the coefficient of variation for Stock Y. Is it possible that most investors might regard Stock Y as being less risky than Stock X? Explain. 8-7 Portfolio required return Suppose you are the money manager of a $4 million investment fund. The fund consists of 4 stocks with the following investments and betas: Stock A B C D Investment $ 400,000 600,000 1,000,000 2,000,000 Beta 1.50 (0.50) 1.25 0.75 If the market's required rate of return is 14 percent and the risk-free rate is 6 percent, what is the fund's required rate of return? 8-8 Beta coefficient Given the following information, determine the beta coefficient for Stock J that is consistent with equilibrium: rJ 12.5%; rRF 4.5%; rM 10.5%. ^ Chapter 8 Risk and Rates of Return 283 8-9 Required rate of return Stock R has a beta of 1.5, Stock S has a beta of 0.75, the expected rate of return on an average stock is 13 percent, and the risk-free rate of return is 7 percent. By how much does the required return on the riskier stock exceed the required return on the less risky stock? CAPM and required return Bradford Manufacturing Company has a beta of 1.45, while Farley Industries has a beta of 0.85. The required return on an index fund that holds the entire stock market is 12.0 percent. The risk-free rate of interest is 5 percent. By how much does Bradford's required return exceed Farley's required return? CAPM and required return Calculate the required rate of return for Manning Enterprises, assuming that investors expect a 3.5 percent rate of inflation in the future. The real risk-free rate is 2.5 percent and the market risk premium is 6.5 percent. Manning has a beta of 1.7, and its realized rate of return has averaged 13.5 percent over the past 5 years. CAPM and market risk premium Consider the following information for three stocks, Stocks X, Y, and Z. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.) Stock X Y Z Expected Return 9.00% 10.75 12.50 Standard Deviation 15% 15 15 Beta 0.8 1.2 1.6 8-10 8-11 8-12 Fund P has half of its funds invested in Stock X and half invested in Stock Y. Fund Q has one-third of its funds invested in each of the three stocks. The risk-free rate is 5.5 percent, and the market is in equilibrium. (That is, required returns equal expected returns.) What is the market risk premium (rM rRF)? 8-13 Required rate of return Suppose rRF 9%, rM 14%, and bi 1.3. a. What is ri, the required rate of return on Stock i? b. Now suppose rRF (1) increases to 10 percent or (2) decreases to 8 percent. The slope of the SML remains constant. How would this affect rM and ri? c. Now assume rRF remains at 9 percent but rM (1) increases to 16 percent or (2) falls to 13 percent. The slope of the SML does not remain constant. How would these changes affect ri? Portfolio beta Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio's beta is 1.12. Now suppose you decided to sell one of the stocks in your portfolio with a beta of 1.0 for $7,500 and to use these proceeds to buy another stock with a beta of 1.75. What would your portfolio's new beta be? CAPM and required return HR Industries (HRI) has a beta of 1.8, while LR Industries' (LRI) beta is 0.6. The risk-free rate is 6 percent, and the required rate of return on an average stock is 13 percent. Now the expected rate of inflation built into rRF falls by 1.5 percentage points, the real risk-free rate remains constant, the required return on the market falls to 10.5 percent, and all betas remain constant. After all of these changes, what will be the difference in the required returns for HRI and LRI? CAPM and portfolio return You have been managing a $5 million portfolio that has a beta of 1.25 and a required rate of return of 12 percent. The current risk-free rate is 5.25 percent. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 0.75, what will be the required return on your $5.5 million portfolio? Portfolio beta A mutual fund manager has a $20,000,000 portfolio with a beta of 1.5. The risk-free rate is 4.5 percent and the market risk premium is 5.5 percent. The manager expects to receive an additional $5,000,000, which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund's required return to be 13 percent. What should be the average beta of the new stocks added to the portfolio? Expected returns Suppose you won the lottery and had two options: (1) receiving $0.5 million or (2) a gamble in which you would receive $1 million if a head were flipped but zero if a tail came up. a. What is the expected value of the gamble? b. Would you take the sure $0.5 million or the gamble? c. If you chose the sure $0.5 million, would that indicate that you are a risk averter or a risk seeker? d. Suppose the payoff was actually $0.5 million--that was the only choice. You now face the choice of investing it in either a U.S. Treasury bond that will return $537,500 Challenging Problems 1421 8-14 8-15 8-16 8-17 8-18 284 Part 3 Financial Assets at the end of a year or a common stock that has a 5050 chance of being either worthless or worth $1,150,000 at the end of the year. (1) The expected profit on the T-bond investment is $37,500. What is the expected dollar profit on the stock investment? (2) The expected rate of return on the T-bond investment is 7.5 percent. What is the expected rate of return on the stock investment? (3) Would you invest in the bond or the stock? (4) Exactly how large would the expected profit (or the expected rate of return) have to be on the stock investment to make you invest in the stock, given the 7.5 percent return on the bond? (5) How might your decision be affected if, rather than buying one stock for $0.5 million, you could construct a portfolio consisting of 100 stocks with $5,000 invested in each? Each of these stocks has the same return characteristics as the one stock--that is, a 5050 chance of being worth either zero or $11,500 at yearend. Would the correlation between returns on these stocks matter? 8-19 Evaluating risk and return Stock X has a 10 percent expected return, a beta coefficient of 0.9, and a 35 percent standard deviation of expected returns. Stock Y has a 12.5 percent expected return, a beta coefficient of 1.2, and a 25 percent standard deviation. The riskfree rate is 6 percent, and the market risk premium is 5 percent. a. Calculate each stock's coefficient of variation. b. Which stock is riskier for a diversified investor? c. Calculate each stock's required rate of return. d. On the basis of the two stocks' expected and required returns, which stock would be more attractive to a diversified investor? e. Calculate the required return of a portfolio that has $7,500 invested in Stock X and $2,500 invested in Stock Y. f. If the market risk premium increased to 6 percent, which of the two stocks would have the larger increase in its required return? Realized rates of return Stocks A and B have the following historical returns: Year 2001 2002 2003 2004 2005 Stock A's Returns, rA (18.00%) 33.00 15.00 (0.50) 27.00 Stock B's Returns, rB (14.50%) 21.80 30.50 (7.60) 26.30 8-20 a. b. c. d. e. Calculate the average rate of return for each stock during the period 2001 through 2005. Assume that someone held a portfolio consisting of 50 percent of Stock A and 50 percent of Stock B. What would the realized rate of return on the portfolio have been in each year? What would the average return on the portfolio have been during this period? Calculate the standard deviation of returns for each stock and for the portfolio. Calculate the coefficient of variation for each stock and for the portfolio. Assuming you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why? 8-21 Security Market Line You plan to invest in the Kish Hedge Fund, which has total capital of $500 million invested in five stocks: Stock A B C D E Investment $160 million 120 million 80 million 80 million 60 million Stock's Beta Coefficient 0.5 2.0 4.0 1.0 3.0 Kish's beta coefficient can be found as a weighted average of its stocks' betas. The riskfree rate is 6 percent, and you believe the following probability distribution for future market returns is realistic: Chapter 8 Risk and Rates of Return 285 Probability 0.1 0.2 0.4 0.2 0.1 Market Return 7% 9 11 13 15 a. b. c. What is the equation for the Security Market Line (SML)? (Hint: First determine the expected market return.) Calculate Kish's required rate of return. Suppose Rick Kish, the president, receives a proposal from a company seeking new capital. The amount needed to take a position in the stock is $50 million, it has an expected return of 15 percent, and its estimated beta is 2.0. Should Kish invest in the new company? At what expected rate of return should Kish be indifferent to purchasing the stock? COMPREHENSIVE/SPREADSHEET PROBLEM 8-22 Evaluating risk and return Bartman Industries' and Reynolds Inc.'s stock prices and dividends, along with the Winslow 5000 Index, are shown here for the period 20002005. The Winslow 5000 data are adjusted to include dividends. BARTMAN INDUSTRIES Year Stock Price Dividend 2005 2004 2003 2002 2001 2000 $17.250 14.750 16.500 10.750 11.375 7.625 $1.15 1.06 1.00 0.95 0.90 0.85 REYNOLDS INC. Stock Price Dividend $48.750 52.300 48.750 57.250 60.000 55.750 $3.00 2.90 2.75 2.50 2.25 2.00 WINSLOW 5000 Includes Dividends 11,663.98 8,785.70 8,679.98 6,434.03 5,602.28 4,705.97 a. b. c. d. e. f. g. h. Use the data to calculate annual rates of return for Bartman, Reynolds, and the Winslow 5000 Index, and then calculate each entity's average return over the 5-year period. (Hint: Remember, returns are calculated by subtracting the beginning price from the ending price to get the capital gain or loss, adding the dividend to the capital gain or loss, and dividing the result by the beginning price. Assume that dividends are already included in the index. Also, you cannot calculate the rate of return for 2000 because you do not have 1999 data.) Calculate the standard deviations of the returns for Bartman, Reynolds, and the Winslow 5000. (Hint: Use the sample standard deviation formula, 8-3a, to this chapter, which corresponds to the STDEV function in Excel.) Now calculate the coefficients of variation for Bartman, Reynolds, and the Winslow 5000. Construct a scatter diagram that shows Bartman's and Reynolds's returns on the vertical axis and the Winslow Index's returns on the horizontal axis. Estimate Bartman's and Reynolds's betas by running regressions of their returns against the index's returns. Are these betas consistent with your graph? Assume that the risk-free rate on long-term Treasury bonds is 6.04 percent. Assume also that the average annual return on the Winslow 5000 is not a good estimate of the market's required return--it is too high, so use 11 percent as the expected return on the market. Now use the SML equation to calculate the two companies' required returns. If you formed a portfolio that consisted of 50 percent Bartman and 50 percent Reynolds, what would the beta and the required return be? Suppose an investor wants to include Bartman Industries' stock in his or her portfolio. Stocks A, B, and C are currently in the portfolio, and their betas are 0.769, 0.985, and 1.423, respectively. Calculate the new portfolio's required return if it consists of 25 percent of Bartman, 15 percent of Stock A, 40 percent of Stock B, and 20 percent of Stock C. 286 Part 3 Financial Assets Integrated Case Merrill Finch Inc. 8-23 Risk and return Assume that you recently graduated with a major in finance, and you just landed a job as a financial planner with Merrill Finch Inc., a large financial services corporation. Your first assignment is to invest $100,000 for a client. Because the funds are to be invested in a business at the end of 1 year, you have been instructed to plan for a 1-year holding period. Further, your boss has restricted you to the investment alternatives in the following table, shown with their probabilities and associated outcomes. (Disregard for now the items at the bottom of the data; you will fill in the blanks later.) RETURNS ON ALTERNATIVE INVESTMENTS ESTIMATED RATE OF RETURN State of the Economy Recession Below average Average Above average Boom r ^ s CV b a Probability 0.1 0.2 0.4 0.2 0.1 T-Bills 5.5% 5.5 5.5 5.5 5.5 0.0 High Tech (27.0%) (7.0) 15.0 30.0 45.0 Collections 27.0% 13.0 0.0 (11.0) (21.0) 1.0% 13.2 13.2 0.87 U.S. Rubber 6.0%a (14.0) 3.0 41.0 26.0 9.8% 18.8 1.9 0.88 Market Portfolio (17.0%) (3.0) 10.0 25.0 38.0 10.5% 15.2 1.4 2-Stock Portfolio 0.0% 7.5 12.0 3.4 0.5 Note that the estimated returns of U.S. Rubber do not always move in the same direction as the overall economy. For example, when the economy is below average, consumers purchase fewer tires than they would if the economy was stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a new car may choose to wait and instead purchase new tires for the car they currently own. Under these circumstances, we would expect U.S. Rubber's stock price to be higher if there is a recession than if the economy was just below average. Merrill Finch's economic forecasting staff has developed probability estimates for the state of the economy, and its security analysts have developed a sophisticated computer program, which was used to estimate the rate of return on each alternative under each state of the economy. High Tech Inc. is an electronics firm; Collections Inc. collects past-due debts; and U.S. Rubber manufactures tires and various other rubber and plastics products. Merrill Finch also maintains a "market portfolio" that owns a market-weighted fraction of all publicly traded stocks; you can invest in that portfolio, and thus obtain average stock market results. Given the situation as described, answer the following questions. a. (1) Why is the T-bill's return independent of the state of the economy? Do T-bills promise a completely risk-free return? (2) Why are High Tech's returns expected to move with the economy whereas Collections' are expected to move counter to the economy? b. Calculate the expected rate of return on each alternative and fill in the blanks on the row for r in the table ^ above. c. You should recognize that basing a decision solely on expected returns is only appropriate for riskneutral individuals. Because your client, like virtually everyone, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns. (1) Calculate this value for each alternative, and fill in the blank on the row for s in the table. (2) What type of risk is measured by the standard deviation? (3) Draw a graph that shows roughly the shape of the probability distributions for High Tech, U.S. Rubber, and T-bills. d. Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as being a better measure of stand-alone risk than the standard deviation when the alternatives being considered have widely differing expected returns. Calculate the missing CVs, and fill in the blanks on the row for CV in the table. Does the CV produce the same risk rankings as the standard deviation? e. Suppose you created a 2-stock portfolio by investing $50,000 in High Tech and $50,000 in Collections. (1) Calculate the expected return (rp), the standard deviation (sp), and the coefficient of variation (CVp) ^ for this portfolio and fill in the appropriate blanks in the table. (2) How does the riskiness of this 2-stock portfolio compare with the riskiness of the individual stocks if they were held in isolation? Chapter 8 Risk and Rates of Return 287 f. g. h. Suppose an investor starts with a portfolio consisting of one randomly selected stock. What would happen (1) to the riskiness and (2) to the expected return of the portfolio as more and more randomly selected stocks were added to the portfolio? What is the implication for investors? Draw a graph of the 2 portfolios to illustrate your answer. (1) Should portfolio effects impact the way investors think about the riskiness of individual stocks? (2) If you decided to hold a 1-stock portfolio, and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all of your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying? The expected rates of return and the beta coefficients of the alternatives as supplied by Merrill Finch's computer program are as follows: Security High Tech Market U.S. Rubber T-bills Collections Return (r ) ^ 12.4% 10.5 9.8 5.5 1.0 Risk (Beta) 1.32 1.00 0.88 0.00 (0.87) i. j. (1) What is a beta coefficient, and how are betas used in risk analysis? (2) Do the expected returns appear to be related to each alternative's market risk? (3) Is it possible to choose among the alternatives on the basis of the information developed thus far? Use the data given at the start of the problem to construct a graph that shows how the T-bill's, High Tech's, and the market's beta coefficients are calculated. Then discuss what betas measure and how they are used in risk analysis. The yield curve is currently flat, that is, long-term Treasury bonds also have a 5.5 percent yield. Consequently, Merrill Finch assumes that the risk-free rate is 5.5 percent. (1) Write out the Security Market Line (SML) equation, use it to calculate the required rate of return on each alternative, and then graph the relationship between the expected and required rates of return. (2) How do the expected rates of return compare with the required rates of return? (3) Does the fact that Collections has an expected return that is less than the T-bill rate make any sense? (4) What would be the market risk and the required return of a 5050 portfolio of High Tech and Collections? Of High Tech and U.S. Rubber? (1) Suppose investors raised their inflation expectations by 3 percentage points over current estimates as reflected in the 5.5 percent risk-free rate. What effect would higher inflation have on the SML and on the returns required on high- and low-risk securities? (2) Suppose instead that investors' risk aversion increased enough to cause the market risk premium to increase by 3 percentage points. (Inflation remains constant.) What effect would this have on the SML and on returns of high- and low-risk securities? Please go to the ThomsonNOW Web site to access the Cyberproblems. Access the Thomson ONE problems though the ThomsonNOW Web site. Use the Thomson ONE--Business School Edition online database to work this chapter's questions. Using Past Information to Estimate Required Returns Chapter 8 discussed the basic trade-off between risk and return. In the Capital Asset Pricing Model (CAPM) discussion, beta is identified as the correct measure of risk for diversified shareholders. Recall that beta measures the extent to which the returns of a given 288 Part 3 Financial Assets stock move with the stock market. When using the CAPM to estimate required returns, we would ideally like to know how the stock will move with the market in the future, but since we don't have a crystal ball we generally use historical data to estimate this relationship with beta. As mentioned in the Web Appendix for this chapter, beta can be estimated by regressing the individual stock's returns against the returns of the overall market. As an alternative to running our own regressions, we can instead rely on reported betas from a variety of sources. These published sources make it easy for us to readily obtain beta estimates for most large publicly traded corporations. However, a word of caution is in order. Beta estimates can often be quite sensitive to the time period in which the data are estimated, the market index used, and the frequency of the data used. Therefore, it is not uncommon to find a wide range of beta estimates among the various published sources. Indeed, Thomson One reports multiple beta estimates. These multiple estimates reflect the fact that Thomson One puts together data from a variety of different sources. Discussion Questions 1. Begin by taking a look at the historical performance of the overall stock market. If you want to see, for example, the performance of the S&P 500, select INDICES and enter S&PCOMP. Click on PERFORMANCE and you will immediately see a quick summary of the market's performance in recent months and years. How has the market performed over the past year? The past 3 years? The past 5 years? The past 10 years? 2. Now let's take a closer look at the stocks of four companies: Colgate Palmolive (Ticker CL), Gillette (G), Merrill Lynch (MER), and Microsoft (MSFT). Before looking at the data, which of these companies would you expect to have a relatively high beta (greater than 1.0), and which of these companies would you expect to have a relatively low beta (less than 1.0)? 3. Select one of the four stocks listed in question 2 by selecting COMPANIES, entering the company's ticker symbol, and clicking on GO. On the overview page, you should see a chart that summarizes how the stock has done relative to the S&P 500 over the past 6 months. Has the stock outperformed or underperformed the overall market during this time period? 4. Return to the overview page for the stock you selected. If you scroll down the page you should see an estimate of the company's beta. What is the company's beta? What was the source of the estimated beta? 5. Click on the tab labeled PRICES. What is the company's current dividend yield? What has been its total return to investors over the past 6 months? Over the past year? Over the past 3 years? (Remember that total return includes the dividend yield plus any capital gains or losses.) 6. What is the estimated beta on this page? What is the source of the estimated beta? Why might different sources produce different estimates of beta? [Note if you want to see even more beta estimates, click OVERVIEWS (on second line of tabs) and then select the SEC DATABASE MARKET DATA. Scroll through the STOCK OVERVIEW SECTION and you will see a range of different beta estimates.] 7. Select a beta estimate that you believe is best. (If you are not sure, you may want to consider an average of the given estimates.) Assume that the risk-free rate is 5 percent and the market risk premium is 6 percent. What is the required return on the company's stock? 8. Repeat the same exercise for each of the 3 remaining companies. Do the reported betas confirm your earlier intuition? In general, do you find that the higher-beta stocks tend to do better in up markets and worse in down markets? Explain. C H APTE R 9 STOCKS AND THEIR VALUATION Searching for the Right Stock A recent study by the securities industry found that roughly half of all U.S. households have invested in common stocks. As noted in Chapter 8, the longrun performance of the U.S. stock market has been quite good. Indeed, during the past 75 years the market's average annual return has exceeded 12 percent. However, there is no guarantee that stocks will perform in the future as well as they have in the past. The stock market doesn't always go up, and investors can make or lose a lot of money in a short period of time. For example, in 2004, Apple Computer's stock more than tripled following sizzling sales of its iPod products. On the other hand, Merck's stock fell more than 30 percent in 2004, when it was forced to withdraw one of its best-selling drugs, Vioxx. The broader market as represented by the Dow Jones Industrial Average declined 2.6 percent during the first quarter of 2005. The triggers here were concerns about rising interest rates, higher oil prices, and declining consumer confidence. During this quarter, several well-respected companies experienced much larger declines--for example, Microsoft fell 9.5 percent, Home Depot 10.5 percent, and General Motors 26.6 percent. This shows, first, that diversification is important, and second, that when it comes to picking stocks, it is not enough to simply pick a good company--the stock must also be "fairly" priced. To determine if a stock is fairly priced, you first need to estimate the stock's true or "intrinsic value," a concept first discussed in Chapter 1. With this objective in mind, this chapter describes some models that analysts have used to estimate a stock's intrinsic value. As you will see, it is difficult to predict future stock prices, but we are not completely in the dark. After studying this chapter, you should have a reasonably good understanding of the factors that influence stock prices, and with that knowledge--plus a little luck--you should be able to successfully navigate the stock market's often treacherous ups and downs. Source: Justin Lahart, "Last Year's Winners Had Little in Common," The Wall Street Journal, January 3, 2005, p. R8. STEVE GREENBERG/INDEX STOCK IMAGERY/PICTUREQUEST 290 Part 3 Financial Assets Putting Things In Perspective In Chapter 7 we examined bonds. We now turn to common and preferred stocks, beginning with some important background material that helps establish a framework for valuing these securities. While it is generally easy to predict the cash flows received from bonds, forecasting the cash flows on common stocks is much more difficult. However, two fairly straightforward models can be used to help estimate the "true," or intrinsic, value of a common stock: (1) the dividend growth model and (2) the total corporate value model. A stock should be bought if its estimated intrinsic value exceeds its market price but sold if the price exceeds its intrinsic value. The same valuation concepts and models are also used in Chapter 10, where we estimate the cost of capital, a critical element in corporate investment decisions. Key trends in the securities industry are listed and explained at http://www.sia.com/ research/html/key_ industry_trends_.html. 9.1 LEGAL RIGHTS AND PRIVILEGES OF COMMON STOCKHOLDERS Its common stockholders are the owners of a corporation, and as such they have certain rights and privileges, as discussed in this section. Control of the Firm A firm's common stockholders have the right to elect its directors, who, in turn, elect the officers who manage the business. In a small firm, the major stockholder typically is also the president and chair of the board of directors. In large, publicly owned firms, the managers typically have some stock, but their personal holdings are generally insufficient to give them voting control. Thus, the managements of most publicly owned firms can be removed by the stockholders if the management team is not effective. State and federal laws stipulate how stockholder control is to be exercised. First, corporations must hold elections of directors periodically, usually once a year, with the vote taken at the annual meeting. Frequently, one-third of the directors are elected each year for a three-year term. Each share of stock has one vote; thus, the owner of 1,000 shares has 1,000 votes for each director.1 Stockholders can appear at the annual meeting and vote in person, but typically they transfer their right to vote to another person by means of a proxy. Management always solicits stockholders' proxies and usually gets them. However, if earnings are poor and stockholders are dissatisfied, an outside group may solicit the 1 Proxy A document giving one person the authority to act for another, typically the power to vote shares of common stock. In the situation described, a 1,000-share stockholder could cast 1,000 votes for each of three directors if there were three contested seats on the board. An alternative procedure that may be prescribed in the corporate charter calls for cumulative voting. There the 1,000-share stockholder would get 3,000 votes if there were three vacancies, and he or she could cast all of them for one director. Cumulative voting helps small groups obtain representation on the board. Chapter 9 Stocks and Their Valuation 291 proxies in an effort to overthrow management and take control of the business. This is known as a proxy fight. The question of control has become a central issue in finance in recent years. The frequency of proxy fights has increased, as have attempts by one corporation to take over another by purchasing a majority of the outstanding stock. These actions are called takeovers. Some well-known examples of takeover battles include KKR's acquisition of RJR Nabisco, Chevron's acquisition of Gulf Oil, and the QVC/Viacom fight to take over Paramount. Managers without majority control (more than 50 percent of their firms' stock) are very much concerned about proxy fights and takeovers, and many of them have attempted to obtain stockholder approval for changes in their corporate charters that would make takeovers more difficult. For example, a number of companies have gotten their stockholders to agree (1) to elect only one-third of the directors each year (rather than electing all directors each year), (2) to require 75 percent of the stockholders (rather than 50 percent) to approve a merger, and (3) to vote in a "poison pill" provision that would allow the stockholders of a firm that is taken over by another firm to buy shares in the second firm at a reduced price. The poison pill makes the acquisition unattractive and, thus, wards off hostile takeover attempts. Managements seeking such changes generally cite a fear that the firm will be picked up at a bargain price, but it often appears that management's concern about its own position is an even more important consideration. Management moves to make takeovers more difficult have been countered by stockholders, especially large institutional stockholders, who do not like barriers erected to protect incompetent managers. To illustrate, the California Public Employees Retirement System (Calpers), which is one of the largest institutional investors, has led proxy fights with several corporations whose financial performances were poor in Calpers' judgment. Calpers wants companies to give outside (nonmanagement) directors more clout and to force managers to be more responsive to stockholder complaints. Prior to 1993, SEC rules prohibited large investors such as Calpers from getting together to force corporate managers to institute policy changes. However, the SEC changed its rules in 1993, and now large investors can work together to force management changes. This ruling has helped keep managers focused on stockholder concerns, which means the maximization of stock prices. Proxy Fight An attempt by a person or group to gain control of a firm by getting its stockholders to grant that person or group the authority to vote their shares to replace the current management. Takeover An action whereby a person or group succeeds in ousting a firm's management and taking control of the company. The Preemptive Right Common stockholders often have the right, called the preemptive right, to purchase any additional shares sold by the firm. In some states, the preemptive right is automatically included in every corporate charter; in others, it must be specifically inserted into the charter. The purpose of the preemptive right is twofold. First, it prevents the management of a corporation from issuing a large number of additional shares and purchasing these shares itself. Management could thereby seize control of the corporation and frustrate the will of the current stockholders. The second, and far more important, reason for the preemptive right is to protect stockholders against a dilution of value. For example, suppose 1,000 shares of common stock, each with a price of $100, were outstanding, making the total market value of the firm $100,000. If an additional 1,000 shares were sold at $50 a share, or for $50,000, this would raise the total market value to $150,000. When the new total market value is divided by new total shares outstanding, a value of $75 a share is obtained. The old stockholders would thus lose $25 per share, and the new stockholders would have an instant profit of $25 per share. Thus, selling common stock at a price below the market value would dilute its price and transfer Preemptive Right A provision in the corporate charter or bylaws that gives common stockholders the right to purchase on a pro rata basis new issues of common stock (or convertible securities). 292 Part 3 Financial Assets wealth from the present stockholders to those who were allowed to purchase the new shares. The preemptive right prevents this. Identify some actions that companies have taken to make takeovers more difficult. What is the preemptive right, and what are the two primary reasons for its existence? 9.2 TYPES OF COMMON STOCK Classified Stock Common stock that is given a special designation, such as Class A, Class B, and so forth, to meet special needs of the company. Founders' Shares Stock owned by the firm's founders that has sole voting rights but restricted dividends for a specified number of years. Although most firms have only one type of common stock, in some instances classified stock is used to meet special needs. Generally, when special classifications are used, one type is designated Class A, another Class B, and so on. Small, new companies seeking funds from outside sources frequently use different types of common stock. For example, when Genetic Concepts went public recently, its Class A stock was sold to the public and paid a dividend, but this stock had no voting rights for five years. Its Class B stock, which was retained by the organizers of the company, had full voting rights for five years, but the legal terms stated that dividends could not be paid on the Class B stock until the company had established its earning power by building up retained earnings to a designated level. The use of classified stock thus enabled the public to take a position in a conservatively financed growth company without sacrificing income, while the founders retained absolute control during the crucial early stages of the firm's development. At the same time, outside investors were protected against excessive withdrawals of funds by the original owners. As is often the case in such situations, the Class B stock was also called founders' shares. Note that "Class A," "Class B," and so on, have no standard meanings. Most firms have no classified shares, but a firm that does could designate its Class B shares as founders' shares and its Class A shares as those sold to the public, while another could reverse these designations. Still other firms could use stock classifications for entirely different purposes. For example, when General Motors acquired Hughes Aircraft for $5 billion, it paid in part with a new Class H common, GMH, which had limited voting rights and whose dividends were tied to Hughes's performance as a GM subsidiary. The reasons for the new stock were that (1) GM wanted to limit voting privileges on the new classified stock because of management's concern about a possible takeover and (2) Hughes employees wanted to be rewarded more directly on Hughes's own performance than would have been possible through regular GM stock. These Class H shares disappeared in 2003 when GM decided to sell off the Hughes unit. What are some reasons why a company might use classified stock? 9.3 COMMON STOCK VALUATION Common stock represents an ownership interest in a corporation, but to the typical investor, a share of common stock is simply a piece of paper characterized by two features: 1. It entitles its owner to dividends, but only if the company has earnings out of which dividends can be paid and management chooses to pay dividends rather than retaining and reinvesting all the earnings. Whereas a bond con- Chapter 9 Stocks and Their Valuation 293 tains a promise to pay interest, common stock provides no such promise--if you own a stock, you may expect a dividend, but your expectations may not in fact be met. To illustrate, Long Island Lighting Company (LILCO) had paid dividends on its common stock for more than 50 years, and people expected those dividends to continue. However, when the company encountered severe problems a few years ago, it stopped paying dividends. Note, though, that LILCO continued to pay interest on its bonds, because if it had not, then it would have been declared bankrupt and the bondholders could have taken over the company. 2. Stock can be sold, hopefully at a price greater than the purchase price. If the stock is actually sold at a price above its purchase price, the investor will receive a capital gain. Generally, when people buy common stock they expect to receive capital gains; otherwise, they would not buy the stock. However, after the fact, they can end up with capital losses rather than capital gains. LILCO's stock price dropped from $17.50 to $3.75 in one year, so the expected capital gain on that stock turned out to be a huge actual capital loss. Definitions of Terms Used in Stock Valuation Models Common stocks provide an expected future cash flow stream, and a stock's value is found as the present value of the expected future cash flows, which consist of two elements: (1) the dividends expected in each year and (2) the price investors expect to receive when they sell the stock. The final price includes the return of the original investment plus an expected capital gain. We saw in Chapter 1 that managers should seek to maximize the value of their firms' stock. Therefore, managers need to know how alternative actions are likely to affect stock prices, and we develop some models to help show how the value of a share of stock is determined. We begin by defining the following terms: Dt dividend the stockholder expects to receive at the end of each Year t. D0 is the most recent dividend, which has already been paid; D1 is the first dividend expected, and it will be paid at the end of this year; D2 is the dividend expected at the end of two years; and so forth. D1 represents the first cash flow a new purchaser of the stock will receive. Note that D0, the dividend that has just been paid, is known with certainty. However, all future dividends are expected values, those expectations differ somewhat from investor to investor, and those differences lead to differences in estimates of the stock's intrinsic value.2 actual market price of the stock today. expected price of the stock at the end of each Year t (pro^ nounced "P hat t"). Pt is the intrinsic value of the stock today as seen by the particular investor doing the analy^ sis; P1 is the price expected at the end of one year; and so ^ on. Note that P0 is the intrinsic value of the stock today based on a particular investor's estimate of the stock's expected dividend stream and the riskiness of that stream. Hence, whereas the market price P0 is fixed and P0 ^ Pt Market Price, P0 The price at which a stock sells in the market. ^ Intrinsic Value, P0 The value of an asset that, in the mind of a particular investor, is justified by the facts; ^ P0 may be different from the asset's current market price. 2 Stocks generally pay dividends quarterly, so theoretically we should evaluate them on a quarterly basis. However, in stock valuation, most analysts work on an annual basis because the data generally are not precise enough to warrant refinement to a quarterly model. For additional information on the quarterly model, see Charles M. Linke and J. Kenton Zumwalt, "Estimation Biases in Discounted Cash Flow Analysis of Equity Capital Cost in Rate Regulation," Financial Management, Autumn 1984, pp. 1521. 294 Part 3 Financial Assets Growth Rate, g The expected rate of growth in dividends per share. g Required Rate of Return, rs The minimum rate of return on a common stock that a stockholder considers acceptable. Expected Rate of Return, rs ^ The rate of return on a common stock that a stockholder expects to receive in the future. Actual Realized Rate of Return, rs The rate of return on a common stock actually received by stockholders in some past period. rs may be greater or less than rs ^ and/or rs. Dividend Yield The expected dividend divided by the current price of a share of stock. Capital Gains Yield The capital gain during a given year divided by the beginning price. Expected Total Return The sum of the expected dividend yield and the expected capital gains yield. rs rs ^ rs D1/P0 ^ P1 P0 P0 Expected total return ^ is identical for all investors, P0 could differ among investors, depending on how optimistic they are regarding ^ the company. P0, the individual investor's estimate of the intrinsic value today, could be above or below P0, the current stock price. An investor would buy the stock only if ^ their estimate of P0 were equal to or greater than P0. As there are many investors in the market, there can be ^ many values for P0. However, we can think of an "average," or "marginal," investor whose actions actually determine the market price. For the marginal investor, P0 must ^ equal P0; otherwise, a disequilibrium would exist, and buying and selling in the market would change P0 until ^ P0 P0 for the marginal investor. expected growth rate in dividends as predicted by the marginal investor. If dividends are expected to grow at a constant rate, g is also equal to the expected rate of growth in earnings and in the stock's price. Different investors use different g's to evaluate a firm's stock, but the market price, P0, is set on the basis of g as estimated by the marginal investor. minimum acceptable, or required, rate of return on the stock, considering both its riskiness and the returns available on other investments. Again, this term generally relates to the marginal investor. The determinants of rs include the real rate of return, expected inflation, and risk as discussed in Chapter 8. expected rate of return that an investor who buys the stock expects to receive in the future. rs (pronounced "r ^ hat s") could be above or below rs, but one would buy the stock only if rs were equal to or greater than rs. ^ actual, or realized, after-the-fact rate of return, pronounced "r bar s." You may expect to obtain a return of rs 10% if you buy a stock today, but if the market goes down, you may end up next year with an actual realized return that is much lower, perhaps even negative. expected dividend yield on the stock during the coming year. If the stock is expected to pay a dividend of D1 $1 during the next 12 months, and if its current price is P0 $20, then the expected dividend yield is $1/$20 0.05 5%. expected capital gains yield on the stock during the coming year. If the stock sells for $20 today, and if it is expected to rise to $21.00 at the end of one year, then the ^ expected capital gain is P1 P0 $21.00 $20.00 $1.00, and the expected capital gains yield is $1.00/$20 0.05 5%. rs expected dividend yield (D1/P0) plus expected capi^ ^ tal gains yield [(P1 P0)/P0]. In our example, the expected total return rs 5% 5% 10%. ^ Expected Dividends as the Basis for Stock Values In our discussion of bonds, we found the value of a bond as the present value of interest payments over the life of the bond plus the present value of the bond's maturity (or par) value: Chapter 9 Stocks and Their Valuation 295 VB Stock prices are likewise determined as the present value of a stream of cash flows, and the basic stock valuation equation is similar to the bond valuation equation. What are the cash flows that corporations provide to their stockholders? First, think of yourself as an investor who buys a stock with the intention of holding it (in your family) forever. In this case, all that you (and your heirs) would receive is a stream of dividends, and the value of the stock today is calculated as the present value of an infinite stream of dividends: INT 11 rd 2 1 INT 11 rd 2 2 ### INT 11 rd 2 N M 11 rd 2 N Value of stock ^ P0 PV of expected future dividends D1 D2 1 11 rs 2 11 rs 2 2 Dt a 11 r 2 t t 1 s ### 11 D rs 2 (9-1) What about the more typical case, where you expect to hold the stock for a finite ^ period and then sell it--what will be the value of P0 in this case? Unless the company is likely to be liquidated or sold and thus to disappear, the value of the stock is again determined by Equation 9-1. To see this, recognize that for any individual investor, the expected cash flows consist of expected dividends plus the expected sale price of the stock. However, the sale price the current investor receives will depend on the dividends some future investor expects. Therefore, for all present and future investors in total, expected cash flows must be based on expected future dividends. Put another way, unless a firm is liquidated or sold to another concern, the cash flows it provides to its stockholders will consist only of a stream of dividends; therefore, the value of a share of its stock must be established as the present value of that expected dividend stream. The general validity of Equation 9-1 can also be confirmed by asking the following question: Suppose I buy a stock and expect to hold it for one year. I will ^ receive dividends during the year plus the value P1 when I sell out at the end of the ^1? The answer is that it will be deteryear. But what will determine the value of P mined as the present value of the dividends expected during Year 2 plus the stock price at the end of that year, which, in turn, will be determined as the present value of another set of future dividends and an even more distant stock price. This process can be continued ad infinitum, and the ultimate result is Equation 9-1.3 Explain the following statement: "Whereas a bond contains a promise to pay interest, a share of common stock typically provides an expectation of, but no promise of, dividends plus capital gains." What are the two parts of most stocks' expected total return? If D1 $2.00, g 6%, and P0 $40, what are the stock's expected dividend yield, capital gains yield, and total expected return for the coming year? (5%, 6%, 11%) 3 We should note that investors periodically lose sight of the long-run nature of stocks as investments and forget that in order to sell a stock at a profit, one must find a buyer who will pay the higher price. If you analyze a stock's value in accordance with Equation 9-1, conclude that the stock's market price exceeds a reasonable value, and then buy the stock anyway, then you would be following the "bigger fool" theory of investment--you think you may be a fool to buy the stock at its excessive price, but you also think that when you get ready to sell it, you can find someone who is an even bigger fool. The bigger fool theory was widely followed in the summer of 1987, just before the stock market lost more than one-third of its value in the October 1987 crash. 296 Part 3 Financial Assets 9.4 CONSTANT GROWTH STOCKS Equation 9-1 is a generalized stock valuation model in the sense that the time pattern of Dt can be anything: Dt can be rising, falling, fluctuating randomly, or it can even be zero for several years and Equation 9-1 will still hold. With a computer spreadsheet we can easily use this equation to find a stock's intrinsic value for any pattern of dividends. In practice, the hard part is obtaining an accurate forecast of the future dividends. In many cases, the stream of dividends is expected to grow at a constant rate. If this is the case, Equation 9-1 may be rewritten as follows: ^ P0 D0 11 11 D0 11 g2 rs g Constant Growth (Gordon) Model Used to find the value of a constant growth stock. rs 2 g2 1 1 D0 11 11 D1 rs g rs 2 g2 2 2 ### D0 11 g2 11 rs 2 (9-2) The last term of Equation 9-2 is called the constant growth model, or the Gordon model, after Myron J. Gordon, who did much to develop and popularize it.4 Illustration of a Constant Growth Stock Assume that Allied Food Products just paid a dividend of $1.15 (that is, D0 $1.15). Its stock has a required rate of return, rs, of 13.4 percent, and investors expect the dividend to grow at a constant 8 percent rate in the future. The estimated dividend one year hence would be D1 $1.15(1.08) $1.24; D2 would be $1.34; and the estimated dividend five years hence would be $1.69: D5 D0 11 g2 5 $1.15 11.082 5 $1.69 We could use this procedure to estimate all future dividends, then use Equation ^ 9-1 to determine the current stock value, P0. In other words, we could find each expected future dividend, calculate its present value, and then sum all the present values to find the intrinsic value of the stock. Such a process would be time consuming, but we can take a short cut--just insert the illustrative data into Equation 9-2 to find the stock's intrinsic value, $23: ^ P0 $1.15 11.082 0.134 0.08 $1.242 0.054 $23.00 Note that a necessary condition for the derivation of Equation 9-2 is that the required rate of return, rs, be greater than the long-run growth rate, g. If the equation is used in situations where rs is not greater than g, the results will be wrong, meaningless, and possibly misleading. The concept underlying the valuation process for a constant growth stock is graphed in Figure 9-1. Dividends are growing at the rate g 8 percent, but because rs g, the present value of each future dividend is declining. For example, the dividend in Year 1 is D1 D0(1 g)1 $1.15(1.08) $1.242. However, the present value of this dividend, discounted at 13.4 percent, is PV(D1) $1.242/(1.134)1 $1.095. The dividend expected in Year 2 grows to $1.242 (1.08) $1.341, but the present value of this dividend falls to $1.043. Continuing, 4 The last term in Equation 9-2 is derived in the Web/CD Extension of Chapter 5 of Eugene F. Brigham and Phillip R. Daves, Intermediate Financial Management, 8th ed. (Mason, OH: Thomson/ South-Western, 2004). In essence, Equation 9-2 is the sum of a geometric progression, and the final result is the solution value of the progression. Chapter 9 Stocks and Their Valuation 297 FIGURE 9-1 Present Values of Dividends of a Constant Growth Stock where D0 $1.15, g 8%, rs 13.4% Dividend ($) Dollar Amount of Each Dividend = D 0 (1 + g) t 1.15 PV D1 = 1.10 PV of Each Dividend = D0 (1 + g)t (1 + rs ) t ^ P0 = t=1 PV Dt 8 = Area under PV Curve = $23.00 0 5 10 15 20 Years D3 $1.449 and PV(D3) $0.993, and so on. Thus, the expected dividends are growing, but the present value of each successive dividend is declining, because the dividend growth rate (8 percent) is less than the rate used for discounting the dividends to the present (13.4 percent). If we summed the present values of each future dividend, this summation ^ would be the value of the stock, P0. When g is a constant, this summation is g), as shown in Equation 9-2. Therefore, if we extended the equal to D1/(rs lower step-function curve in Figure 9-1 on out to infinity and added up the present values of each future dividend, the summation would be identical to the value given by Equation 9-2, $23.00. Note that if the growth rate exceeded the required return, the PV of each future dividend would exceed that of the prior year. If this situation were graphed in Figure 9-1, both step-function curves would be increasing, suggesting an infinitely high stock price. Moreover, the stock price as calculated using Equation 9-2 would be negative. Obviously, stock prices can be neither infinite nor negative, and this illustrates why Equation 9-2 cannot be used unless rs g. We will return to this point later in the chapter. Dividend and Earnings Growth Growth in dividends occurs primarily as a result of growth in earnings per share (EPS). Earnings growth, in turn, results from a number of factors, including (1) the amount of earnings the company retains and reinvests, (2) the rate of 298 Part 3 Financial Assets return the company earns on its equity (ROE), and (3) inflation. Regarding inflation, if output (in units) is stable but both sales prices and input costs rise at the inflation rate, then EPS will also grow at the inflation rate. Even without inflation, EPS will also grow as a result of the reinvestment, or plowback, of earnings. If the firm's earnings are not all paid out as dividends (that is, if some fraction of earnings is retained), the dollars of investment behind each share will rise over time, which should lead to growth in earnings and dividends. Even though a stock's value is derived from expected dividends, this does not necessarily mean that corporations can increase their stock prices by simply raising the current dividend. Shareholders care about all dividends, both current and those expected in the future. Moreover, there is a trade-off between current dividends, and future dividends. Companies that pay most of their current earnings out as dividends are obviously not retaining and reinvesting much in the business, and that reduces future earnings and dividends. So, the issue is this: Do shareholders prefer higher current dividends at the cost of lower future dividends, lower current dividends, and more growth, or are they indifferent between growth and dividends? As we will see in the chapter on distributions to shareholders, there is no simple answer to this question. Shareholders should prefer to have the company retain earnings, hence pay less current dividends, if it has highly profitable investment opportunities, but they should prefer to have the company pay earnings out if investment opportunities are poor. Taxes also play a role--since capital gains are tax deferred while dividends are taxed immediately, this might lead to a preference for retention and growth over current dividends. We will consider dividend policy in detail later in Part 5 of this text. When Can the Constant Growth Model Be Used? The constant growth model is most appropriate for mature companies with a stable history of growth and stable future expectations. Expected growth rates vary somewhat among companies, but dividends for mature firms are often expected to grow in the future at about the same rate as nominal gross domestic product (real GDP plus inflation). On this basis, one might expect the dividends of an average, or "normal," company to grow at a rate of 5 to 8 percent a year. Note too that Equation 9-2 is sufficiently general to handle the case of a zero growth stock, where the dividend is expected to remain constant over time. If g 0, Equation 9-2 reduces to Equation 9-3: Zero Growth Stock A common stock whose future dividends are not expected to grow at all; that is, g 0. ^ P0 D rs (9-3) This is conceptually the same equation as the one we developed in Chapter 2 for a perpetuity, and it is simply the current dividend divided by the discount rate. Write out and explain the valuation formula for a constant growth stock. Explain how the formula for a zero growth stock is related to that for a constant growth stock. A stock is expected to pay a dividend of $1 at the end of the year. The required rate of return is rs 11%. What would the stock's price be if the growth rate were 5 percent? What would the price be if g 0%? ($16.67; $9.09) Chapter 9 Stocks and Their Valuation 299 9.5 EXPECTED RATE OF RETURN ON A CONSTANT GROWTH STOCK We can solve Equation 9-2 for rs, again using the hat to indicate that we are dealing with an expected rate of return:5 Expected rate of return r ^s Expected dividend yield D1 g P0 Expected growth rate, or capital gains yield (9-4) Thus, if you buy a stock for a price P0 $23, and if you expect the stock to pay a dividend D1 $1.242 one year from now and to grow at a constant rate g 8% in the future, then your expected rate of return will be 13.4 percent: r ^s $1.242 $23 8% 5.4% 8% 13.4% In this form, we see that rs is the expected total return and that it consists of an ^ expected dividend yield, D1/P0 5.4%, plus an expected growth rate or capital gains yield, g 8%. Suppose this analysis had been conducted on January 1, 2006, so P0 $23 is the January 1, 2006, stock price, and D1 $1.242 is the dividend expected at the end of 2006. What is the expected stock price at the end of 2006? We would again apply Equation 9-2, but this time we would use the year-end dividend, D2 D1(1 g) $1.242(1.08) $1.3414: ^ P12>31>06 D2007 rs g $1.3414 0.134 0.08 $24.84 Notice that $24.84 is 8 percent greater than P0, the $23 price on January 1, 2006: $23 11.082 $24.84 $1.84 during Thus, we would expect to make a capital gain of $24.84 $23.00 2006, which would provide a capital gains yield of 8 percent: Capital gains yield2006 Capital gain Beginning price $1.84 $23.00 0.08 8% The popular Motley Fool Web site, http:// www.fool.com/school/ introductiontovaluation .htm, provides a good We could extend the analysis on out, and in each future year the expected capital gains yield would always equal g, the expected dividend growth rate. For example, the dividend yield in 2007 could be estimated as follows: Dividend yield2007 D2007 ^ P12>31>06 $1.3414 $24.84 0.054 5.4% The dividend yield for 2008 could also be calculated, and again it would be 5.4 percent. Thus, for a constant growth stock, the following conditions must hold: 1. The expected dividend yield is a constant. 2. The dividend is expected to grow forever at a constant rate, g. 5 description of some of the benefits and drawbacks of a few of the more commonly used valuation procedures. The rs value in Equation 9-2 is a required rate of return, but when we transform to obtain Equation ^ 9-4, we are finding an expected rate of return. Obviously, the transformation requires that rs = rs. This equality holds if the stock market is in equilibrium, a condition that we discussed in Chapter 5. 300 Part 3 Financial Assets 3. The stock price is expected to grow at this same rate. 4. The expected capital gains yield is also a constant, and it is equal to g. The term expected should be clarified--it means expected in a probabilistic sense, as the "statistically expected" outcome. Thus, when we say that the growth rate is expected to remain constant at 8 percent, we mean that the best prediction for the growth rate in any future year is 8 percent, not that we literally expect the growth rate to be exactly 8 percent in each future year. In this sense, the constant growth assumption is reasonable for many large, mature companies. What conditions must hold if a stock is to be evaluated using the constant growth model? What does the term "expected" mean when we say expected growth rate? Suppose an analyst says that she values GE based on a forecasted growth rate of 6 percent for earnings, dividends, and the stock price. If the growth rate next year turns out to be 5 or 7 percent, would this mean that the analyst's forecast was faulty? Explain. 9.6 VALUING STOCKS EXPECTED TO GROW AT A NONCONSTANT RATE For many companies, it is not appropriate to assume that dividends will grow at a constant rate because firms typically go through life cycles with different growth rates at different parts of the cycle. During their early years, they generally grow much faster than the economy as a whole; then they match the economy's growth; and finally they grow at a slower rate than the economy.6 Automobile manufacturers in the 1920s, computer software firms such as Microsoft in the 1980s, and wireless firms in the early 2000s are examples of firms in the early part of the cycle; these firms are called supernormal, or nonconstant, growth firms. Figure 9-2 illustrates nonconstant growth and also compares it with normal growth, zero growth, and negative growth.7 Supernormal (Nonconstant) Growth The part of the firm's life cycle in which it grows much faster than the economy as a whole. 6 The concept of life cycles could be broadened to product cycle, which would include both small start-up companies and large companies like Microsoft and Procter & Gamble, which periodically introduce new products that give sales and earnings a boost. We should also mention business cycles, which alternately depress and boost sales and profits. The growth rate just after a major new product has been introduced, or just after a firm emerges from the depths of a recession, is likely to be much higher than the "expected long-run average growth rate," which is the proper number for DCF analysis. 7 A negative growth rate indicates a declining company. A mining company whose profits are falling because of a declining ore body is an example. Someone buying such a company would expect its earnings, and consequently its dividends and stock price, to decline each year, and this would lead to capital losses rather than capital gains. Obviously, a declining company's stock price will be relatively low, and its dividend yield must be high enough to offset the expected capital loss and still produce a competitive total return. Students sometimes argue that they would never be willing to buy a stock whose price was expected to decline. However, if the present value of the expected dividends exceeds the stock price, the stock would still be a good investment that would provide a good return. Chapter 9 Stocks and Their Valuation 301 FIGURE 9-2 Dividend ($) Illustrative Dividend Growth Rates Normal Growth, 8% End of Supernormal Growth Period Supernormal Growth, 30% Normal Growth, 8% 1.15 Zero Growth, 0% Declining Growth, 8% 0 1 2 3 4 5 Years In the figure, the dividends of the supernormal growth firm are expected to grow at a 30 percent rate for three years, after which the growth rate is expected to fall to 8 percent, the assumed average for the economy. The value of this firm's stock, like any other asset, is the present value of its expected future dividends as determined by Equation 9-1. When Dt is growing at a constant rate, we ^ can simplify Equation 9-1 to P0 D1/(rs g). In the supernormal case, however, the expected growth rate is not a constant--it declines at the end of the period of supernormal growth. Because Equation 9-2 requires a constant growth rate, we obviously cannot use it to value stocks that have nonconstant growth. However, assuming that a company currently enjoying supernormal growth will eventually slow down and become a constant growth stock, we can combine Equations 9-1 and 9-2 to form a new formula, Equation 9-5, for valuing it. First, we assume that the dividend will grow at a nonconstant rate (generally a relatively high rate) for N periods, after which it will grow at a constant rate, g. N is often called the terminal date, or horizon date. Second, we can use the constant growth formula, Equation 9-2, to determine what the stock's horizon, or terminal, value will be N periods from today: Terminal Date (Horizon Date) The date when the growth rate becomes constant. At this date it is no longer necessary to forecast the individual dividends. Horizon (Terminal) Value The value at the horizon date of all dividends expected thereafter. Horizon value ^ PN DN 1 rs g ^ The stock's intrinsic value today, P0, is the present value of the dividends during the nonconstant growth period plus the present value of the horizon value: 302 Part 3 Financial Assets ^ P0 D1 D2 DN ### 1 2 11 rs 2 11 rs 2 N 11 rs 2 14444444444444444444444244444444444444444444443 PV of dividends during the nonconstant growth period, t 1, N DN 1 D ### 11 rs 2 11 rs 2 N 1 1444444444444444424444444444444443 Horizon value PV of dividends during the constant growth period, t N + 1, ^ PN 11 rs 2 N 1442443 PV of horizon ^ value, PN: 11 12> ^ P0 D1 D2 DN ### 1 2 11 rs 2 11 rs 2 N 11 rs 2 14444444444444444444444244444444444444444444443 PV of dividends during the nonconstant growth period t 1, N (9-5) 3 1DN 1rs rs 2 N g2 4 To implement Equation 9-5, we go through the following three steps: 1. Find the PV of each dividend during the period of nonconstant growth and sum them. 2. Find the expected price of the stock at the end of the nonconstant growth period, at which point it has become a constant growth stock so it can be valued with the constant growth model, and discount this price back to the present. ^ 3. Add these two components to find the intrinsic value of the stock, P0. Figure 9-3 can be used to illustrate the process for valuing nonconstant growth stocks. Here we assume the following five facts exist: rs N gs stockholders' required rate of return 13.4%. This rate is used to discount the cash flows. years of nonconstant growth 3. rate of growth in both earnings and dividends during the nonconstant growth period 30%. This rate is shown directly on the time line. (Note: The growth rate during the nonconstant growth period could vary from year to year. Also, there could be several different nonconstant growth periods, for example, 30 percent for three years, then 20 percent for three years, and then a constant 8 percent.) rate of normal, constant growth after the nonconstant period 8%. This rate is also shown on the time line, between Periods 3 and 4. last dividend the company paid $1.15. gn D0 The valuation process as diagrammed in Figure 9-3 is explained in the steps set forth below the time line. The value of the nonconstant growth stock is calculated to be $39.21. Note that in this example we have assumed a relatively short three-year horizon to keep things simple. When evaluating stocks, most analysts would use a much longer horizon (for example, 10 years) to estimate intrinsic values. This Chapter 9 Stocks and Their Valuation 303 FIGURE 9-3 0 Process for Finding the Value of a Nonconstant Growth Stock 1 30% gs = 30% 2 D2 = 1.9435 30% 3 gn = 8% 4 D1 = 1.4950 1.3183 1.5113 13.4% 13.4% 13.4% D3 = 2.5266 D4 = 2.7287 36.3838 ^ 39.2134 = $39.21 = P0 ^ P3 = 50.5310 53.0576 Notes to Figure 9-3: Step 1. Calculate the dividends expected at the end of each year during the nonconstant growth period. Calculate the first dividend, D1 D0(1 gs) $1.15(1.30) $1.4950. Here gs is the growth rate during the three-year nonconstant growth period, 30 percent. Show the $1.4950 on the time line as the cash flow at Time 1. Then, calculate D2 D1(1 gs) $1.4950(1.30) $1.9435, and then D3 D2(1 gs) $1.9435(1.30) $2.5266. Show these values on the time line as the cash flows at Time 2 and Time 3. Note that D0 is used only to calculate D1. Step 2. The price of the stock is the PV of dividends from Time 1 to infinity, so in theory we could project each future dividend, with the normal growth rate, gn 8%, used to calculate D4 and subsequent dividends. However, we know that after D3 has been paid, which is at Time 3, the stock becomes a constant growth stock. Therefore, we can use ^ the constant growth formula to find P3, which is the PV of the dividends from Time 4 to infinity as evaluated at Time 3. First, we determine D4 $2.5266(1.08) $2.7287 for use in the formula, and then ^ we calculate P as follows: 3 ^ P3 rs D4 gn $2.7287 0.134 0.08 $50.5310 Step 3. We show this $50.5310 on the time line as a second cash flow at Time 3. The $50.5310 is a Time 3 cash flow in the sense that the stockholder could sell it for $50.5310 at Time 3 and also in the sense that $50.5310 is the present value of the dividend cash flows from Time 4 to infinity. Note that the total cash flow at Time 3 consists of the sum of ^ D3 P $2.5266 $50.5310 $53.0576. 3 Now that the cash flows have been placed on the time line, we can discount each cash flow at the required rate of return, rs 13.4%. We could discount each cash flow by dividing by (1.134)t, where t 1 for Time 1, t 2 for Time 2, and t 3 for Time 3. This produces the PVs shown to the left below the time line, and the sum of the PVs is the value of the nonconstant growth stock, $39.21. With a financial calculator, you can find the PV of the cash flows as shown on the time line with the cash flow (CFLO) register of your calculator. Enter 0 for CF0 because you receive no cash flow at Time 0, CF1 1.495, CF2 1.9435, and CF3 2.5266 50.5310 53.0576. Then enter I/YR 13.4, and press the NPV key to find the value of the stock, $39.21. requires a few more calculations, but analysts use spreadsheets so the arithmetic is not a problem. In practice, the real limitation is obtaining reliable forecasts for future growth. Explain how one would find the value of a nonconstant growth stock. Explain what is meant by "terminal (horizon) date" and "horizon (terminal) value." 304 Part 3 Financial Assets Evaluating Stocks That Don't Pay Dividends The dividend growth model assumes that the firm is currently paying a dividend. However, many firms, even highly profitable ones, including Cisco, Dell, and Apple, have never paid a dividend. If a firm is expected to begin paying dividends in the future, we can modify the equations presented in the chapter and use them to determine the value of the stock. A new business often expects to have low sales during its first few years of operation as it develops its product. Then, if the product catches on, sales will grow rapidly for several years. Sales growth brings with it the need for additional assets--a firm cannot increase sales without also increasing its assets, and asset growth requires an increase in liability and/or equity accounts. Small firms can generally obtain some bank credit, but they must maintain a reasonable balance between debt and equity. Thus, additional bank borrowings require increases in equity, and getting the equity capital needed to support growth can be difficult for small firms. They have limited access to the capital markets, and, even when they can sell common stock, their owners are reluctant to do so for fear of losing voting control. Therefore, the best source of equity for most small businesses is retained earnings, and for this reason most small firms pay no dividends during their rapid growth years. Eventually, though, successful small firms do pay dividends, and those dividends generally grow rapidly at first but slow down to a sustainable constant rate once the firm reaches maturity. If a firm currently pays no dividends but is expected to pay dividends in the future, the value of its stock can be found as follows: 1. Estimate when dividends will be paid, the amount of the first dividend, the growth rate during the supernormal growth period, the length of the supernormal period, the long-run (constant) growth rate, and the rate of return required by investors. Use the constant growth model to determine the price of the stock after the firm reaches a stable growth situation. Set out on a time line the cash flows (dividends during the supernormal growth period and the stock price once the constant growth state is reached), and then find the present value of these cash flows. That present value represents the value of the stock today. To illustrate this process, consider the situation for MarvelLure Inc., a company that was set up in 2004 to produce and market a new high-tech fishing lure. MarvelLure's sales are currently growing at a rate of 200 percent per year. The company expects to experience a high but declining rate of growth in sales and earnings during the next 10 years, after which analysts estimate that it will grow at a steady 10 percent per year. The firm's management has announced that it will pay no dividends for five years, but if earnings materialize as forecasted, it will pay a dividend of $0.20 per share at the end of Year 6, $0.30 in Year 7, $0.40 in Year 8, $0.45 in Year 9, and $0.50 in Year 10. After Year 10, current plans are to increase dividends by 10 percent per year. MarvelLure's investment bankers estimate that investors require a 15 percent return on similar stocks. Therefore, we find the value of a share of MarvelLure's stock as follows: P0 $0 11.152 t $0.30 11.152 7 $0.45 11.152 9 a 0.15 ### $0 11.152 5 $0.40 11.152 8 $0.50 11.152 10 ba $0.20 11.152 6 $0.50 11.102 0.10 1 b 11.152 10 $3.30 The last term finds the expected price of the stock in Year 10 and then finds the present value of that price. Thus, we see that the dividend growth model can be applied to firms that currently pay no dividends, provided we can estimate future dividends with a fair degree of confidence. However, in many cases we can have more confidence in the forecasts of free cash flows, and in these situations it is better to use the corporate valuation model as discussed in the next section. 2. 3. Chapter 9 Stocks and Their Valuation 305 9.7 VALUING THE ENTIRE CORPORATION8 Thus far we have discussed the discounted dividend approach to valuing a firm's common stock. This procedure is widely used, but it is based on the assumption that the analyst can forecast future dividends reasonably well. This is often true for mature companies that have a history of steady dividend payments. The model can be applied to firms that are not paying dividends, but as we show in the preceding box, this requires forecasting the time at which the firm will commence paying dividends, the amount of the initial dividend, and the growth rate of dividends once they commence. This suggests that a reliable dividend forecast must be based on forecasts of the firm's future sales, costs, and capital requirements. An alternative approach, the total company, or corporate valuation, model, can be used to value firms in situations where future dividends are not easily predictable. Consider a start-up formed to develop and market a new product. Such companies generally expect to have low sales during their first few years as they develop and begin to market their products. Then, if the products catch on, sales will grow rapidly for several years. For example, eBay's sales were $48 million in 1998, the year it first went public, but in 1999 sales grew by nearly 400 percent and they hit $4.5 billion in 2005. Obviously, eBay has been more successful than most new businesses, but growth rates of 100, 500, or even 1,000 percent are not uncommon during a firm's early years. Growing sales require additional assets--and eBay could not have grown without increasing its assets. Over the five-year period 19992004, its sales grew by 658 percent, and that growth required a 583 percent increase in assets. The increase in assets had to be financed, so eBay's liability and equity accounts also grew by 583 percent as was required to keep the balance sheet in balance. Small firms can generally borrow some funds from their bank, but banks insist that the debt/equity ratio be kept at a reasonable level, which means that equity must also be raised. However, small firms have little or no access to the stock market, so they generally obtain new equity by retaining earnings, which means that they pay little or no dividends during their rapid growth years. Eventually, though, most successful firms do pay dividends, and those dividends grow rapidly at first but then slow down as the firm approaches maturity. It is difficult to forecast the future dividend stream of any firm that is expected to go through such a transition, and even in the case of large firms such as Cisco, Dell, and Apple that have never paid a dividend, it's hard to forecast when dividends will commence and how large they will be. Another problem arises when it is necessary to find the value of a division as opposed to an entire firm. For example, in 2005 Kerr-McGee, a large oil and chemical company, decided to sell its chemical division. The parent company had been paying dividends for many years, so the discounted dividend model could be applied to it. However, the chemical division had no history of dividends, and it would likely be bought by another chemical company and folded into the purchaser's other operations. How could Kerr-McGee's chemical division be valued? The answer is, "Use the corporate valuation model as discussed in this section." Total Company or Corporate Valuation Model A valuation model used as an alternative to the dividend growth model to determine the value of a firm, especially one with no history of dividends or a division of a larger firm. This model first calculates the firm's free cash flows and then finds their present value to determine the firm's value. 8 The corporate valuation model presented in this section is widely used by analysts, and it is in many respects superior to the discounted dividend model. However, it is rather involved as it requires the estimation of sales, costs, and cash flows on out into the future before beginning the discounting process. Therefore, some instructors may prefer to omit Section 9.7 and skip to Section 9.8 in the introductory course. 306 Part 3 Financial Assets The Corporate Valuation Model In Chapter 3 we explained that a firm's value is determined by its ability to generate cash flow, both now and in the future. Therefore, market value can be expressed as follows: Market value VCompany 11 PV of expected future free cash flows of company 11 FCF2 WACC2 2 FCF1 WACC2 1 ### 11 FCF WACC2 (9-6) Here FCFt is the free cash flow in Year t and WACC is the weighted average cost of the firm's capital. Recall from Chapter 3 that free cash flow is the cash inflow during a given year less the cash needed to finance required asset additions. Inflows are equal to net after-tax operating income (also called NOPAT) plus noncash charges (depreciation and amortization), which were deducted when calculating NOPAT, while the required asset additions are the capital expenditures plus the net addition to working capital. This was discussed in Chapter 3, where we developed the following equation: FCF cEBIT(1 T) Depreciation d and amortization Capital expenditures Net operating working capital Depreciation and amortization can be shifted from the first bracketed term to the second term (and given a minus sign). Then the first term becomes EBIT(1 T), also called NOPAT, and the second term becomes the net (rather than gross) new investment in operating capital. The result is Equation 9-7, which shows that free cash flow is equal to after-tax operating income (NOPAT) less the net new investment in operating capital: FCF NOPAT Net new investment in operating capital (9-7) Turning to the discount rate, WACC, note first that free cash flow is the cash generated before making any payments to any investors--the common stockholders, preferred stockholders, and bondholders--and that cash flow must provide a return to all these investors. Each of these investor groups has a required rate of return that depends on the risk of the particular security, and as we discuss in Chapter 10, the average of those required returns is the WACC. With this background, we can summarize the steps used to implement the corporate valuation model. This type of analysis is performed both internally by the firm's financial staff and also by external security analysts, who are generally experts on the industry and quite familiar with the firm's history and future plans. For illustrative purposes, we discuss an analysis conducted by Susan Buskirk, senior food analyst for the investment banking firm Morton Staley and Company. Her analysis is summarized in Table 9-1, which was reproduced from the chapter Excel model. Based on Allied's history and her knowledge of the firm's business plan, Susan estimated sales, costs, and cash flows on an annual basis for five years. Growth will vary during those years, but she assumes that things will stabilize and growth will be constant after the fifth year. She could have projected variability for more years if she thought it would take longer to reach a steady-state, constant growth situation. Chapter 9 Stocks and Their Valuation 307 TA B L E 9 - 1 Allied Food Products: Free Cash Flow Valuation Susan next calculated the expected free cash flows (FCFs) for each of the five nonconstant growth years, and she found the PV of those cash flows, discounted at the WACC. After Year 5 she assumed that FCF growth would be constant, hence the constant growth model could be used to find Allied's total market value at Year 5. This "horizon, or terminal, value" is the sum of the PVs of the FCFs from Year 6 on out into the future, discounted back to Year 5 at the WACC. Next, she discounted the Year 5 terminal value back to the present to find its PV at Year 0. She then summed all the PVs, the annual cash flows during the nonconstant period plus the PV of the horizon value, to find the firm's estimated total market value. She then subtracted the value of the debt and preferred stock to find the value of the common equity. 308 Part 3 Financial Assets Other Approaches to Valuing Common Stocks While the dividend growth and the corporate value models presented in this chapter are the most widely used methods for valuing common stocks, they are by no means the only approaches. Analysts often use a number of different techniques to value stocks. Two of these alternative approaches are described here. ings--you also have a claim on all future earnings. All else equal, companies with stronger growth opportunities will generate larger future earnings and thus should trade at higher P/E ratios. Therefore, eBay is not necessarily overvalued just because its P/E ratio is 52.8 at a time when the median firm has a P/E of 20.1. Investors believe that eBay's growth potential is well above average. Whether the stock's future prospects justify its P/E ratio remains to be seen, but in and of itself a high P/E ratio does not mean that a stock is overvalued. Nevertheless, P/E ratios can provide a useful starting point in stock valuation. If a stock's P/E ratio is well above its industry average, and if the stock's growth potential and risk are similar to other firms in the industry, this may indicate that the stock's price is too high. Likewise, if a company's P/E ratio falls well below its historical average, this may signal that the stock is undervalued--particularly if the company's growth prospects and risk are unchanged, and if the overall P/E for the market has remained constant or increased. One obvious drawback of the P/E approach is that it depends on reported accounting earnings. For this reason, some analysts choose to rely on other multiples to value stocks. For example, some analysts The P/E Multiple Approach Investors have long looked for simple rules of thumb to determine whether a stock is fairly valued. One such approach is to look at the stock's price-toearnings (P/E) ratio. Recall from Chapter 4 that a company's P/E ratio shows how much investors are willing to pay for each dollar of reported earnings. As a starting point, you might conclude that stocks with low P/E ratios are undervalued, since their price is "low" given current earnings, while stocks with high P/E ratios are overvalued. Unfortunately, however, valuing stocks is not that simple. We should not expect all companies to have the same P/E ratio. P/E ratios are affected by risk-- investors discount the earnings of riskier stocks at a higher rate. Thus, all else equal, riskier stocks should have lower P/E ratios. In addition, when you buy a stock, you not only have a claim on current earn- Finally, she divided the equity value by the number of shares outstanding, and the result was her estimate of Allied's intrinsic value per share. This value was quite close to the stock's market price, so she concluded that Allied's stock is priced at its equilibrium level. Consequently, she issued a "Hold" recommendation on the stock. If the estimated intrinsic value had been significantly below the market price, she would have issued a "Sell" recommendation, and had it been well above, she would have called the stock a "Buy." Comparing the Total Company and Dividend Growth Models Analysts use both the discounted dividend model and the corporate model when valuing mature, dividend-paying firms, and they generally use the corporate model when valuing firms that do not pay dividends and divisions. In principle, we should find the same intrinsic value using either model, but differences are often observed. When a conflict exists, then the assumptions embedded in the corporate model can be reexamined, and once the analyst is convinced they are reasonable, then the results of that model are used. In our Allied example, the estimates were extremely close--the dividend growth model predicted a price of $23.00 per share versus $23.38 using the total company model, and both are essentially equal to Allied's actual $23 price. Chapter 9 Stocks and Their Valuation 309 look at a company's price-to-cash-flow ratio, while others look at the price-to-sales ratio. The EVA Approach In recent years, analysts have looked for more rigorous alternatives to the dividend growth model. More than a quarter of all stocks listed on the NYSE pay no dividends. This proportion is even higher on Nasdaq. While the dividend growth model can still be used for these stocks (see box, "Evaluating Stocks That Don't Pay Dividends"), this approach requires that analysts forecast when the stock will begin paying dividends, what the dividend will be once it is established, and the future dividend growth rate. In many cases, these forecasts contain considerable errors. An alternative approach is based on the concept of Economic Value Added (EVA), which we discussed back in Chapter 3. Also, recall from the box in Chapter 4 entitled, "EVA and ROE" that EVA can be written as (Equity capital)(ROE Cost of equity capital) on alternative investments with the same level of risk. When you buy stock in a company, you receive more than just the book value of equity--you also receive a claim on all future value that is created by the firm's managers (the present value of all future EVAs). It follows that a company's market value of equity can be written as Market value of equity Book value PV of all future EVAs We can find the "fundamental" value of the stock, P0, by simply dividing the above expression by the number of shares outstanding. As is the case with the dividend growth model, we can simplify the above expression by assuming that at some point in time annual EVA becomes a perpetuity, or grows at some constant rate over time.a This equation suggests that companies can increase their EVA by investing in projects that provide shareholders with returns that are above their cost of capital, which is the return they could expect to earn a What we have presented here is a simplified version of what is often referred to as the Edwards-Bell-Ohlson (EBO) model. For a more complete description of this technique and an excellent summary of how it can be used in practice, take a look at the article "Measuring Wealth," by Charles M. C. Lee, in CA Magazine, April 1996, pp. 3237. In practice, intrinsic value estimates based on the two models normally deviate both from one another and from actual stock prices, leading different analysts to reach different conclusions about the attractiveness of a given stock. The better the analyst, the more often his or her valuations will turn out to be correct, but no one can make perfect predictions because too many things can change randomly and unpredictably in the future. Given all this, does it matter whether you use the total company model or the dividend growth model to value stocks? We would argue that it does. If we had to value, say, 100 mature companies whose dividends were expected to grow steadily in the future, we would probably use the dividend growth model. Here we would only need to estimate the growth rate in dividends, not the entire set of pro forma financial statements, hence it would be more feasible to use the dividend model. However, if we were studying just one or a few companies, especially companies still in the high-growth stage of their life cycles, we would want to project future financial statements before estimating future dividends. Then, because we would already have projected future financial statements, we would go ahead and apply the total company model. Intel, which pays a quarterly dividend of 8 cents versus quarterly earnings of about $1.24, is an example of a company where either model could be used, but we think the corporate model would be better. Now suppose you were trying to estimate the value of a company that has never paid a dividend, such as eBay, or a new firm that is about to go public, or 310 Part 3 Financial Assets Kerr-McGee's chemical division that it plans to sell. In all of these situations, you would be much better off using the corporate valuation model. Actually, even if a company is paying steady dividends, much can be learned from the corporate valuation model, so analysts today use it for all types of valuations. The process of projecting future financial statements can reveal a great deal about the company's operations and financing needs. Also, such an analysis can provide insights into actions that might be taken to increase the company's value, and for this reason it is integral to the planning and forecasting process, as we discuss in a later chapter. Write out the equation for free cash flows, and explain it. Why might someone use the corporate valuation model even for companies that have a history of paying dividends? What steps are taken to find a stock price as based on the firm's total value? Why might the calculated intrinsic stock value differ from the stock's current market price? Which would be "correct," and what does "correct" mean? 9.8 STOCK MARKET EQUILIBRIUM Recall that rX, the required return on Stock X, can be found using the Security Market Line (SML) equation from the Capital Asset Pricing Model (CAPM) as discussed back in Chapter 8: rX rRF 1rM rRF 2 bX rRF 1RPM 2bX If the risk-free rate is 6 percent, the market risk premium is 5 percent, and Stock X has a beta of 2, then the marginal investor would require a return of 16 percent on the stock: rX 6% 16% 15% 22.0 Marginal Investor A representative investor whose actions reflect the beliefs of those people who are currently trading a stock. It is the marginal investor who determines a stock's price. This 16 percent required return is shown as the point on the SML in Figure 9-4 associated with beta 2.0. A marginal investor will buy Stock X if its expected return is more than 16 percent, will sell it if the expected return is less than 16 percent, and will be indifferent, hence will hold but not buy or sell, if the expected return is exactly 16 percent. Now suppose the investor's portfolio contains Stock X, and he or she analyzes its prospects and concludes that its earnings, dividends, and price can be expected to grow at a constant rate of 5 percent per year. The last dividend was D0 $2.8571, so the next expected dividend is D1 $2.8571 11.052 $3 The investor observes that the present price of the stock, P0, is $30. Should he or she buy more of Stock X, sell the stock, or maintain the present position? The investor can calculate Stock X's expected rate of return as follows: r ^X D1 P0 g $3 $30 5% 15% Chapter 9 Stocks and Their Valuation 311 FIGURE 9-4 Expected and Required Returns on Stock X Rate of Return (%) SML: r i = rRF+ (rM rRF ) b i r x = 16 r x = 15 > X rM= 11 r RF =6 0 1.0 2.0 Risk, bi This value is plotted on Figure 9-4 as Point X, which is below the SML. Because the expected rate of return is less than the required return, he or she, and many other investors, would want to sell the stock. However, few people would want to buy at the $30 price, so the present owners would be unable to find buyers unless they cut the price of the stock. Thus, the price would decline, and the decline would continue until the price hit $27.27. At that point the stock would be in equilibrium, defined as the price at which the expected rate of return, 16 percent, is equal to the required rate of return: r ^X $3 $27.27 5% 11% 5% 16% rX Had the stock initially sold for less than $27.27, say, $25, events would have been reversed. Investors would have wanted to purchase the stock because its expected rate of return would have exceeded its required rate of return, buy orders would have come in, and the stock's price would be driven up to $27.27. To summarize, in equilibrium two related conditions must hold: 1. A stock's expected rate of return as seen by the marginal investor must equal its required rate of return: ri ri. ^ 2. The actual market price of the stock must equal its intrinsic value as esti^ mated by the marginal investor: P0 P0. ^ Of course, some individual investors may believe that ri ri and P0 P0 , hence ^ they would invest most of their funds in the stock, while other investors might have an opposite view and thus sell all of their shares. However, investors at the margin establish the actual market price, and for these investors, we must have ^ ri ri and P0 P0. If these conditions do not hold, trading will occur until they do. ^ Equilibrium The condition under which the expected return on a security is just equal to its required return, r = r. ^ ^ Also, P = P0, and the price is stable. Changes in Equilibrium Stock Prices Stock prices are not constant--they undergo violent changes at times. For example, on October 27, 1997, the Dow Jones Industrials fell 554 points, a 7.18 percent 312 Part 3 Financial Assets drop in value. Even worse, on October 19, 1987, the Dow lost 508 points, causing an average stock to lose 23 percent of its value on that one day, and some individual stocks lost more than 70 percent. To see what could cause such changes to occur, assume that Stock X is in equilibrium, selling at a price of $27.27 per share. If all expectations were exactly met, during the next year the price would gradually rise to $28.63, or by 5 percent. However, suppose conditions changed as indicated in the second column of the following table: VARIABLE VALUE Original Risk-free rate, rRF Market risk premium, rM rRF Stock X's beta coefficient, bX Stock X's expected growth rate, gX D0 Price of Stock X 6% 5% 2.0 5% $2.8571 $27.27 New 5% 4% 1.25 6% $2.8571 ? Now give yourself a test: How would the change in each variable, by itself, affect the price, and what new price would result? Every change, taken alone, would lead to an increase in the price. The first three changes all lower rX, which declines from 16 to 10 percent: Original rx New rx 6% 5% 5% 12.02 ^ Using these values, together with the new g, we find that P0 rises from $27.27 to $75.71, or by 178 percent:9 4% 11.252 16% 10% ^ Original P0 ^ New P0 $2.8571 11.052 0.16 0.05 $2.8571 11.062 0.10 0.06 $3 0.11 $27.27 $75.71 $3.0285 0.04 Note too that at the new price, the expected and required rates of return will be equal:10 r ^X $3.0285 $75.71 6% 10% rX Evidence suggests that stocks, especially those of large companies, adjust rapidly when their fundamental positions change. Such stocks are followed closely by a number of security analysts, so as soon as things change, so does the stock price. Consequently, equilibrium ordinarily exists for any given stock, and required and expected returns are generally close to equal. Stock prices certainly 9 A price change of this magnitude is by no means rare. The prices of many stocks double or halve during a year. For example, during 2004, Starbucks Corporation, which operates a chain of retail stores that sell whole bean coffees, increased in value by 88.1 percent. Novellus Systems, a semiconductor equipment manufacturer, fell by 33.3 percent. 10 It should be obvious by now that actual realized rates of return are not necessarily equal to expected and required returns. Thus, an investor might have expected to receive a return of 15 percent if he or she had bought Novellus or Starbucks stock in 2004, but, after the fact, the realized return on Starbucks was far above 15 percent, whereas that on Novellus was far below. Chapter 9 Stocks and Their Valuation 313 change, sometimes violently and rapidly, but this simply reflects changing conditions and expectations. There are, of course, times when a stock will continue to react for several months to unfolding favorable or unfavorable developments. However, this does not signify a long adjustment period; rather, it simply indicates that as more new information about the situation becomes available, the market adjusts to it. For a stock to be in equilibrium, what two conditions must hold? If a stock is not in equilibrium, explain how financial markets adjust to bring it into equilibrium. 9.9 INVESTING IN INTERNATIONAL STOCKS As noted in Chapter 8, the U.S. stock market amounts to only 40 percent of the world stock market, and as a result many U.S. investors hold at least some foreign stock. Analysts have long touted the benefits of investing overseas, arguing that foreign stocks both improve diversification and provide good growth opportunities. For example, after the U.S. stock market rose an average of 17.5 percent a year during the 1980s, many analysts thought that the U.S. market in the 1990s was due for a correction, and they suggested that investors should increase their holdings of foreign stocks. To the surprise of many, however, U.S. stocks outperformed foreign stocks in the 1990s--they gained about 15 percent a year versus only 3 percent for foreign stocks. However, the Dow Jones STOXX Index (which tracks 600 European companies) outperformed the S&P 500 from 2002 through 2004. Table 9-2 shows how stocks in different countries performed in 2004. Column 2 indicates how stocks in each country performed in terms of the U.S. dollar, while Column 3 shows how the country's stocks performed in terms of its local currency. For example, in 2004 Brazilian stocks rose by 25.12 percent, but the Brazilian real increased over 11 percent versus the U.S. dollar. Therefore, if U.S. investors had bought Brazilian stocks, they would have made 25.12 percent in Brazilian real terms, but those Brazilian reals would have bought 11.1 percent more U.S. dollars, so the effective return would have been 36.22 percent. Thus, the results of foreign investments depend in part on what happens to the exchange rate. Indeed, when you invest overseas, you are making two bets: (1) that foreign stocks will increase in their local markets, and (2) that the currencies in which you will be paid will rise relative to the dollar. For Brazil and most of the other countries shown in Table 9-2, both of these situations occurred during 2004. Although U.S. stocks have generally outperformed foreign stocks in recent years, this by no means suggests that investors should avoid foreign stocks. Holding some foreign investments still improves diversification, and it is inevitable that there will be years when foreign stocks outperform domestic stocks, such as the period from 20022004. When this occurs, U.S. investors will be glad they put some of their money into overseas markets. What are the key benefits of adding foreign stocks to a portfolio? When a U.S. investor purchases foreign stocks, what two things is he or she hoping will happen? 314 Part 3 Financial Assets TA B L E 9 - 2 Dow Jones Global Stock Indexes in 2004 (Ranked by Performance in U.S.-Dollar Terms) U.S. Dollars Local Currency Country Austria South Africa Mexico Norway Belgium Greece Ireland Brazil Sweden Indonesia Philippines New Zealand Denmark Australia Italy Spain Chile South Korea Canada Portugal Singapore Hong Kong France United Kingdom Japan Germany Switzerland Netherlands Malaysia United States Taiwan Finland Thailand Venezuela 67.96% 52.17 46.53 46.47 43.07 40.02 37.91 36.22 33.50 31.84 30.09 30.03 28.75 28.69 27.59 26.07 25.59 23.99 21.98 21.24 19.09 17.99 17.07 16.93 16.62 14.29 14.18 11.84 11.11 10.16 10.03 5.84 8.77 18.83 55.61% 28.12 45.45 32.96 32.55 29.72 27.77 25.12 23.15 45.30 31.46 17.87 19.01 23.38 18.21 16.80 17.68 7.63 12.61 12.32 14.49 18.13 8.47 8.92 11.27 5.89 4.78 3.62 11.12 10.16 2.68 1.94 10.55 31.12 World World ex. U.S. 14.47 19.23 -- -- Source: Craig Karmin, "Currency Effect Enhances Overseas Returns," The Wall Street Journal, January 3, 2005, p. R6. Chapter 9 Stocks and Their Valuation 315 9.10 PREFERRED STOCK Preferred stock is a hybrid--it is similar to bonds in some respects and to common stock in others. This hybrid nature becomes apparent when we try to classify preferred in relation to bonds and common stock. Like bonds, preferred stock has a par value and a fixed dividend that must be paid before dividends can be paid on the common stock. However, the directors can omit (or "pass") the preferred dividend without throwing the company into bankruptcy. So, although preferred stock calls for a fixed payment like bonds, not making the payment will not lead to bankruptcy. As noted earlier, a preferred stock entitles its owners to regular, fixed dividend payments. If the payments last forever, the issue is a perpetuity whose value, Vp, is found as follows: Vp Dp rp (9-8) Vp is the value of the preferred stock, Dp is the preferred dividend, and rp is the required rate of return on the preferred. Allied Food has no preferred outstanding, but suppose it did, and this stock paid a dividend of $10 per year. If its required return were 10.3 percent, then the preferred's value would be $97.09, found as follows: Vp $10.00 0.103 $97.09 In equilibrium, the expected return, rp, must be equal to the required return, rp. ^ Thus, if we know the preferred's current price and dividend, we can solve for the expected rate of return as follows: r ^p Dp Vp (9-8a) Some preferreds have a stated maturity, often 50 years. Assume that our illustrative preferred matured in 50 years, paid a $10 annual dividend, and had a required return of 8 percent. We could then find its price as follows: Enter N 50, I/YR 8, PMT 10, and FV 100. Then press PV to find the price, Vp $124.47. If rp 10 percent, change I/YR to 10, in which case Vp PV $100. If you know the price of a share of preferred stock, you can solve for I/YR to find the expected rate of return, rp. ^ Explain the following statement: "Preferred stock is a hybrid security." Is the equation used to value preferred stock more like the one used to evaluate a bond or the one used to evaluate a "normal," constant growth common stock? Explain. 316 Part 3 Financial Assets G L O B A L P E R S P E C T I V E S Investing in Emerging Markets Given the possibilities of better diversification and higher returns, U.S. investors have been putting more and more money into foreign stocks. While most investors limit their foreign holdings to developed countries such as Japan, Germany, Canada, and the United Kingdom, some have broadened their portfolios to include emerging markets such as South Korea, Mexico, Singapore, Taiwan, and Russia. Emerging markets provide opportunities for larger returns, but they also entail greater risks. For example, Russian stocks rose more than 150 percent in the first half of 1996, as it became apparent that Boris Yeltsin would be reelected president. By contrast, if you had invested in Taiwanese stocks, you would have lost 30 percent in 1995--a year in which most stock markets performed extremely well. Rapidly declining currency values caused many Asian markets to fall by more than 30 percent in 1997; however, more recently most Asian markets have recovered, and they ended 2004 on a positive note. Factors that helped these markets rise included peaceful elections, inflows of foreign capital, economic growth, and the positive expectations for China's economy. During 2004, only Thai and Chinese stocks in the Asian region posted negative returns. Stocks in emerging markets are intriguing for two reasons. First, developing nations have the greatest potential for growth. Second, while stock returns in developed countries often move in sync with one another, stocks in emerging markets generally march to their own drummers. Therefore, the correlations between U.S. stocks and those in emerging markets are generally lower than between U.S. stocks and those of other developed countries. Thus, correlations suggest that emerging markets improve the diversification of U.S. investors' portfolios. (Recall from Chapter 8 that the lower the correlation, the greater the benefit of diversification.) On the other hand, stocks in emerging markets are often extremely risky, illiquid, and involve higher transactions costs, and most U.S. investors do not have ready access to information on the companies involved. To reduce these problems, mutual funds focused on specific countries have been created-- they are called "country funds." Country funds help investors avoid the proble