corporate finance - Corporate Finance Tibor Neugebauer...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Corporate Finance Tibor Neugebauer Luxembourg School of Finance BAPG Our lecture Tibor Neugebauer, LSF, University of Luxembourg Behavioral Financial Economist Email: [email protected] Textbook: Stephen Ross et al. Corporate Finance, American Edition 8, 2008 Additional readings: Aswath Damodaran, Investment valuation, edition 2, 2002 Shefrin, Behavioral Corporate Finance MBF, Corporate Finance, 2010 2 Chapters of the book « Corporate Finance » I II III IV V VI VII VIII Overview Valuation Risk Capital structure Long-term finance Options and futures Short-term finance Special topics 19 Public issues 22 Options 26 S-term Planning 29Mergers & Acquis. 20 Longterm debt 23 Extensions 27 Cash managemt 30Financial distress 21 Leasing 24 Warrants 28 Credit managemt 31 Internat. C Finance 1Introduction 4 DCF Valuation 9 Risk & Return 2 Corporate Governance 5 Bonds & Stock 10 CAPM 3 Fin. Statem. Analysis 6 NPV 11 APT 15 Basic concepts 7 Investm Decisions 12 Risk, Cost of Capital 16 Limits to use of debt 8 Real options 13 EMH 17leverage valuation 18 Divis & payouts 25 Derivative securities Corporate Finance - chapter 1 - Introduction to corporate finance Corporate Finance, 1 Introduction What is Corporate Finance? Corporate Finance addresses the following three questions: 1. What long-term investments should the firm choose? 2. How should the firm raise funds for the selected investments? 3. How should short-term assets be managed and financed? The primary goal of corporate finance is to maximize corporate value while reducing the firm's financial risks. MBF, Corporate Finance, 2010 5 Corporate Finance, 1 Introduction Balance Sheet Model of the Firm Total Value of Assets: Total Firm Value to Investors: Current Liabilities Current Assets Long-Term Debt Fixed Assets 1 Tangible Shareholders’ Equity 2 Intangible MBF, Corporate Finance, 2010 6 Corporate Finance, 1 Introduction The Capital Budgeting Decision Current Liabilities Current Assets Fixed Assets 1 Tangible 2 Intangible Long-Term Debt What long-term investments should the firm choose? MBF, Corporate Finance, 2010 Shareholders’ Equity 7 Corporate Finance, 1 Introduction The Capital Structure Decision Current Liabilities Current Assets Fixed Assets 1 Tangible How should the firm raise funds for the selected investments? Long-Term Debt Shareholders’ Equity 2 Intangible MBF, Corporate Finance, 2010 8 Corporate Finance, 1 Introduction Short-Term Asset Management Current Assets Fixed Assets 1 Tangible 2 Intangible Current Liabilities Net Working Capital How should short-term assets be managed and financed? MBF, Corporate Finance, 2010 Long-Term Debt Shareholders’ Equity 9 Corporate Finance, 1 Introduction Capital Structure The value of the firm can be thought of as a pie. The goal of the manager is to increase the size of the pie. 70% 30% 25%50% DebtDebtquity E The Capital Structure decision can be viewed as how best to slice the pie. 75% 50% Equity If how you slice the pie affects the size of the pie, then the capital structure decision matters. MBF, Corporate Finance, 2010 10 Corporate Finance, 1 Introduction The Financial Manager The Financial Manager’s primary goal is to increase the value of the firm by: 1. Selecting value creating projects 2. Making smart financing decisions MBF, Corporate Finance, 2010 11 Corporate Finance, 1 Introduction Hypothetical Organization Chart Board of Directors Chairman of the Board and Chief Executive Officer (CEO) Vice President and Chief Financial Officer (CFO) Treasurer Controller Cash Manager Credit Manager Tax Manager Cost Accounting Capital Expenditures Financial Planning Financial Accounting Data Processing MBF, Corporate Finance, 2010 12 Firm Invests in assets (B) Current assets Fixed assets Firm issues securities (A) Financial markets Retained cash flows (F) Short-term debt Cash flow from firm (C) Dividends and debt payments (E) Long-term debt Equity shares Taxes (D) Corporate Finance, 1 Introduction The Firm and the Financial Markets Ultimately, the firm must be a cash generating activity. Government MBF, Corporate Finance, 2010 The cash flows from the firm must exceed the cash flows from the 13 financial markets. Corporate Finance, 1 Introduction The Corporate Firm The corporate form of business is the standard method for solving the problems encountered in raising large amounts of cash. However, businesses can take other forms. MBF, Corporate Finance, 2010 14 Corporate Finance, 1 Introduction Forms of Business Organization The Sole Proprietorship The Partnership General Partnership Limited Partnership The Corporation MBF, Corporate Finance, 2010 15 Corporate Finance, 1 Introduction A Comparison Corporation Partnership Liquidity Shares can be easily exchanged Subject to substantial restrictions Voting Rights Usually each share gets one vote General partner in charge; limited partners may have some voting rights Taxation Double Partners pay taxes on distributions Reinvestment and dividend payout Broad latitude All net cash flow is distributed to partners Liability Limited liability Continuity Perpetual life General partners may have unlimited liability; limited partners enjoy limited liability Limited life MBF, Corporate Finance, 2010 16 Corporate Finance, 1 Introduction Wait a second … There are two mutually exclusive “projects.” You have to choose ONE, A) or B). A) The first project: You win 2 Euro. Choose the first gamble by ticking here B) The second project: A die is rolled, and there are two equiprobable outcomes. 1) You win 15 Euro if the die shows 1, 3, or 5 eyes. 2) You lose 5 Euro if the die shows 2, 4, or 6 eyes. Please choose again if the project B is changed in the following way. If you win 15 Euro, you must give 5 Euro to the lecturer. If you lose 5 Euro, the lecturer has to pay you back your 5 Euro. MBF, Corporate Finance, 2010 17 Corporate Finance, 1 Introduction The Agency Problem Agency relationship Principal hires an agent to represent his/her interest Stockholders (principals) hire managers (agents) to run the company Agency problem Conflict of interest between principal and agent Managerial goals may be different from shareholder goals Expensive perquisites Survival Independence Increased growth and size are not necessarily equivalent to increased shareholder wealth MBF, Corporate Finance, 2010 18 Corporate Finance, 1 Introduction Managing Managers Managerial compensation Incentives can be used to align management and stockholder interests The incentives need to be structured carefully to make sure that they achieve their intended goal Other stakeholders MBF, Corporate Finance, 2010 19 Corporate Finance, 1 Introduction Financial Markets Primary Market Issuance of a security for the first time Secondary Markets Buying and selling of previously issued securities Securities may be traded in either a dealer or auction market NYSE Euronext (www.nyse.com) (history; http://en.wikipedia.org/wiki/NYSE_Euronext) NASDAQ (www.nasdaq.com) MBF, Corporate Finance, 2010 20 Corporate Finance, 1 Introduction Financial Markets Firms Stocks and Bonds Money Investors Bob securities Sue money Primary Market Secondary Market MBF, Corporate Finance, 2010 21 Corporate Finance - chapter 2 - Financial Statements and Cash Flow Corporate Finance, 2 Statement & Cash Flow Sources of Information Wall Street Journal (http://www.wsj.com/) Yahoo (http://finance.yahoo.com) SEC (http://www.sec.gov/) EDGAR (Electronic Data Gathering, Analysis, and Retrieval system ) 10K, 10Q reports, Annual reports MBF, Corporate Finance, 2010 23 Corporate Finance, 2 Statement & Cash Flow The Balance Sheet again Total Value of Assets: Total Firm Value to Investors: Current Liabilities Current Assets Long-Term Debt Fixed Assets 1 Tangible Shareholders’ Equity 2 Intangible An accountant’s snapshot of the firm’s accounting value at a specific point in time The Balance Sheet Identity is: Assets ≡ Liabilities + Stockholder’s Equity MBF, Corporate Finance, 2010 24 Johnson & Johnson and Subsidiaries Consolidated Balance Sheets At January 3, 2010 and December 28, 2008 (Dollars in Millions Except Share and Per Share Data) change in cash is 5,142 2009 2008 Assets Current assets Cash and cash equivalents Marketable securities Accounts receivable Inventories Deferred taxes on income Prepaid expenses and other receivables Total current assets $ 15 810 10 768 3 615 2 041 9 646 9 719 5 180 5 052 2 793 3 430 2 497 3 367 39 541 34 377 Property, plant and equipment, net Intangible assets, net Goodwill Deferred taxes on income Other assets 14 759 16 323 14 862 5 507 3 690 14 365 13 976 13 719 5 841 2 634 2009 Current liabilities Loans and notes payable Accounts payable Accrued liabilities Accrued rebates Accrued salaries Accrued taxes on income Total current liabilities Long-term debt Deferred taxes on income Employee related obligations Other liabilities Total liabilities Total assets $ 94 682 84 912 change in total assets 9,770 $ 6 318 5 541 5 796 2 028 1 606 442 2008 3 732 7 503 5 531 2 237 1 432 417 21 731 20 852 8 223 1 424 6 769 5 947 8 120 1 432 7 791 4 206 44 094 42 401 Common stock par value $1 3 120 3 120 Accumulated other comprehensive income -3 058 -4 955 Retained earnings 70 306 63 379 (treasury stock 366 shares) at cost -19 780 -19 033 Total shareholders' equity 50 588 42 511 Total liabilities and shareholders' equity $ 94 682 84 912 Corporate Finance, 2 Statement & Cash Flow Balance Sheet Analysis When analyzing a balance sheet, the Finance Manager should be aware of three concerns: 1. Liquidity 2. Value versus cost 3. Debt versus equity MBF, Corporate Finance, 2010 26 Corporate Finance, 2 Statement & Cash Flow Debt versus equity?–claims on total firm value Payoff to debtholders Payoffs to debtholders and equity shareholders Payoff to equity shareholders B B total firm value B Payoff to debtholders B total firm value B : amount borrowed MBF, Corporate Finance, 2010 27 Johnson & Johnson and Subsidiaries Consolidated Statements of Earnings (Dollars in Millions) The operations section of the income statement reports the firm’s revenues and expenses from principal operations. Sales to customers 2009 $ 2008 61 897 63 747 Cost of products sold 18 447 18 511 Selling, marketing and administrative expenses 17 027 19 658 Depreciation & amortization 2 774 2 832 Research expense The non-operating section of the income statement includes all financing costs, incl. interest expense. Usually a separate section reports the amount of taxes levied on income. Net income is the “bottom line.” 6 986 7 577 Operating income 16 663 15 988 Other income (expense) (457) Earnings before interest and taxes 16 206 Interest expense 451 Pretax income 1 376 17 364 435 15 755 3 489 Provision for taxes on income 16 929 3 980 12 949 Net earnings $ 12 266 Addition to retained earnings $ 6 939 7 925 Cash dividends $ 5 327 5 024 Corporate Finance, 2 Statement & Cash Flow Income Statement Analysis There are three things to keep in mind when analyzing an income statement: 1. 1. 1. Generally Accepted Accounting Principles (GAAP) Income is reported when it is earned, even though no cash flow may have occurred. Non-Cash Items Thus, net income is not cash. Time and Costs MBF, Corporate Finance, 2010 29 Corporate Finance, 2 Statement & Cash Flow Taxes The one thing we can rely on with taxes is that they are always changing Marginal vs. average tax rates Marginal – the percentage paid on the next dollar earned Average – the tax bill / taxable income Other taxes MBF, Corporate Finance, 2010 30 Corporate Finance, 2 Statement & Cash Flow Net Working Capital Net Working Capital ≡ Current Assets – Current Liabilities NWC usually grows with the firm MBF, Corporate Finance, 2010 31 Johnson & Johnson and Subsidiaries Consolidated Balance Sheets At January 3, 2010 and December 28, 2008 (Dollars in Millions Except Share and Per Share Data) change in cash is 5,042 2009 2008 Assets Current assets Cash and cash equivalents Marketable securities Accounts receivable Inventories Deferred taxes on income Prepaid expenses and other receivables Total current assets $ 15 810 10 768 3 615 2 041 9 646 9 719 5 180 5 052 2 793 3 430 2 497 3 367 39 541 34 377 Property, plant and equipment, net Intangible assets, net Goodwill Deferred taxes on income Other assets 14 759 16 323 14 862 5 507 3 690 14 365 13 976 13 719 5 841 2 634 NWC 2009 = 17,810 = 39,541-21,731 NWC 2008 = 13,525 = 34,377-20,852 2009 Current liabilities Loans and notes payable Accounts payable Accrued liabilities Accrued rebates Accrued salaries Accrued taxes on income Total current liabilities Long-term debt Deferred taxes on income Employee related obligations Other liabilities Total liabilities $ 6 318 5 541 5 796 2 028 1 606 442 2008 3 732 7 503 5 531 2 237 1 432 417 21 731 20 852 8 223 1 424 6 769 5 947 8 120 1 432 7 791 4 206 44 094 42 401 Common stock par value $1 3 120 The NWC increase of $ 4,285 (= 17,810-13,525) million from 2009 to3 120 Accumulated other comprehensive income -3 058 -4 955 2010 is an investment of the firm. Retained earnings 70 306 63 379 (treasury stock 366 shares) at cost -19 780 -19 033 Total shareholders' equity 50 588 42 511 Total liabilities and shareholders' equity $ 94 682 84 912 Non-cash NWC changed by$– 75784 9125,042 – 4,285) (= Total assets 94 682 Corporate Finance, 2 Statement & Cash Flow The Statement of Cash Flows There is an official accounting statement called the statement of cash flows. This helps explain the change in accounting cash, which for JNJ is $5,042 million in 2009. The three components of the statement of cash flows are: Cash flow from operating activities Cash flow from investing activities Cash flow from financing activities MBF, Corporate Finance, 2010 33 JNJ (Accountancy) statement of Cash Flows To calculate cash flow from operations, start with net income, add back non-cash items like depreciation and adjust for changes in current assets and liabilities (other than cash). Cash flow from investing activities involves changes in capital assets: acquisition of fixed assets and sales of fixed assets (i.e., net capital expenditures). Cash flows to and from creditors and owners include changes in equity and debt. (Dollars in Millions) (Note 1) Operations Net earnings $ Depreciation and amortization of property and Stock based compensation Deferred tax provision Changes in assets and liabilities Accounts receivable allowances Decrease/(increase) in accounts receivable Decrease/(increase) in inventories (Decrease)/increase in accounts payable and accrued liabilities Decrease/(increase) in other current and non-current assets Increase in other current and non-current liabilities Net cash flows from operating activities Investing Activities Additions to property, plant and equipment Proceeds from the disposal of assets Acquisitions, net of cash acquired (Note 20) Purchases of investments Sales of investments Other (primarily intangibles) Net cash used by investing activities Financing activities Dividends to shareholders Repurchase of common stock Proceeds from short-term debt Retirement of short-term debt Proceeds from long-term debt Retirement of long-term debt Proceeds from the exercise of stock options/excess tax benefits Net cash used by financing activities Effect of exchange rate changes on cash and cash equivalents Increase in cash and cash equivalents 2009 12 266 2 774 628 -436 58 453 95 -507 1 209 31 16 571 -2 365 154 -2 470 -10 040 7 232 -109 -7 598 -5 327 -2 130 9 484 -6 791 9 -219 882 -4 092 161 5 042 Asset value & financial cash flow identity Book value of the firm‘s assets equals the combined book value of liabilities and the value of equity value of assets = value of equity + value of debt The cash flow from the assets to the firm equals the combined cash flow to debt and equity investors CF(assets) = CF(debt) + CF(equity) Standard Measures of Free Cash Flows Cash flows can be measured to All claimholders in the firm EBIT (1- tax rate) - ( Capital Expenditures - Depreciation) - Change in non-cash working capital = Free Cash Flow to Firm (FCFF) FCFF = 16,202 (1 – .23) - (2,365 – 2,774) - (-757) = 13,641.54 Jus t Equity Inves tors Net Income - (Capital Expenditures - Depreciation) - Change in non-cash Working Capital - (Principal Repaid - New Debt Issues) - Preferred Dividend FCFE (broad definition) = 12,266 - (2,365 – 2,774) - (-757) - 2,483 -0 = 10,949 Dividends + Stock Buybacks FCFE (narrow) = 5,327 + 2,130 = 7,457 Asset value revisited - outlook Value of the firm‘s assets from cash flows Value of assets = Present Value of CF(assets) Value of equity = PV CF(equity) Value of debt = PV CF(debt) Value of assets = value of equity + value of debt Corporate Finance - chapter 3 - Financial Statements Analysis and Long-Term Planning Corporate Finance, 3 Financial ratio analysis Financial ratio analysis For a better comparison between companies or between points of time, financial analysts use common-size balance sheets (i.e., they divide every number in the bs by the value of total assets) Ratios also allow for better comparison through time or between companies. Think about what the ratio indicate? … MBF, Corporate Finance, 2010 39 Corporate Finance, 3 Financial ratio analysis Five major categories of ratios I. I. I. I. I. S-T Solvency or liquidity Can we make required payments? L-T solvency, financial leverage or debt management Right mix of debt and equity? Asset management or turnover ratios right amount of assets vs. sales? Profitability Are sales high enough? Market value stock price is overvalued or undervalued? The following examples use the data from the JNJ 2009 statements MBF, Corporate Finance, 2010 40 Corporate Finance, 3 Financial ratio analysis Computing Liquidity Ratios (based on JNJ 2009 report) Current Ratio = CA / CL 39,541 / 21,731 = 1.82 times Quick Ratio = (CA – Inventory) / CL (39,541 – 5,180) / 21,731 = 1.58 times Cash Ratio = Cash / CL 15,810 / 21,731 = .73 times MBF, Corporate Finance, 2010 41 Corporate Finance, 3 Financial ratio analysis Computing Leverage Ratios (based on JNJ 2009 report – book values) Total Debt Ratio = (TA – TE) / TA (94,682 – 50,588) / 94,682 = 47% Debt/Equity = TD / TE (94,682 – 50,588) / 50,588 = 87% Equity Multiplier = TA / TE = 1 + D/E 94,682 / 50,588 = 1 + 87% = 1.87 MBF, Corporate Finance, 2010 42 Corporate Finance, 3 Financial ratio analysis Computing Coverage Ratios (based on JNJ 2009 report) Times Interest Earned = EBIT / Interest 16,202 / 451 = 35.9 times Cash Coverage = (EBIT + Depreciation) / Interest (16,202 + 2,832) / 451 = 42.2 times MBF, Corporate Finance, 2010 43 Corporate Finance, 3 Financial ratio analysis Computing Inventory Ratios (based on JNJ 2009 report) Inventory Turnover = Cost of Goods Sold / Inventory 18,724 / 5,180 = 3.6 times Days’ Sales in Inventory = 365 / Inventory Turnover 365 / 3.6 = 102 days MBF, Corporate Finance, 2010 44 Corporate Finance, 3 Financial ratio analysis Computing Receivables Ratios (based on JNJ 2009 report) Receivables Turnover = Sales / Accounts Receivable 62,502 / 9,464 = 6.5 times Days’ Sales in Receivables = 365 / Receivables Turnover 365 / 6.5 = 56 days MBF, Corporate Finance, 2010 45 Corporate Finance, 3 Financial ratio analysis Computing Total Asset Turnover (based on JNJ 2009 report) Total Asset Turnover = Sales / Total Assets 62,502 / 94,682 = 0.66 times It is not unusual for TAT < 1 if a firm has a large amount of fixed assets. MBF, Corporate Finance, 2010 46 Corporate Finance, 3 Financial ratio analysis Computing Profitability Measures (based on JNJ 2009 report) Profit Margin = Net Income / Sales 12,266 / 62,502 = 19.6% Return on Assets (ROA) = Net Income / Total Assets 12,266 / 94,682 = 13.0% Return on Equity (ROE) = Net Income / Total Equity 12,266 / 50,588 = 24.2% ROE = NI / Sales × Sales / TA × TA / TE = Profit Margin × TAT × Equity Multiplier (Du Pont identity) = 19.6% × 0.66 × 1.87 = ROA × Equity Multiplier Dividend payout ratio = Cash dividends / NI 5,404 / 12,266 = 44% MBF, Corporate Finance, 2010 47 Corporate Finance, 3 Financial ratio analysis Computing Market Value Measures (based on JNJ 2009 report) Market Price = $51.61 per share (average 2009) Shares outstanding = 2,754 million PE Ratio = Price per share / Earnings per share 51.61 / (12,266/2,754) = 11.6 times Market-to-book ratio = market value per share / equity book value per share 51.61 / (50,588/2,754) = 2.81 times MBF, Corporate Finance, 2010 48 Corporate Finance, 3 Financial ratio analysis Financing and Growth At low growth levels, internal financing (retained earnings) may exceed the required investment in assets. As the growth rate increases, the internal financing will not be enough, and the firm will have to go to the capital markets for financing. Examining the relationship between growth and external financing required is a useful tool in long-range planning. MBF, Corporate Finance, 2010 49 Corporate Finance, 3 Financial ratio analysis The Internal Growth Rate (based on JNJ 2009 report) The internal growth rate tells us how much the firm can grow using retained earnings as the only source of financing. Using the information from the JNJ ROA = 12,266 / 94,682 = 13.0% Payout ratio = 5,404 / 12,266 = 44% b = retention rate = 1 - payout ratio = 56% ROA × b Internal growth rate = 1 - ROA × b .130 × .56 = = 7.81% 1 − .13 × .56 MBF, Corporate Finance, 2010 50 Corporate Finance, 3 Financial ratio analysis The Sustainable Growth Rate (based on JNJ 2009 report) The sustainable growth rate tells us how much the firm can grow by using internally generated funds and issuing debt to maintain a constant debt ratio. Using the JNJ ROE = 12,266 / 50,588 = 24.2% b = .56 retention rate ROE × b Sustainable growth rate = 1 - ROE × b .242 ×.56 = = 15.69% 1 −.242 ×.56 MBF, Corporate Finance, 2010 51 Corporate Finance, 3 Financial ratio analysis Chapter 3 – problem Problem ROA & ROE. Firm A and Firm B have debt-total asset ratios of 60 percent and 40 percent and returns on total assets of 20 percent and 30 percent, respectively. Which firm has a greater return on equity? MBF, Corporate Finance, 2010 52 Appendix: Alternative presentations of return on investment and internal growth rate ROI Presentation in the book ROA = NI t TAt ROE = NI t Et Alternative presentation return on invested capital ROI = NI t TAt −1 ROEI = NI t E t −1 Internal growth rate = = retained earnings t NI t NI t − payout to shareholders = TAt −1 TAt −1 NI t NI t NI − payout to shareholders × b = ROI × b , where b = = 1 − payout ratio TAt −1 NI (Book presentation) IGR = b × = b× NI t NI TAt NI TAt NI TAt =b× t =b× t =b× t TAt −1 TAt TAt −1 TAt TAt − NI t × b TAt TAt − NI t × b NI t TAt / TAt 1 ROA × b = b × ROA × = TAt TAt / TAt − NI t / TAt × b 1 − ROA × b 1 − ROA × b Appendix: Relative valuation What is it?: The value of any asset can be estimated by looking at how the market prices “similar” or ‘comparable” assets. Philosophical Basis: The intrinsic value of an asset is impossible (or close to impossible) to estimate. The value of an asset is whatever the market is willing to pay for it (based upon its characteristics) Information Needed: To do a relative valuation, you need an identical asset, or a group of comparable or similar assets a standardized measure of value (in equity, this is obtained by dividing the price by a common variable, such as earnings or book value) and if the assets are not perfectly comparable, variables to control for the differences Market Inefficiency: Pricing errors made across similar or comparable assets are easier to spot, easier to exploit and are much more quickly corrected. Multiples are just standardized estimates of price… You can standardize either the equity value of an asset or the value of the asset itself, which goes in the numerator. You can standardize by dividing by the Earnings of the asset Book value of the asset Price/Book Value(of Equity) (PBV) Revenues generated by the asset Price/Earnings Ratio (PE) and variants (PEG and Relative PE) Price/Sales per Share (PS) Asset or Industry Specific Variable (Price/kwh, Price per ton of steel ....) Value of Stock = DPS 1/(ke - g) PE=Payout Ratio (1+g)/(r-g) PE=f(g, payout, risk) PEG=Payout ratio (1+g)/g(r-g) PBV=ROE (Payout ratio) (1+g)/(r-g) PEG=f(g, payout, risk) PBV=f(ROE,payout, g, risk) PS= Net Margin (Payout ratio) (1+g)/(r-g) PS=f(Net Mgn, payout, g, risk) Equit y Mult iple s Firm Mult iple s V/FCFF=f(g, WACC) Value/FCFF=(1+g)/ (WACC-g) V/EBIT(1-t)=f(g, RIR, WACC) Value/EBIT(1-t) = (1+g) (1- RIR)/(WACC-g) V/EBIT=f(g, RIR, WACC, t) Value/EBIT=(1+g)(1RiR)/(1-t)(WACC-g) Value of Firm = FCFF1/(WACC -g) VS=f(Oper Mgn, RIR, g, WACC) VS= Oper Margin (1RIR) (1+g)/(WACC-g) Regression Results The regression of PE ratios on these variables provides the following – PE = 16.16 - 7.94 Interest Rates + 154.40 Growth in GDP - 0.1116 Country Risk R Squared = 73% Predicted PE Ratios Country PE Ratio Argentina Brazil Chile Hong Kong India Indonesia Malaysia Mexico Pakistan Peru Phillipines Singapore South Korea Thailand Turkey Venezuela 14 21 25 20 17 15 14 19 14 15 15 24 21 21 12 20 Interest Rates 18.00% 14.00% 9.50% 8.00% 11.48% 21.00% 5.67% 11.50% 19.00% 18.00% 17.00% 6.50% 10.00% 12.75% 25.00% 15.00% GDP Real G rowth 2.50% 4.80% 5.50% 6.00% 4.20% 4.00% 3.00% 5.50% 3.00% 4.90% 3.80% 5.20% 4.80% 5.50% 2.00% 3.50% Country Risk 45 35 15 15 25 50 40 30 45 50 45 5 25 25 35 45 Predicted PE 13.57 18.55 22.22 23.11 18.94 15.09 15.87 20.39 14.26 16.71 15.65 23.11 19.98 20.85 13.35 15.35 PE versus Growth • Expected growth rate : www.finance.yahoo.com 3 00 2 00 1 00 C urrent P E 0 - 1 00 R sq = 0.1500 - 20 0 20 40 60 Expecte d Gr owth in EPS : next 5 ye ars 80 1 00 Regressions of Multiples on Fundamentals: Market Wide http://pages.stern.nyu.edu/~adamodar/New_Home_ Market-wide Regressions of Multiples: US Companies in January 2011 (T stats in parentheses below coefficients) Regression R2 PE = 6.37 + 83.55 gEPS + 5.83 Payout + 5.06 Beta (5.85) (16.93) (4.30) (8.18) 19.8% PEG = 0.33 Beta + 0.58 Payout –0.83 ln(gEPS) (5.84) (3.82) (22.79) 25.1% PBV= 8.74 gEPS +0.57 Payout + 0.27 Beta + 11.52 ROE (18.70) (5.52) (0.50) (46.89) 51.9% PS= 6.58 gEPS - 0.15 Payout + 0.28 Beta + 13.77 Net Margin (14.26) (1.24) (5.11) (40.22) 49.0% European companies in January 2011 Regression R2 PE = 11.55 + 53.32 gEPS + 6.00 Payout -1.35 Beta (11.71) (20.77) (5.51) (1.92) 29.8% PBV= 1.49 + 0.98 gEPS +0.32 Payout -0.55 Beta + 7.89 ROE (10.51) (4.80) (2.74) (7.08) (26.06) 44.0% PS=1.00 + 0.60 gEPS + 0.16 Beta + 6.44 Net Margin (9.96) (3.04) (2.38) (17.08) 17.6% Japanese Companies in January 2011 Regression R2 PE = 16.60 + 17.24gEPS + 14.68 Beta (10.22) (5.77) (7.98) 19.6% PBV= 0.87 + + 6.09 ROE (42.19) (36.89) 28.2% PS= 0.10 gEPS + 0.08 Beta + 16.51Net Margin - 0.39 Payout (1.57) (2.18) (41.81) (6.40) 68.1% Emerging Market companies in January 2011 Regression R2 PE = 19.47+ 17.10 gEPS + 2.45 Payout (36.94) (13.16) (2.77) 7.8% PBV= 0.87 + 1.17 gEPS + 0.57 Payout + 7.20 ROE (9.45) (9.23) (6.03) (23.87) 28.1% PS= 0.85 + 1.02 gEPS+ 0.32Payout + 11.76 Net Margin (11.37) (8.14) (3.56) (35.85) 51.4% P/BV Coca Cola, Ticker KO Using the regressions should be pretty straightforward, if you can get the data on the independent variables for your company and stay true to decimal format. (25% gets entered as 0.25). As an example, assume that you are looking at Coca Cola in January 2011 and decide to use the US market regression for price to book ratio. http://finance.yahoo.com/q/ae?s=KO+Analyst+Estimates Here are the inputs: g = The analyst estimate of earnings growth rate for the next 5 years is 8% (if you do not have analyst estimates, substitute your own). ROE =The return on equity last year was 41.5% Beta =0.54 Payout ratio = Dividend per share/ Earnings per share = 1.88/5.37 = 35% Using the PBV regression: PBV for Coca Cola = 8.74 (0.08) +0.57 (0.35) + 0.27 (0.54) + 11.52 (0.415) = 5.825 At its actual price to book ratio of 4.6, Coca Cola is undervalued by about 26.7%. P/E Johnson & Johnson, Ticker: JNJ We need gEPS, payout ratio, beta, earnings estimates http://finance.yahoo.com/q/ae?s=JNJ+Analyst+Estimates gEPS = 5.43% Payout ratio = 1/3 Beta = 0.60 Earnings = 4.18 PE = 6.37 + 83.55 gEPS + 5.83 Payout + 5.06 Beta = 6.37 + 83.55 x 0.0543 + 5.83 x 0.33 + 5.06 x 0.6 = 15.87 Estimated Price = 77.27 = 15.87 x 4.18 Appendix: Notation gEPS = Expected growth rate in EPS for next 5 years (analyst estimates) g = Expected growth rate in revenues for next 5 years (if not available, use g EPS) Payout = Dividends/Earnings ROIC = Return on capital = EBIT (1- tax rate)/ Invested Capital Operating Margin = EBIT/ Sales Invested Capital = Book value of equity + Book value of debt - Cash ROE = Net Income/ Book value of Equity Tax Rate = Effective tax rate Debt/Capital = Debt/ (Market value of Equity + Debt) RIR = Reinvestment Rate = (Cap Ex – Depreciation + Chg in WC)/ EBIT (1-t) Advantages of Relative Valuation Relative valuation is much more likely to reflect market perceptions and moods than discounted cash flow valuation. This can be an advantage when it is important that the price reflect these perceptions as is the case when the objective is to sell a security at that price today (as in the case of an IPO) investing on “momentum” based strategies With relative valuation, there will always be a significant proportion of securities that are under valued and over valued. Since portfolio managers are judged based upon how they perform on a relative basis (to the market and other money managers), relative valuation is more tailored to their needs Relative valuation generally requires less information than discounted cash flow valuation (especially when multiples are used as screens) Disadvantages of Relative Valuation A portfolio that is composed of stocks which are under valued on a relative basis may still be overvalued, even if the analysts’ judgments are right. It is just less overvalued than other securities in the market. Relative valuation is built on the assumption that markets are correct in the aggregate, but make mistakes on individual securities. To the degree that markets can be over or under valued in the aggregate, relative valuation will fail Relative valuation may require less information in the way in which most analysts and portfolio managers use it. However, this is because implicit assumptions are made about other variables (that would have been required in a discounted cash flow valuation). To the extent that these implicit assumptions are wrong the relative valuation will also be wrong. Conventional Usage: A Summary As a general rule of thumb, the following table provides a way of picking a multiple for a sector Sector Multiple Used Rationale . Cyclical Manufacturing PE, Relative PE Often with normalized earnings High Tech, High Growth PEG Big differences in growth across firms High Growth/No Earnings PS, VS Assume future margins will be good Heavy Infrastructure VEBITDA Firms in sector have losses in early years and earnings can vary depending on depreciation method REIT P/CF Generally no cap ex investments from equity earnings Financial Services PBV Book value often marked to market Retailing PS If leverage is similar across firms VS If leverage is different . Relative valuation - problem Compute for three companies the PE, for three others the PS and again three others the PBV. Make a price prediction and recommend them as being over- or undervalued. Corporate Finance - chapter 4 - Discounted Cash Flow Valuation The Time-Value-of-Money Corporate Finance, 4 DCF The basic Time-Value-of-Money relationship is as follows: Ct+T = Ct (1 + r)T where r is the interest rate per period T is the duration of the investment, stated in the compounding time unit Ct (PV) is the value at period t (beginning of the investment) Ct+T (FV) is the value at period t+T (end of the investment) Compounding frequency: how often is interest calculated LSF, Corporate Finance, Nov. / December 2008 73 Future Value and Compounding Corporate Finance, 4 DCF • Compounding: How much will $1 invested today at 9% be worth in two years? (The time line) end of year 0 C 1 2 $1 $1.1881 2 Future value (C 2) = $1 x 1.09 = $1.1881 LSF, Corporate Finance, Nov. / December 2008 74 Example: the one-period case Corporate Finance, 4 DCF If you were to invest $10,000 at 5-percent interest for one year, your investment would grow to $10,500. $500 would be your interest ($10,000 × .05) $10,000 is the principal repayment ($10,000 × 1) $10,500 is the total due. It can be calculated as: $10,500 = $10,000 × (1.05) The total amount due at the end of the investment is call the Future Value (FV). LSF, Corporate Finance, Nov. / December 2008 75 Present Value and Discounting Corporate Finance, 4 DCF • Discounting: How much is $1 that we will receive in two years worth today (r = 9%)? year 0 1 C $0.842 2 $1 Present value (C0 ) = $1 / 1.092 = $0.842 The interest rate (9%) is also called the discount rate. LSF, Corporate Finance, Nov. / December 2008 76 Corporate Finance, 4 DCF How long must we wait…? If we deposit $5000 today in an account paying 10%, how long do we have to wait for it to grow to $10,000? Solve for T: C0+T = C0 x (1 + r)T $10000 = $5000 x (1.10)T (1.10)T =2 T = ln(2) / ln(1.10) = 7.27 years LSF, Corporate Finance, Nov. / December 2008 77 Corporate Finance, 4 DCF What interest rate must be earned? Assume the total cost of a college education will be $50,000 when your child enters college in 18 years. You make an investment of C 0 = $5,000 today. What rate of interest must you earn on your investment to cover the costs of your child’s education? Solve for r : C0+T 50000 (1 + r)18 (1 + r) r = C0 x (1 + r)T = 5000 x (1 + r)18 = 10 = 10(1/18) = 0.13646 = 13.646% per year LSF, Corporate Finance, Nov. / December 2008 78 Net Present Value (NPV) Corporate Finance, 4 DCF The formula for calculating NPV: NPV = -C0 + C1/(1+r) + C2/(1+r)2 + .. + CT/(1+r)T Some hints for computing NPV: Only add (subtract) cash flows from the same time period You may use the time line Specify a cash flow for each time period (even when it is $0) If a constant cash flow starts in the future period t, compute the NPV for the time t-1 first. MBF, Corporate Finance, 2010 79 Net Present Value (NPV) : example Corporate Finance, 4 DCF Consider an investment that pays $200 one year from now, with cash flows increasing by $200 per year through year 4. If the interest rate is 12%, what is the present value of this stream of cash flows? If the issuer offers this investment for $1,500, should you purchase it? MBF, Corporate Finance, 2010 80 Multiple Cash Flows Corporate Finance, 4 DCF 0 1 2 3 4 400 600 800 -1,500 200 178.57 318.88 427.07 508.41 1,432.93 Present Value < Cost → Do Not Purchase NPV = -67.07 = -1,500 + 1,432.92 MBF, Corporate Finance, 2010 81 Effective annual interest rates and compounding periods Corporate Finance, 4 DCF Compounding periods (m) How often is interest paid? Stated (nominal) annual interest rate (r) What the bank usually quotes … Effective annual interest rate (EAR): EAR = (1 + r / m) m - 1 LSF, Corporate Finance, Nov. / December 2008 82 Example: EAR Corporate Finance, 4 DCF Find the effective annual interest rate (EAR) of a monthly compounded loan that pays r = 18% of interest (nominal). The monthly interest rate is 1.5%, a year involves m = 12 compoundings. The EAR is 19.56%; the annual return is equivalent to a loan with an annual interest rate of 19.56%. r 1 + m T ×m 12 .18 = 1 + = (1.015)12 = 1.1956 12 LSF, Corporate Finance, Nov. / December 2008 83 Continuous Compounding Corporate Finance, 4 DCF EAR of continuous compounding = er – 1 Daily compounding is a good approximation for continous compounding Continuous compounding: Ct+T = Ct × e (r × T) where r is the stated annual interest rate MBF, Corporate Finance, 2010 84 Corporate Finance, 4 DCF Simplifications Perpetuity A constant cash-flow stream that lasts forever Growing perpetuity A cash-flow stream that grows forever at a constant rate Annuity A constant cash-flow stream that lasts for a fixed number of periods Growing annuity A cash-flow stream that grows at a constant rate for a fixed number of periods MBF, Corporate Finance, 2010 85 Perpetuity Corporate Finance, 4 DCF A constant stream of cash flows that lasts forever C 0 C C 1 2 3 … C C C PV = + + + 2 3 (1 + r ) (1 + r ) (1 + r ) C PV = r MBF, Corporate Finance, 2010 86 Example : consol Corporate Finance, 4 DCF What is the value of a British consol that promises to pay £15 every year for ever? The interest rate is 10-percent. C £15 £15 £15 year 0 1 2 3 … £15 PV = = £150 .10 MBF, Corporate Finance, 2010 87 Growing perpetuity Corporate Finance, 4 DCF A growing stream of cash flows that lasts forever C 0 C×(1+g) C ×(1+g)2 1 2 3 (1 + g ) C PV = ∑ (1 + r ) (1 + r ) t =0 C PV = r−g MBF, Corporate Finance, 2010 … t 88 Growing perpetuity: example Corporate Finance, 4 DCF The expected dividend next year is $1.30, and dividends are expected to grow at 5% forever. If the discount rate is 10%, what is the value of this promised dividend stream? $1.30 0 1 $1.30×(1.05) 2 $1.30 ×(1.05)2 $1.30 PV = = $26.00 .10 − .05 MBF, Corporate Finance, 2010 … 3 89 Annuity Corporate Finance, 4 DCF A constant stream of cash flows with a fixed maturity C C C C 0 1 2 3 T C C C C PV = + + + 2 3 T (1 + r ) (1 + r ) (1 + r ) (1 + r ) 1 C C 1 1 PV = − = C − T T r r (1 + r ) r r (1 + r ) MBF, Corporate Finance, 2010 PV of a perpetuity (of one monetary unit) starting in T+1 90 Corporate Finance, 4 DCF Annuity: example If you can afford a $400 monthly car payment, how much car can you afford if the interest rate is 7% on a 36-month loan? $400 $400 $400 $400 0 1 2 3 36 $400 1 PV = 1 − (1 + .07 12) 36 = $12,954.59 .07 / 12 MBF, Corporate Finance, 2010 91 1.G. Annuity - another example: What is the present value of a four-year annuity of $100 per year that makes its first payment two years from today if the discount rate is 9%? Corporate Finance, 4 DCF 4 PV1 = ∑ t =1 $297.22 0 $100 $100 $100 $100 $100 = + + + = $323.97 t 1 2 3 4 (1.09) (1.09) (1.09) (1.09) (1.09) $323.97 1 $100 2 $100 3 $327.97 PV = = $297.22 0 1.09 MBF, Corporate Finance, 2010 $100 4 $100 5 92 Growing annuity Corporate Finance, 4 DCF A growing stream of cash flows with a fixed maturity C C×(1+g) C ×(1+g)2 C×(1+g)T-1 0 PV = 1 2 3 T +1 C C × (1 + g ) C × (1 + g ) − + r−g (1 + r ) T +1 (1 + r ) T + 2 T C PV = r−g T T + ... = C 1 + g C 1 + g − ∑ r − g 1 + r 1 + r t =0 1 + r 1+ g 1 − (1 + r ) MBF, Corporate Finance, 2010 T 93 t Corporate Finance, 4 DCF Growing annuity: example A defined-benefit retirement plan offers to pay $20,000 per year for 40 years and increase the annual payment by 3% each year. What is the present value at retirement if the discount rate is 10%? $20,000 $20,000×(1.03) $20,000×(1.03)39 0 1 2 40 1.03 40 $20,000 PV = = $265,121.57 1 − .10 − .03 1.10 MBF, Corporate Finance, 2010 94 Appendix : Perpetuity ∞ C C = ∑ (1 + r )t r t =1 Corporate Finance, 4 DCF Proof of ∞ Lemma S= ∞ C 1 = C∑ ∑ (1 + r )t t =1 (1 + r )t t =1 =C = S− 1 (1 + r ) − 111 + + + ... a a 2 a3 S 1 / a + 1 / a 2 + 1 / a 3 + ... = a a S1 1 1 = 2 + 3 + 4 + ... aa aa 1 /(1 + r ) 1 − 1 /(1 + r ) =C t 1/ a 1 lim ∑ = ,a >1 t →∞ a 1 −1/ a t =1 T (1 + r ) (1 + r ) S1 = aa ⇔S= C r 1 1 ⇔ S (1 − ) = a a 1/ a 1−1/ a Example: a = 2, S = 1 … ½ 0 ½ + ½2 1 Appendix : Growing Perpetuity Corporate Finance, 4 DCF Proof of T lim ∑ a t = t →∞ t =0 1 ,a <1 1− a C C (1 + g ) C (1 + g ) 2 C + + + ... = ,r > g 1 + r (1 + r ) 2 (1 + r ) 3 r−g C C (1 + g ) C (1 + g ) 2 C (1 + g ) (1 + g ) 2 + + + ... = 1+ + + ... 1 + r (1 + r ) 2 (1 + r ) 3 1 + r (1 + r ) (1 + r ) 2 C ∞ (1 + g ) = ∑ (1 + r ) t =0 (1 + r ) = C 1 1 + r 1 − (1 + g ) (1 + r ) C /(1 + r ) 1 + r (1 + g ) − 1 + r (1 + r ) C = r−g = t Appendix : Annuity & Growing Annuity Corporate Finance, 4 DCF Proof of C C (1 + g ) C (1 + g )T −1 C + + ... + = 1 + r (1 + r ) 2 (1 + r )T r−g 1 1− (1 + r )T , r > g ≥ 0 t C ∞ (1 + g ) C C (1 + g ) C (1 + g )T −1 C (1 + g )T ∑ (1 + r ) = 1 + r + (1 + r ) 2 + ... + (1 + r )T + (1 + r )T +1 + ... (1 + r ) t =0 C T −1 (1 + g ) C ∞ (1 + g ) = ∑ (1 + r ) + (1 + r ) ∑ (1 + r ) (1 + r ) t =0 t =T t t t t t (1 + g ) (1 + g ) (1 + g ) C C C = − ∑ ∑ ∑ (1 + r ) t =0 (1 + r ) (1 + r ) t =0 (1 + r ) (1 + r ) t =T (1 + r ) T −1 ∞ ∞ C C 1 − r−g r − g (1 + r )T C 1 = 1 − (1 + r )T (r − g ) = Chapter 4 - problems Corporate Finance, 4 DCF 1: You are planning to save for retirement over the next 30 years. To do this, you will invest 700 a month in a stock account and 300 in a bond account. The return of the stock account is expected to be 11 %, and the bond account will pay 7%. When you retire, you will combine your money into an account with 9% return. How much can you withdraw each month from your account assuming a 25-year withdrawal period? 2: A has been working on an advanced technology in laser eye surgery. His technology will be available in the near term. He anticipates his first annual cash flow from the technology to be 200T received two years from today. Subsequent annual cash flow will grow at 5% in perpetuity. What is the present value of the technology if the discount rate is 10%? MBF, Corporate Finance, 2010 98 Corporate Finance, 4 DCF Experiment: cash-flow valuation MBF, Corporate Finance, 2010 99 Corporate Finance - chapter 5 - How to Value Bonds and Stocks Corporate Finance, 5 Bonds Definition of a bond A bond is a legally binding agreement between a borrower and a lender that specifies the: Par (face) value Coupon rate Coupon payment Maturity date The yield to maturity YTM is the required market interest rate on the bond. MBF, Corporate Finance, 2010 101 How to value bonds : Corporate Finance, 5 Bonds Primary principle: Value of financial securities = PV of expected future cash flows The bond value is, therefore, determined by the present value of the coupon payments and par (face) value, F. Interest rates are inversely related to present (bond) values. The bond pricing equation : (R = YTM) PVCB = C R 1 F 1+ (1 + R) T (1 + R ) T MBF, Corporate Finance, 2010 102 When the YTM < coupon, the bond trades at a premium. 1300 bond value Corporate Finance, 5 Bonds YTM and bond value 1200 When the YTM = coupon, the bond trades at par. 1100 1000 800 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 6 3/8 When the YTM > coupon,Finance, 2010 the bond MBF, Corporate trades at a discount. 0.08 0.09 0.1 discount rate 103 Corporate Finance, 5 Bonds YTM with Semiannual Coupons : Example Suppose a bond with a 10% coupon rate and semiannual coupons has a face value of $1,000, 20 years to maturity, and is selling for $1,197.93. Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there? T = 40; PV = -1,197.93; coupon payment = 50 => 4% on price (is this the YTM?) F = 1,000; YTM = 4% × 2 = 8% MBF, Corporate Finance, 2010 104 Corporate Finance, 5 Bonds Pure Discount Bond: Example Find the value of a 30-year zero-coupon bond with a F = $1,000 par (face) value and a YTM of 6%. $0 $0 $0 $1,000 0$ 0$,1 0 1 2930 02 0 1 PVZB 2 29 30 F $1,000 = = = $174.11 T 30 (1 + R ) (1.06) MBF, Corporate Finance, 2010 105 Corporate Finance, 5 Bonds Bond types Coupon bonds Periodic (typically semiannual) constant coupon payments in addition to the maturity value The bond combines annuity and terminal (maturity) value. Effective annual rate (EAR) = (1 + R/m)m – 1 MBF, Corporate Finance, 2010 106 Coupon Bond: Example Corporate Finance, 5 Bonds Consider a U.S. government bond with a 6 3/8% coupon that expires in December 2010. The par value of the bond is $1,000. Coupon payments are made semi-annually (June 30 and December 31 for this particular bond). Since the coupon rate is 6 3/8%, the payment is $31.875. On January 1, 2006 the size and timing of cash flows are: $31.875 $31.875 $1,031.875 1 1 / 1 / 06 $31.875 2 9 10 6 / 30 / 06 12 / 31 / 06 6 / 30 / 10 12 / 31 / 10 MBF, Corporate Finance, 2010 107 Corporate Finance, 5 Bonds Coupon Bond: Example Find the present value (as of January 1, 2006), of a 6 3/8% coupon bond with semi-annual payments, and a maturity date of December 2010 if the YTM is 5%. PVCB $1,000 $31.875 1 = 1 − (1.025)10 + (1.025)10 = $1,060.17 .05 2 How do we find the PV as of February 1, 2006 under the same conditions. MBF, Corporate Finance, 2010 108 Corporate Finance, 5 Bonds The bond market http://finance.yahoo.com/bonds/composite_bond_rates http://Cxa.marketwatch.com/finra/bondcenter/default.aspx MBF, Corporate Finance, 2010 109 Corporate Finance, 5 Stocks Common stock : Yahoo quote http://finance.yahoo.com/q?s=YHOO MBF, Corporate Finance, 2010 110 Corporate Finance, 5 Stocks Common stock T Present value (price) of common stock : Ct P0 = ∑ (1 + R )T t =0 Issues: How do we define cash flows? What about the discount rate? What about timing? MBF, Corporate Finance, 2010 111 Corporate Finance, 5 Stocks Common stock • Sources of payoffs: – Capital gain (tomorrows price) – Dividend Value of a stock Div1 ∞ Divt P 1 =∑ P0 = + t 1 + R 1 + R t =1 (1 + R) Three scenarios for the valuation of stock Case 1: zero growth Case 2: constant growth Case 3: differential growth MBF, Corporate Finance, 2010 112 Corporate Finance, 5 Stocks Case 1: zero growth Assume that dividends will remain at the same level forever Div1 = Div 2 = Div 3 = • Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity: Div 3 Div1 Div 2 P0 = + + + 1 2 3 (1 + R ) (1 + R ) (1 + R ) Div P0 = R MBF, Corporate Finance, 2010 113 Case 2: constant growth Corporate Finance, 5 Stocks Assume that dividends will grow at a constant rate, g, forever, i.e., Div1 = Div 0 (1 + g ) Div 2 = Div1 (1 + g ) = Div 0 (1 + g ) 2 Div 3 = Div 2 (1 + g ) = Div 0 (1 + g ) 3 … Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity: Div1 P0 = R−g MBF, Corporate Finance, 2010 114 Case 3: differential growth Corporate Finance, 5 Stocks Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter. To value a Differential Growth Stock, we need to: Estimate future dividends in the foreseeable future. Estimate the future stock price when the stock becomes a Constant Growth Stock (case 2). Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate. MBF, Corporate Finance, 2010 115 Case 3: differential growth Corporate Finance, 5 Stocks • Assume that dividends will grow at rate g1 for T years and grow at rate g2 thereafter. Div 0 (1 + g1 ) Div 0 (1 + g1 ) 2 … 0 1 Div 0 (1 + g1 )T … 2 DivT (1 + g 2 ) = Div 0 (1 + g1 )T (1 + g 2 ) … T T+1 MBF, Corporate Finance, 2010 116 Corporate Finance, 5 Stocks Case 3: differential growth Consolidating gives: Div T +1 Div1 (1 + g1 )T R − g 2 P= + 1 − T T R − g1 (1 + R ) (1 + R ) MBF, Corporate Finance, 2010 117 Corporate Finance, 5 Stocks Differential growth : example A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity. What is the stock worth? The discount rate is 12%. LSF, Corporate Finance, Nov. / December 2008 118 Corporate Finance, 5 Stocks Example : using the formula $2(1.08)3 (1.04) .12 − .04 (1.08) 3 $2 × (1.08) P= 1− + 3 .12 − .08 (1.12) (1.12) 3 ( $32.75) P = $54 × [1 − .8966] + 3 (1.12) P = $5.58 + $23.31 P = $28.89 LSF, Corporate Finance, Nov. / December 2008 119 Example : using cash flows Corporate Finance, 5 Stocks $2(1.08) $2(1.08) 2 3 3 $2(1.08) $2(1.08) (1.04) … 0 1 $2.16 0 1 2 3 $2.33 $2.62 $2.52 + .08 2 3 4 The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3. P3 = $2.62 = $32.75 .08 $2.16 $2.33 $2.52 + $32.75 P0 = + + = $28.89 2 3 1.12 (1.12) (1.12) LSF, Corporate Finance, Nov. / December 2008 120 Corporate Finance, 5 Stocks Estimates of parameters The value of a firm depends upon its growth rate, g, and its discount rate, R. Where does g come from? g = retention ratio × return on retained earnings Where does R come from? The discount rate can be broken into two parts. The dividend yield The growth rate (in dividends) In practice, there is a great deal of estimation error involved in estimating R. 121 Find R using the DGM Corporate Finance, 5 Stocks Start with the dividend growth model DGM (it is applied to firms with a growth opportunity in every year): D 0 (1 +g) D1 P0 = = R -g R -g Given P0, rearrange and solve for R: D 0 (1 + g) D1 R= +g= +g P0 P0 MBF, Corporate Finance, 2010 122 Corporate Finance, 5 Stocks Example : PV using DGM The earnings per share EPS of Cumberland Book Publisher are $10. The firm has a dividend payout ratio of 40%, $4 per share, a discount rate of R = 16%, and a return on its retained earnings of 20%. The retention ratio is 60%, implying a growth rate in dividends of g = 12% (=.6 × .2). From the dividend growth model, the price of a share of stock today is Div1 $4 P0 = = = $100 R − g .16 − .12 MBF, Corporate Finance, 2010 123 Corporate Finance, 5 Stocks Growth opportunity model : NPVGO Growth opportunities are opportunities to invest in positive NPV projects. The value of a firm can be conceptualized as the sum of the value of a firm that (perpetually) pays out 100% of its earnings as dividends (so called ‘cash cow’) and the net present value of the growth opportunities. EPS P= + NPVGO R MBF, Corporate Finance, 2010 124 Corporate Finance, 5 Stocks Price-Earnings Ratio Many analysts frequently relate earnings per share to price. The price-earnings ratio is calculated as the current stock price divided by annual EPS. The Wall Street Journal uses last 4 quarter’s earnings Price (per share) P/E ratio = EPS P= EPS + NPVGO R PPS 1 NPVGO ⇒ P / E ratio = =+ EPS R EPS MBF, Corporate Finance, 2010 125 Corporate Finance, 5 Stocks The NPVGO model: example Cumb. Publ.’s EPS is $10 at the end of each year, which usually is paid out to the shareholders. This year, however the firm decides to (perpetually) change its payout rate to 40%. From its investment of $6 dollar retention in the first year, the firm earns $1.20 (= 6 × .20) per year in perpetuity, as the return on retained earnings is 20%. Assume R = .16. The per-share NPV from the investment of date 1: NPVGO1 = -6 + $1.20 / .16 = $1.50 LSF, Corporate Finance, Nov. / December 2008 126 The NPVGO model: example … Corporate Finance, 5 Stocks Since we consider a constant growth rate of the EPS, the net present value of the policy change (growing perpetuity): NPVGO = NPVGO1 $1.50 = = $37.50 R−g .16 − .12 The value of the firm as a cash cow is as follows: EPS / R = $10 / .16 = $62.50 By summation, the NPVGO model yields as the value of the firm: P= EPS + NPVGO = $62.50 + 37.50 = $100 R LSF, Corporate Finance, Nov. / December 2008 127 Chapter 5 – Problem Corporate Finance, 5 Stocks 1. 2. 3. 4. Quepos Real Estate Inc. expects to earn $110 million per year in perpetuity if it does not undertake any new projects. The firm has an opportunity to invest $12 million today and $7million in one year in real estate. The new investment will generate annual earnings of $10 million in perpetuity, beginning two years from today. The firm has 20 million shares of common stock outstanding, and the required rate of return on the stock is 15%. Land investments are not depreciable. Ignore taxes. Draw the time line. What is the price of a share of stock if the firm does not undertake the new investment? What is the value of the investment? What is the per-share stock price if the firm undertakes the investment? MBF, Corporate Finance, 2010 128 Corporate Finance - chapter 6 - Net Present Value and Other Investment Rules Corporate Finance, 6 Investement rules Why Use Net Present Value? Accepting positive NPV projects benefits shareholders. NPV uses cash flows NPV uses all the cash flows of the project NPV discounts the cash flows properly Reinvestment assumption: the NPV rule assumes that all cash flows can be reinvested at the discount rate. MBF, Corporate Finance, 2010 130 Corporate Finance, 6 Investement rules The Payback Period Method How long does it take the project to “pay back” its initial investment? Payback Period = number of years to recover initial costs Minimum Acceptance Criteria: Set by management Ranking Criteria: Set by management MBF, Corporate Finance, 2010 131 Corporate Finance, 6 Investement rules The Payback Period Method Disadvantages: Ignores the time value of money Ignores cash flows after the payback period A project accepted based on the payback criteria may not have a positive NPV Advantages: Easy to understand Biased toward liquidity MBF, Corporate Finance, 2010 132 Corporate Finance, 6 Investement rules The Internal Rate of Return IRR: the discount rate that sets NPV to zero Minimum Acceptance Criteria: Accept if the IRR exceeds the required return Ranking Criteria: Select alternative with the highest IRR Reinvestment assumption: All future cash flows assumed reinvested at the IRR MBF, Corporate Finance, 2010 133 Corporate Finance, 6 Investement rules IRR: Example Consider the following project: $50 0 -$200 $100 $150 1 2 3 The internal rate of return for this project is 19.44% $50 $100 $150 NPV = 0 = −200 + + + 2 (1 + IRR) (1 + IRR) (1 + IRR) 3 MBF, Corporate Finance, 2010 134 If we graph NPV versus the discount rate, we can see the IRR as the x-axis intercept. 0% 4% 8% 12% 16% 20% 24% 28% 32% 36% 40% 44% $100.00 $73.88 $51.11 $31.13 $13.52 ($2.08) ($15.97) ($28.38) ($39.51) ($49.54) ($58.60) ($66.82) NPV Corporate Finance, 6 Investement rules NPV payoff profile $120.00 $100.00 $80.00 $60.00 $40.00 $20.00 $0.00 ($20.00) -1% ($40.00) ($60.00) ($80.00) IRR = 19.44% 9% 19% 29% 39% Discount rate MBF, Corporate Finance, 2010 135 Corporate Finance, 6 Investement rules Calculating IRR and NPV with EXCEL You start with the cash flows. You use the “NPV(interest;cf-range)” function. You first enter the interest rate and then your range of cash flows, beginning with period 1. Then you add the initial cash flow (the cost). You use the IRR function: You can enter a guess, but it is not necessary. The default format is a whole percent – you will normally want to increase the decimal places to at least two. MBF, Corporate Finance, 2010 136 Corporate Finance, 6 Investement rules Internal Rate of Return (IRR) Disadvantages: IRR may not exist, or there may be multiple IRRs Problems with mutually exclusive investments Timing problem Advantages: Easy to understand and communicate MBF, Corporate Finance, 2010 137 Corporate Finance, 6 Investement rules 3.3. The Timing Problem $10,000 $1,000 $1,000 Project A 0 1 2 3 ­$10,000 $1,000 $1,000 $12,000 Project B 0 1 2 3 ­$10,000 MBF, Corporate Finance, 2010 138 $5,000.00 Project A $4,000.00 Project B $3,000.00 $2,000.00 NPV Corporate Finance, 6 Investement rules 3.3. The timing problem $1,000.00 10.55% = crossover rate $0.00 ($1,000.00) 0% 10% 20% 30% 40% ($2,000.00) ($3,000.00) ($4,000.00) ($5,000.00) 12.94% = IRRB 16.04% = IRRA Discount rate MBF, Corporate Finance, 2010 139 Compute the IRR for either project “A-B” or “B-A” (incremental approach) Year Project A Project B Project A-B Project B-A 0 ($10 000) ($10 000) $0 $0 1 $10 000 $1 000 $9 000 ($9 000) 2 $1 000 $1 000 $0 $0 3 $1 000 $12 000 ($11 000) $11 000 $3,000.00 $2,000.00 NP V Corporate Finance, 6 Investement rules Calculating the Crossover Rate – incremental IRR procedure $1,000.00 $0.00 ($1,000.00) 0% 10.55% = IRR 5% 10% 15% 20% A-B B-A ($2,000.00) ($3,000.00) Discount rate MBF, Corporate Finance, 2010 140 Corporate Finance, 6 Investement rules NPV versus IRR NPV and IRR will generally give the same decision. Exceptions: Non-conventional cash flows – cash flow signs change more than once Mutually exclusive projects Initial investments are substantially different Timing of cash flows is substantially different MBF, Corporate Finance, 2010 141 Survey Evidence Survey of CFOs who belong to FEI. 75% of CFOs report using IRR and 75% NPV. On a scale of 0 to 4, where 4 is very important, mean responses associated with both were 3.1. 57% of CFOs reported using the payback rule. Used by older, longer-tenure CEOs without MBAs. Payback most intuitive, NPV least intuitive. MBF, Corporate Finance, 2010 142 Corporate Finance, 6 Investement rules Investment rules : example Compute the IRR, NPV, and payback period for the following two projects. Assume the required return is 10%. Year 0 1 2 3 Project A -$200 $200 $800 -$800 MBF, Corporate Finance, 2010 Project B -$150 $50 $100 $150 143 Corporate Finance, 6 Investement rules Example of investment rules CF0 PV0 of CF1-3 NPV = IRR = Project A -$200.00 Project B -$150.00 $241.92 $240.80 $41.92 0%, 100% $90.80 36.19% MBF, Corporate Finance, 2010 144 NPV Corporate Finance, 6 Investement rules NPV profiles $400 $300 IRR 1(A) IRR (B) IRR 2(A) $200 $100 $0 -15% 0% 15% 30% 45% 70% 100% 130% 160% 190% ($100) ($200) Cross-over Rate Discount rates MBF, Corporate Finance, 2010 Project A Project B145 Corporate Finance, 6 Investement rules Investment rules : example Payback Period: Time 0 1 2 3 CF -200 200 800 -800 Project A Cum. CF -200 0 800 0 CF -150 50 100 150 Project B Cum. CF -150 -100 0 150 Payback period for project B = 2 years. Payback period for project A = 1 or 3 years? MBF, Corporate Finance, 2010 146 Corporate Finance, 6 Investement rules The authors of the book… Claim that the NPV is superior decision rule Are unclear about the use of the payback criterion in practice Why do you think, the payback criterion could be preferred to NPV used in practice? Is the payback / NPV criterion more frequently used by small or large firms? MBF, Corporate Finance, 2010 147 Saint Petersburg gamble (what can we learn from it?) Nicholas Bernoulli (1713) in a letter to Montmort Peter tosses a fair coin repeatedly until it shows heads. He agrees to Paul one ducat if it shows heads on the first toss, two ducats if the first head appears on the second toss, four ducats if the first head appears on the third toss, eight if on the fourth toss, etc. Thought experiment: How much should Peter charge Paul as a price to play this gamble so that the gamble will be fair? 0 p(T) = ½ p(H) = ½ x1 = €1 1 p(T) = ½ p(H) = ½ x2 = €2 2 p(T) = ½ p(H) = ½ x3 = €4 MBF, Corporate Finance, 2010 … p(T) = ½ k p(T) = ½ p(H) = ½ xk = €2k 148 St. Petersburg Paradox (Bernoulli 1732) What is the probability that the coin will be flipped three times? p (T1 , T2 , H 3 ) = 1 1 = 23 8 What is the expected payoff of the gamble? E[ L] = 20 p ( H 1 ) + 21 p (T1 , H 2 ) + ... + 2 k p (T1 , T2 ,..., Tk , H k ) + ... E[ L ] = 1 ⋅ 1 1 1 11 1 + 21 ⋅ 2 + ... + 2 k ⋅ k +1 + ... = + + ... + + ... = ∞ 2 2 2 22 2 Paradox: No-one is willing to pay a very high price for the participation in the St. Petersburg gamble. In experiments most offers are below 5 Euro. We conclude that the expected value is not a good descriptive model for decision making under uncertainty. What can we learn from the paradox? MBF, Corporate Finance, 2010 149 Corporate Finance, 6 Investement rules Chapter 6 - problem A) B) C) D) Consider the following cash flows on two mutually exclusive projects for Tomatina Recreation SA. Both projects require an anuual return of 15 per cent. Choose the project with the shorter payback period. Choose the project with the greater IRR. Choose the better project based on the incremental IRR. Compute the project with the higher NPV. Year 0 1 2 3 deepwater submarine ($600 000) ($1 800 000) $270 000 $1 000 000 $350 000 $700 000 $300 000 $900 000 Corporate Finance - chapter 7 - Making Capital Investment Decisions Corporate Finance, 7 Inflation Inflation and Capital Budgeting Inflation is an important fact of economic life and must be considered in capital budgeting. Consider the relationship between interest rates and inflation, often referred to as the Fisher equation: (1 + Nominal Rate) = (1 + Real Rate) × (1 + Inflation Rate) MBF, Corporate Finance, 2010 152 Corporate Finance, 7 Inflation Inflation and Capital Budgeting For low rates of inflation, this is often approximated: Real Rate ≅ Nominal Rate – Inflation Rate While the nominal interest rate in Europe and in Northern America has fluctuated with inflation, the real interest rate has generally exhibited far less variance than the nominal rate. In capital budgeting, one must compare real cash flows discounted at real rates or nominal cash flows discounted at nominal rates. MBF, Corporate Finance, 2010 153 R&U experiment Corporate Finance - chapter 8 - Risk Analysis, Real Options, and Capital Budgeting Corporate Finance, 8 Break-even & real option Sensitivity, Scenario, and Break-Even Each allows us to look behind the NPV number to see how stable our estimates are. Sensitivity-analysis : “If revenues or other variables are changed by 1%, what effect will it have on the NPV? “ Scenario-analysis: Compare pessimistic, normal and optimistic scenarios. Compute the NPV for each scenario. Break-even analysis: Needed sales to break even, using accounting numbers. Accounting break-even: net income = 0 Cash break-even: operating cash flow = 0 Financial break-even: sales volume at which NPV = 0 MBF, Corporate Finance, 2010 156 Example: Stewart Pharmaceuticals Stewart Pharmaceuticals Corporation is considering investing in the development of a drug that cures the common cold. A corporate planning group has recommended that the firm go ahead with the test and development phase. This preliminary phase will last one year and cost $1 billion. The group believes that there is a 60% chance that tests will prove successful. If the initial tests are successful, Stewart Pharmaceuticals can go ahead with full-scale production. This investment phase will cost $1.6 billion. Production will occur over the following 4 years. MBF, Corporate Finance, 2010 157 Corporate Finance, 8 Break-even & real option NPV Following Successful Test Investment Year 1 Years 2-5 Revenues $7,000 Variable Costs (3,000) Fixed Costs (1,800) Depreciation (400) Pretax profit $1,800 Tax (34%) (612) Net Profit $1,188 Cash Flow $1,588 0 Note that the NPV is calculated as of date 1, the date at which the investment of $1,600 million is made. Later we bring this number back to date 0. Assume a cost of capital of 10%. 1 -$1,600 2 -$1,600 $1,588 3 $1,588 $1,588 4 $1,588 5 MBF, Corporate Finance, 2010 4 NPV 1 = −$1,600 + ∑ t =1 $1,588 (1.10) t NPV 1 = $3,433.75 So, we invest. 158 Corporate Finance, 8 Break-even & real option NPV Following Unsuccessful Test Investment Year 1 Years 2-5 Revenues $4,050 Variable Costs (1,735) Fixed Costs (1,800) Depreciation (400) Pretax profit Note that the NPV is calculated as of date 1, the date at which the investment of $1,600 million is made. Later we bring this number back to date 0. Assume a cost of capital of 10%. $115 Tax (34%) (39.10) Net Profit $75.90 Cash Flow -$1,600 $475.90 4 NPV 1 = −$1,600 + ∑ t =1 $475.90 (1.10) t NPV 1 = −$91.461 So, we don’t invest. MBF, Corporate Finance, 2010 159 Corporate Finance, 8 Break-even & real option Decision Tree for Stewart The firm has two decisions to make: To test or not to test. To invest or not to invest. Success Invest NPV = $3.4 b 60% Test Do not invest 40% Do not test NPV = $0 Failure NPV = $0 MBF, Corporate Finance, 2010 NPV = –$91.46 m Invest 160 Corporate Finance, 8 Break-even & real option Decision to Test Let’s move back to the first stage, where the decision boils down to the simple question: should we invest? The expected payoff evaluated at date 1 is: Expected Prob. Payoff Prob. Payoff = sucess × given success + failure × given failure payoff Expected = ( .60 × $3,433.75) + ( .40 × $0) = $2,060.25 payoff The NPV evaluated at date 0 is: $2,060.25 NPV = −$1,000 + = $872.95 1.10 So, we should test. 161 MBF, Corporate Finance, 2010 Corporate Finance, 8 Break-even & real option Sensitivity Analysis: Stewart We can see that NPV is very sensitive to changes in revenues. In the Stewart Pharmaceuticals example, a drop of $1000/per year in revenue to $6000 leads to a NPV of $1342, implying a 61% drop in NPV. %∆Rev = $6,000 − $7,000 = −14.29% $7,000 $1,341.64 − $3,433.75 %∆NPV = = −60.93% $3,433.75 For every 1% drop in revenue, we can expect roughly a 4.26% drop in NPV: − 4.26 = − 60.93% 14.29% MBF, Corporate Finance, 2010 162 Corporate Finance, 8 Break-even & real option Break-Even Analysis: Stewart Another way to examine variability in our forecasts is break- even analysis. In the Stewart Pharmaceuticals example, we could be concerned with break-even revenue, break-even sales volume, or breakeven price. To find either, we start with the break-even operating cash flow, $504.75 × Σt=1,..,4 1/(1.10)t = $1600 MBF, Corporate Finance, 2010 163 Corporate Finance, 8 Break-even & real option Break-Even Revenue: Stewart Work backwards from OCFBE to Break-Even Revenue Revenue + VC Variable cost Fixed cost Depreciation EBIT +D +FC $104.75 0.66 Tax (34%) Net Income OCF = $104.75 + $400 $5,358.71 $3,000 $1,800 $400 $158.71 $53.96 $104.75 $504.75 164 MBF, Corporate Finance, 2010 Corporate Finance, 8 Break-even & real option Break-Even Analysis: PBE Now that we have break-even revenue of $5,358.71 million, we can calculate break-even price. The original plan was to generate revenues of $7 billion by selling the cold cure at $10 per dose and selling 700 million doses per year, We can reach break-even revenue with a price of only: $5,358.71 million = 700 million × PBE PBE = $5,358.71 700 = $7.66 / dose 165 MBF, Corporate Finance, 2010 Corporate Finance, 8 Break-even & real option Monte Carlo Simulation Monte Carlo simulation is a further attempt to model real-world uncertainty. Interactions between the variables are explicitly specified in Monte Carlo simulation; so, at least theoretically, this methodology provides a more complete analysis. How to proceed: Specify the basic model Specify a distribution of values for each variable The computer draws a realization for each variable and determines the cash flow for each future year Repeat procedure to receive a distribution of cash flows for each future year (basic output of the Monte Carlo simulation) Compute NPV by taking expected values of and appropriately discounting of cash flows 166 MBF, Corporate Finance, 2010 Corporate Finance, 8 Break-even & real option Real Options One of the fundamental insights of modern finance theory is that options have value. The Option to Expand Has value if demand turns out to be higher than expected The Option to Abandon Has value if demand turns out to be lower than expected The Option to Delay Has value if the underlying variables are changing with a favorable trend MBF, Corporate Finance, 2010 167 Corporate Finance, 8 Break-even & real option The Option to Abandon: Example Suppose we are drilling an oil well. The drilling rig costs $300 today, and in one year the well is either a success or a failure. The outcomes are equally likely. The discount rate is 10%. The PV of the successful payoff at time one is $575. The PV of the unsuccessful payoff at time one is $0. MBF, Corporate Finance, 2010 168 Corporate Finance, 8 Break-even & real option The Option to Abandon: Example Traditional NPV analysis would indicate rejection of the project. Expected = Prob. ×Successful + Prob. × Failure Payoff Success Payoff Failure Payoff Expected = (0.50×$575) + (0.50×$0) = $287.50 Payoff $287.50 = –$38.64 NPV = –$300 + 1.10 169 MBF, Corporate Finance, 2010 Corporate Finance, 8 Break-even & real option The Option to Abandon: Example Traditional NPV analysis overlooks the option to abandon. Success: PV = $500 Sit on rig; stare at empty hole: PV = $0. Drill − $500 Failure Do not drill NPV = $0 Sell the rig; salvage value = $250 The firm has two decisions to make: drill or not, abandon or stay. 170 MBF, Corporate Finance, 2010 Corporate Finance, 8 Break-even & real option The Option to Abandon: Example When we include the value of the option to abandon, the drilling project should proceed: Expected = Prob. × Successful + Prob. × Failure Payoff Success Payoff Failure Payoff Expected = (0.50×$575) + (0.50×$250) = $412.50 Payoff NPV = –$300 + $412.50 = $75.00 1.10 171 MBF, Corporate Finance, 2010 Corporate Finance, 8 Break-even & real option Valuing the Option to Abandon Recall that we can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project. M = NPV + Opt $75.00 = –$38.64 + Opt $75.00 + $38.64 = Opt Opt = $113.64 172 MBF, Corporate Finance, 2010 Behavioral Corporate Finance, evidence Behavioral pitfalls: reluctance to terminate losing projects Only 73% of firms use cost of capital techniques to evaluate to abandon existing projects.-Do managers make negative NPV decisions by failing to terminate losing projects? Illustrative Example (Sony and Sunk Costs) Sony's Chromatron color TV project in 1961. Production process yielded only 2 or 3 usable picture tubes per 1000. Retail price of a Chromatron color television set was $550, but the cost of production was more than double. Manager Ibuka would not terminate until Sony was on verge of ruin. 173 MBF, Corporate Finance, 2010 Corporate Finance, 8 Break-even & real option Chapter 8 – problem A young screenwriter has just finished his first script. It has action, drama, and humor, and he thinks it will be a blockbuster. He takes the script to every motion picture studio in town and tries to sell it but to no avail. Finally, one studio offers to buy the script for either (a) 5000, or (b) 1% of the movie’s profit. There are two decisions the studio will have to make. First is to decide if the script is good or bad, and the second if the movie is good or bad. First, there is a 90% chance that the script is bad,. If it is bad, the studio does nothing more and throws the script out. If the script is good, they will shoot the movie. After the movie is shot, the studio will review it, and there is a 70% chance that the movie is bad. If the movie is bad, the movie will not be promoted and will not turn a profit. If the movie is good the studio will promote heavily; the average profit for this type of movie is 10M. The screenwriter rejects the 5000 and says he wants 1% of profits. Was this a good decision? MBF, Corporate Finance, 2010 174 Corporate Finance - chapter 9 - Risk and Return Lessons from Market History Corporate Finance, 9 Risk and return Returns Dollar Return = Dividend + Change in Market Value dollar return percentage return = beginning market value dividend + change in market value = beginning market value = dividend yield + capital gains yield LSF, Corporate Finance, February 2008 176 Corporate Finance, 9 Risk and return Holding Period Returns The holding period return is the return that an investor would get when holding an investment over a period of n years, when the return during year i is given as ri: holding period return = = (1 + r1 ) × (1 + r2 ) × × (1 + rn ) − 1 LSF, Corporate Finance, February 2008 177 Corporate Finance, 9 Risk and return Holding Period Return: Example Suppose your investment provides the following returns over a four- year period: Year Return 1 10% 2 -5% 3 20% 4 15% Your holding period return = = (1 + r1 ) × (1 + r2 ) × (1 + r3 ) × (1 + r4 ) − 1 = (1.10) × (.95) × (1.20) × (1.15) − 1 = .4421 = 44.21% LSF, Corporate Finance, February 2008 178 Corporate Finance, 9 Risk and return Geometric Return: Example Year Return Geometric average return = 1 10% (1 + r ) 4 = (1 + r ) × (1 + r ) × (1 + r ) × (1 + r ) g 1 2 3 4 2 -5% rg = 4 (1.10) × (.95) × (1.20) × (1.15) − 1 3 20% 4 15% = .095844 = 9.58% So, our investor made an average of 9.58% per year, realizing a holding period return of 44.21%. 1.4421 = (1.095844) 4 LSF, Corporate Finance, February 2008 179 Corporate Finance, 9 Risk and return Geometric Return: Example Note that the geometric average is not the same as the arithmetic average: Year Return r1 + r2 + r3 + r4 1 10% Arithmetic average return = 4 2 -5% 3 20% = 10% − 5% + 20% + 15% = 10% 4 4 15% LSF, Corporate Finance, February 2008 180 Corporate Finance, 9 Risk and return Forecasting Return To address the time relation in forecasting returns, use Blume’s formula: τ −1 N −τ R (τ ) = × Geometric Average + × Arithmetic Average N −1 N −1 where, τ is the forecast horizon and N is the number of years of historical data we are working with. τ must be less than N. LSF, Corporate Finance, February 2008 181 Corporate Finance, 9 Risk and return Return statistics The history of capital market returns can be summarized by describing the: average return R= ( R1 + + RT ) T the standard deviation of those returns ( R1 − R ) 2 + ( R2 − R) 2 + ( RT − R) 2 SD = VAR = T −1 the frequency distribution of the returns … LSF, Corporate Finance, February 2008 182 Corporate Finance, 9 Risk and return Historical returns, 1926-2004 Series Average Annual Return Standard Deviation Large Company Stocks 12.3% 20.2% Small Company Stocks 17.4 32.9 Long-Term Corporate Bonds 6.2 8.5 Long-Term Government Bonds 5.8 9.2 U.S. Treasury Bills 3.8 3.1 Inflation 3.1 Distribution 4.3 – 90% 0% + 90% Source: © Stocks, Bonds, Bills, and Inflation 2006 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. LSF, Corporate Finance, February 2008 183 Corporate Finance, 9 Risk and return Risk Statistics There is no universally agreed-upon definition of risk. The measures of risk that we discuss are variance and standard deviation. The standard deviation is the standard statistical measure of the spread of a sample, and it will be the measure we use most of this time. Its interpretation is facilitated by a discussion of the normal distribution. LSF, Corporate Finance, February 2008 184 Corporate Finance, 9 Risk and return Normal Distribution A large enough sample drawn from a normal distribution looks like a bell-shaped curve. Probability The probability that a yearly return will fall within 20.2 percent of the mean of 12.3 percent will be approximately 2/3. – 3σ – 48.3% – 2σ – 28.1% – 1σ – 7.9% 0 12.3% + 1σ 32.5% + 2σ 52.7% 68.26% + 3σ 72.9% Return on large company common stocks 95.44% 99.74% LSF, Corporate Finance, February 2008 185 18% Small-Company Stocks 16% Annual Return Average Corporate Finance, 9 Risk and return The risk-return tradeoff 14% Large-Company Stocks 12% 10% 8% 6% T-Bonds 4% T-Bills 2% 0% 5% 10% 15% 20% 25% 30% 35% Annual Return Standard Deviation LSF, Corporate Finance, February 2008 186 Chapter 9 – problem : Corporate Finance, 9 Risk and return What are the arithmetic and geometric returns for the following stock? The stock has had the following year-end prices and dividends: Year Price Dividend 1 $43.12 - 2 49.07 $0.55 3 51.19 0.60 4 47.24 0.63 5 56.09 0.72 6 67.21 0.81 LSF, Corporate Finance, February 2008 187 Corporate Finance - chapter 10 - Return and Risk The Capital Asset Pricing Model Corporate Finance, 10 CAPM Individual Securities The characteristics of individual securities that are of interest are the: Expected Return Variance and Standard Deviation Covariance and Correlation (to another security or index) LSF, Corporate Finance, February 2008 189 Corporate Finance, 10 CAPM Expected Return, Variance, and Covariance Consider the following two risky asset world. There is a 1/3 chance of each state of the economy, and the only assets are a stock fund and a bond fund. Stock Fund Rate of Scenario Recession Normal Boom Expected return Variance Standard Deviation Return -7% 12% 28% 11.00% 0.0205 14.3% Squared Bond Fund Rate of Deviation 0.0324 0.0001 0.0289 LSF, Corporate Finance, February 2008 R eturn 17% 7% -3% 7.00% 0.0067 8.2% Squared Deviation 0.0100 = (17%-7%)2 0.0000 0.0100 190 Covariance Corporate Finance, 10 CAPM -0.018 = (-7%-11%)(17%-7%) Stock Scenario Recession Normal Boom S um = covariance Bond Deviation Deviation -18% 10% 1% 0% 17% -10% Product -0.0180 0.0000 -0.0170 Weighted -0.0060 = -1.8%/3 0.0000 -0.0057 -0.0117 n Cov ( x, y ) = ∑ pi ( xi − x )( yi − y ) i =1 Deviation compares return in each state i to the expected return. Weighted takes the product of the deviations multiplied by the probability of that state. LSF, Corporate Finance, February 2008 191 Corporate Finance, 10 CAPM Portfolios Scenario Recession Normal Boom Expected return Variance Standard Deviation 5% = 50% × (−7%) + 50% × (17%) Rate of Return Stock fund Bond fund Portfolio -7% 17% 5.0% 12% 7% 9.5% 28% -3% 12.5% 11.00% 0.0205 14.31% 7.00% 0.0067 8.16% squared deviation 0.0016 = (5%-9%)2 0.0000 0.0012 9.0% 0.0010 3.08% Consider an equally weighted portfolio (50% in stocks and 50% in bonds) The rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio: rP = wB rB + wS rS LSF, Corporate Finance, February 2008 192 Corporate Finance, 10 CAPM Correlation Cov ( x, y ) ρ= σ xσ y − .0117 ρ= = −0.998 (.143)(.082) LSF, Corporate Finance, February 2008 193 Corporate Finance, 10 CAPM Portfolios Scenario Recession Normal Boom Expected return Variance Standard Deviation Rate of Return Stock fund Bond fund Portfolio -7% 17% 5.0% 12% 7% 9.5% 28% -3% 12.5% 11.00% 0.0205 14.31% 7.00% 0.0067 8.16% squared deviation 0.0016 0.0000 0.0012 9.0% 0.0010 3.08% The variance of the rate of return on the two risky assets portfolio is 2 σ P = (wB σ B ) 2 + (wS σ S ) 2 + 2(wB σ B )(wS σ S )ρ BS = ( .5 × .0816 )2 + ( .5 × .1431 )2 + 2( .5 × .0816 )( .5 × .1431 )(−.998) where ρBS is the correlation coefficient between the returns LSF, Corporate Finance, February 2008 on the stock and bond funds. 194 Corporate Finance, 10 CAPM Portfolios Scenario Recession Normal Boom Expected return Variance Standard Deviation Rate of Return Stock fund Bond fund Portfolio -7% 17% 5.0% 12% 7% 9.5% 28% -3% 12.5% 11.00% 0.0205 14.31% 7.00% 0.0067 8.16% squared deviation 0.0016 0.0000 0.0012 9.0% 0.0010 3.08% Observe the decrease in risk that diversification offers. An equally weighted portfolio (50% in stocks and 50% in bonds) has less risk than either stocks or bonds held in isolation. LSF, Corporate Finance, February 2008 195 The Efficient Set for Two Assets Risk 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50.00% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100% 8.2% 7.0% 5.9% 4.8% 3.7% 2.6% 1.4% 0.4% 0.9% 2.0% 3.08% 4.2% 5.3% 6.4% 7.6% 8.7% 9.8% 10.9% 12.1% 13.2% 14.3% Return 7.0% 7.2% Portfolo Risk and Return Combinations 7.4% 12,0% 7.6% 11,0% 100% 7.8% 10,0% stocks 9,0% 8.0% 8,0% 8.2% 100% 7,0% 6,0% 8.4% bonds 5,0% 8.6% 0,0% 5,0% 10,0% 15,0% 20,0% 8.8% Portfolio risk (standard deviation) 9.00% 9.2% 9.4% 9.6% 9.8% We can consider other portfolio 10.0% weights besides 50% in stocks and 10.2% 50% in bonds … 10.4% 10.6% 10.8% SF, Corporate Finance, February 2008 L 196 11.0% Exp. portf return Corporate Finance, 10 CAPM % in stocks The Efficient Set for Two Assets Risk Return 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100% 8.2% 7.0% 5.9% 4.8% 3.7% 2.6% 1.4% 0.4% 0.9% 2.0% 3.1% 4.2% 5.3% 6.4% 7.6% 8.7% 9.8% 10.9% 12.1% 13.2% 14.3% 7.0% 7.2% 7.4% 7.6% 7.8% 8.0% 8.2% 8.4% 8.6% 8.8% 9.0% 9.2% 9.4% 9.6% 9.8% 10.0% 10.2% 10.4% 10.6% 10.8% 11.0% Portfolo Risk and Return Combinations Exp. portf. return Corporate Finance, 10 CAPM % in stocks 12,0% 11,0% 100% stocks 10,0% 9,0% 8,0% 100% bonds 7,0% 6,0% 5,0% 0,0% 2,0% 4,0% 6,0% 8,0% 10,0% 12,0% 14,0% 16,0% Portfolio risk (standard deviation) Note that some portfolios are “better” than others. They have higher returns for the same level of risk or less. LSF, Corporate Finance, February 2008 197 Expected return Corporate Finance, 10 CAPM Portfolios with Various Correlations 100% stocks ρ = -1.0 100% bonds ρ = 1.0 ρ = 0.2 σ Relationship depends on correlation coefficient -1.0 < ρ < +1.0 If ρ = +1.0, no risk reduction is possible by diversification If ρ = –1.0, complete risk reduction is possible LSF, Corporate Finance, February 2008 198 return Corporate Finance, 10 CAPM The Efficient Set for Many Securities c effi ie tier ron nt f minimum variance portfolio Individual Assets σP The section of the opportunity set above the minimum variance portfolio is the efficient frontier. LSF, Corporate Finance, February 2008 199 return Corporate Finance, 10 CAPM Riskless Borrowing and Lending CM L 100% stocks Balanced fund rf 100% bonds σ Now investors can allocate their money across the T-bills and a balanced mutual fund. LSF, Corporate Finance, February 2008 200 return Corporate Finance, 10 CAPM Market equilibrium CM L efficient frontier 100% stocks M rf 100% bonds σP Note, all investors have the same Capital Market Line, CML. With homogeneous expectations all investors choose the same mix M of risky securities. Therefore M is called the market portfolio. With the CML identified, all investors choose a point along that line—M in combination with the risk-free rate of interest r f; the allocation the investor chooses depends on his risk tolerance. LSF, Corporate Finance, February 2008 201 Corporate Finance, 10 CAPM Risk when holding the market portfolio Researchers have shown that the risk of a security in a large portfolio can be measured by its beta (β) value. Beta measures the responsiveness of a security to movements in the market portfolio (i.e., systematic risk). βi = Cov ( Ri , RM ) σ 2 ( RM ) LSF, Corporate Finance, February 2008 202 Corporate Finance, 10 CAPM Expected return of security E[Ri] The CAPM : the security market line RF E[ Ri ] = RF + βi ( E[ RM ] − RF ) SML A’ A B C D C’ Beta of security βi In equilibrium, all portfolios including single securities must lie on the security market line, Finance, February 2008 LSF, Corporate SML. 203 Relationship between risk and expected return in equilibrium Corporate Finance, 10 CAPM (CAPM) Expected Return on the Market: R M = RF + 1× Market Risk Premium • Expected return on an individual security: R i = RF + β i × ( R M − RF ) Market Risk Premium The beta, defined as the covariance of the asset divided by the market portfolio, measures the risk added by an investment to the market portfolio. LSF, Corporate Finance, February 2008 204 Expected return Corporate Finance, 10 CAPM Relationship between risk & return R i = RF + β i × ( R M − RF ) RM RF 1.0 LSF, Corporate Finance, February 2008 β 205 Expected return Corporate Finance, 10 CAPM Example: return of an individual security in equilibrium 13.5% 3% 1.5 β i = 1. 5 RF = 3% β R M = 10% R i = 3% + 1.5 × (10% − 3%) = 13.5% LSF, Corporate Finance, February 2008 206 Implications and assumptions of the CAPM Implication Diversification eliminates the unsystematic risk in a portfolio If the return on the market portfolio changes by 1%, the return on the individual security changes by βi%, the relationship between expected return and beta corresponds to a straight line, the SML. Assumptions Perfect capital markets, incl. no transaction costs Agents are rational and have perfect knowledge about the risk and return of each security in the market. LSF, Corporate Finance, February 2008 207 Corporate Finance, 10 CAPM Portfolio risk and number of stocks σP In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not. Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk Portfolio risk Non diversifiable risk; Systematic Risk; Market Risk n Total risk = systematic risk + unsystematic risk LSF, Corporate Finance, February 2008 n = number of different risky assets 208 With a risk-free asset available and the efficient frontier identified, we choose the capital allocation line with the steepest slope. RM = R f + bM σ M max bM = return Corporate Finance, 10 CAPM Appendix: derivation CML & market portfolio CM L efficient frontier Rf RM − R f σM risk Example: 2 risky & the riskless asset RM − R f x1 R1 + (1 − x1 ) R2 − R f , xi being the share of security i max bM = = 2 x1 σM x12σ 12 + 2 x1 (1 − x1 )σ 12 + (1 − x1 ) 2 σ 2 in the market portfolio. => x1 = 2 ( R1 − rf )σ 2 − ( R2 − R f )σ 12 LSF, Corporate Finance, February 2008 2 ( R1 − rf )σ 2 − ( R1 + R2 − 2 R f )σ 12 + ( R2 − R f )σ 12 209 Appendix: Derivation of SML from CML Expected return and risk of portfolio p with two risky securities, one being the market portfolio M the other one i being contained in M Corporate Finance, 10 CAPM RP = aRi + (1 − a ) RM 2 σ P = a 2σ i2 + 2a(1 − a)σ iM + (1 − a ) 2 σ M Take derivatives to see how a change of a affects risk and return of pC dRP = Ri − RM da 1 2 (2aσ i2 + (2 − 4a)σ iM − 2(1 − a )σ M ) dσ P 2 = 2 da a 2σ i2 + 2a(1 − a)σ iM + (1 − a) 2 σ M In the market portfolio a = 0, thus dRP da a =0 dσ P da a =0 = Ri − RM 1 2 (2σ iM − 2σ M ) =2 2 σM Expected risk-return trade-off R − RM dRP / da dR = M= i 2 dσ P / da a =0 dσ M σ iM − σ M σM CML slope: trades-off of RM and σM in M RM − R f R − RM dR dRM =i =M = bM = 2 σ iM − σ M dσ M dσ M σM σM 2 σ iM − σ M ( RM − R f ) = ( Ri − RM ) σ Mσ M Ri = R f + β i ( RM − R f ) SML Chapter 10 problems Corporate Finance, 10 CAPM 1: Based on the following information, calculate the expected return and standard deviation of each of the following stocks. Assume each state of the economy is equally likely to happen. What are the covariance and correlation between the returns of the two stocks? State of the Economy Return on stock B Bear 6.3% -3.7% Normal 10.5% 6.4% Bull Return on stock A 16.7% 25.3% 2: You have been provided the following data about the securities of three firms, the market portfolio, and the risk-free asset: State of the Economy Expected return Standard deviation Firm A 13% 38% Firm B 16% Firm C 25% 65% The market portfolio 15% 20% The risk-free asset 5% Correlation ?i ?ii ?vi Beta 0.90 40% 35% 1.10 ?iii ?iv ?v ?vii ?viii A) fill in the missing values in the table B) is the stock of A correlctly priced according to the CAPM? What about the stock of firm B? Firm C? if these securities are not correctly priced, what is your investment recommendation for someone with a well-diversified portfolio? Corporate Finance - chapter 11 - An Alternative View of Risk and Return The Arbitrage Pricing Theory Arbitrage Pricing Theory Corporate Finance, 11 APT Arbitrage arises if an investor can construct a zero investment portfolio with a sure profit. Since no investment is required, an investor can create large positions to secure large levels of profit. In efficient markets with perfect capital markets, arbitrage opportunities are immediately eliminated by the market. The arbitrage pricing theory is a general model of asset pricing. The risk and return of an individual security may depend on various factors. The one-factor market-portfolio model, the market model, corresponds to the CAPM. MBF, Corporate Finance, 2010 213 Security Returns % Corporate Finance, 10 CAPM Market model: estimating β from data ∈it ine L ic ist ter ac r ha Slope = βi C βi = Cov ( Ri , RM ) σ 2 ( RM ) Return on market % Intercept = αi Rit = α i + βiRM + ∈it Characteristic line : E[Ri] = αi + βi E[RM] α i = E[ Ri ] − β i E[ RM ] MBF, Corporate Finance, 2010 214 Market model described as a one-factor model Corporate Finance, 11 APT The ith stock has the following return: Ri = α i + βi ( RM ) + εi α i = E[ Ri ] − β i E[ RM ] Ri = R i + βi ( RM − R M ) + εi where R M ≡ E[ RM ] Ri = R i + βi F + εi where F = RM − R M The one factor model of the ith stock : Ri − R i = βi F + εi MBF, Corporate Finance, 2010 215 Corporate Finance, 11 APT Relationship between the return on the common factor & excess return Excess return Ri − R i = βi F + εi If we assume that there is no unsystematic risk, then εi = 0. εi The return on the factor F MBF, Corporate Finance, 2010 216 Corporate Finance, 11 APT Relationship between the return on the common factor & excess return Excess return Ri − R i = βi F If we assume that there is no unsystematic risk, then εi = 0. The return on the factor F MBF, Corporate Finance, 2010 217 Corporate Finance, 10 CAPM Portfolio risk and number of securities σP In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not. Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk Portfolio risk Non diversifiable risk; Systematic Risk; Market Risk n = number of n Total risk = systematic risk + unsystematic risk different risky MBF, Corporate Finance, 2010 assets 218 Systematic and unsystematic risk Corporate Finance, 11 APT A systematic risk is any risk that affects a large number of assets, each to a greater or lesser degree. An unsystematic risk is a risk that specifically affects a single asset or small group of assets. Unsystematic risk can be diversified away. Examples of systematic risk include uncertainty about general economic conditions, such as GNP, interest rates or inflation. In APT, the factors F represent the systematic risk. On the other hand, announcements specific to a single company are examples of unsystematic risk. In APT, the ∈ represent the unsystematic risk. MBF, Corporate Finance, 2010 219 Corporate Finance, 11 APT Relationship between the return on the common factor & excess return Excess return β A = 1.5 β B = 1.0 Different securities will βC = 0.50 have different betas. The return on the factor F MBF, Corporate Finance, 2010 220 Factor Models: Announcements, Surprises, and Expected Returns Corporate Finance, 11 APT Any announcement can be broken down into two parts, the anticipated (or expected) part and the surprise (or innovation): Announcement = expected part + surprise. Remember the market-model factor: F = expected return on market - actual return on market The Arbitrage pricing theory APT allows the return of a security to depend on (several) other factors than the surprise factor of the marketportfolio. In general, it suggests a k-factor model, where each factor Fi (i = 1, …, k) represents the systematic risk in the variable i, i.e., the difference between the expected value of the variable and its realization. The betas measure the responsiveness to the factors. Ri = Ri + β1 F1 + β 2 F2 + ... + β k Fk + ∈ MBF, Corporate Finance, 2010 221 Systematic risk and betas Corporate Finance, 11 APT For example, suppose we have identified three systematic risks: inflation, GNP growth, and the dollar-euro spot exchange rate, S($,€). Our model is: Ri = R i + m + ε Ri = R i + β I FI + βGNP FGNP + βS FS + ε R i is the expected part of return m is the systematic risk β I is the inflation beta βGNP is the GNP beta βS is the spot exchange rate beta ε is the unsystematic risk MBF, Corporate Finance, 2010 222 Security return described by a k-factor model Corporate Finance, 11 APT In a multifactor version of the APT, the relationship between risk and return can be expressed as: (where βi stands for the security’s beta with respect to the ith factor, and Ri is the expected return on a security or portfolio whose beta with respect to the i-th factor is 1 and whose beta with respect to all other factors is 0). Ri = RF + ( R1 − RF ) β1 + ( R2 − RF ) β 2 + ... + ( Rk − RF ) β k MBF, Corporate Finance, 2010 223 Corporate Finance, 11 APT Fama-French Multifactor Model Rit − RFt = ( RMt − RFt ) β1 + ( SMBt ) β 2 + ( HMLt ) β 3 + ( MOM t ) β 4 + ε t SMB – small minus big (short 30% big and long 30% small) HML – high minus low (short low book-to-market 30%, long high) MOM – momentum (latest 12 month, short low return 30%, long high) Download factors: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ MBF, Corporate Finance, 2010 224 Chapter 11 – problems Corporate Finance, 11 APT 1: Describe the difference between systematic risk and unsystematic risk. 2: Consider the following statement: For the APT to be useful, the number of systematic risk factors must be small. Do you agree of disagree with this statement? Why? MBF, Corporate Finance, 2010 225 Corporate Finance - chapter 12 - Risk, Cost of Capital, and Capital Budgeting Corporate Finance, 12 Cost of capital Where Do We Stand? Earlier chapters on capital budgeting focused on the appropriate size and timing of cash flows. This chapter discusses the appropriate discount rate when cash flows are risky. MBF, Corporate Finance, 2010 227 Corporate Finance, 12 Cost of capital 12.1 The Cost of Equity Capital Firm with excess cash Pay cash dividend Shareholder invests in financial asset A firm with excess cash can either pay a dividend or make a capital investment Invest in project Shareholder’s Terminal Value Because stockholders can reinvest the dividend in risky financial assets, the expected return on a capital-budgeting project should be at least as great as the expected return on a financial asset of comparable risk. MBF, Corporate Finance, 2010 228 Corporate Finance, 12 Cost of capital The Cost of Equity Capital From the firm’s perspective, the expected return is the Cost of Equity Capital: R i = RF + βi ( R M − RF ) • To estimate a firm’s cost of equity capital, we need to know three things: 1. The risk-free rate, RF 2. The market risk premium, 3. The company beta, R M − RF Cov ( Ri , RM ) σ i , M βi = =2 Var ( RM ) σM MBF, Corporate Finance, 2010 229 Corporate Finance, 12 Cost of capital Example Suppose the stock of Stansfield Enterprises, a publisher of PowerPoint presentations, has a beta of 2.5. The firm is 100% equity financed. Assume a risk-free rate of 5% and a market risk premium of 10%. What is the appropriate discount rate for an expansion of this firm? R i = RF + βi ( R M − RF ) R i = 5% + 2.5 ×10% R i = 30% MBF, Corporate Finance, 2010 230 Corporate Finance, 12 Cost of capital Example Suppose Stansfield Enterprises is evaluating the following independent projects. Each costs $100 and lasts one year. Project Project β A 2.5 Project’s Estimated Cash Flows Next Year $150 B 2.5 $130 30% $0 C 2.5 $110 10% -$15.38 MBF, Corporate Finance, 2010 IRR NPV at 30% 50% $15.38 231 IRR Project Corporate Finance, 12 Cost of capital Using the SML Good A project 30% B 5% C SML Bad project Firm’s risk (beta) 2.5 An all-equity firm should accept projects whose IRRs exceed the cost of equity capital and reject projects whose IRRs fall short of the cost of capital. MBF, Corporate Finance, 2010 232 Corporate Finance, 12 Cost of capital 12.2 Estimation of Beta Market Portfolio - Portfolio of all assets in the economy. In practice, a broad stock market index, such as the S&P Composite, is used to represent the market. Beta - Sensitivity of a stock’s return to the return on the market portfolio. MBF, Corporate Finance, 2010 233 Determinants of Betas Beta of Equity Beta of Firm Nat ure of product or service offered by company: Other things remaining equal, the more discretionary the product or service, the higher the beta. Operat ing Leverage (Fixed Cost s as percent of t ot al cost s): Other things remaining equal the greater the proportion of the costs that are fixed, the higher the beta of the company. Implications 1. Cyclical companies should have higher betas than noncyclical companies. 2. Luxury goods firms should have higher betas than basic goods. 3. High priced goods/service firms should have higher betas than low prices goods/services firms. 4. Growth firms should have higher betas. Implications 1. Firms with high infrastructure needs and rigid cost structures shoudl have higher betas than firms with flexible cost structures. 2. Smaller firms should have higher betas than larger firms. 3. Young firms should have Financial Leverage: Other things remaining equal, the greater the proportion of capital that a firm raises from debt,the higher its equity beta will be Implciations Highly levered firms should have highe betas than firms with less debt. Corporate Finance, 12 Cost of capital Cost of capital in capital budgeting It is the company‘s cost of capital that is relevant in capital budgeting decisions, not the expected return on the common stock (cost of equity). The cost of capital is a weighted average of the returns that investors expect from the various debt and equity securities issued by the firm The cost of capital is related to the firm‘s asset beta, not the equity beta The asset beta is computed as a weighted average of the betas of the various securities When the firm changes its financial leverage, the risk and expected returns of the individual securities change. The asset beta and the company‘s cost of capital do not change. Corporate Finance, 12 Cost of capital Financial Leverage and Beta Operating leverage refers to the sensitivity to the firm’s fixed costs of production. Financial leverage is the sensitivity to a firm’s fixed costs of financing. The relationship between the betas of the firm’s debt, equity, and assets is given by: βAsset = Debt Equity × βDebt + × βEquity Debt + Equity Debt + Equity • Financial leverage always increases the equity beta relative to the asset beta. MBF, Corporate Finance, 2010 236 Corporate Finance, 12 Cost of capital Operating leverage Cash flow = revenue – fixed cost – variable cost PV(asset) = PV(revenue) – PV(fixed cost) – PV(variable cost) Those who receive the fixed costs are like debtholders in the project, they get a fixed payment. Those who receive the net cash flow from the assets are like shareholders, they get whatever is left over. β asset = β revenue PV (revenue) PV ( fixed cos t ) PV (var cos t ) − β fixed cos t − β var cos t PV (asset ) PV (asset ) PV (asset ) Beta of fixed cost is zero by definition; the receiver of the fixed costs holds a safe asset. The betas of revenue and of variable costs should be approximately the same; they respond to the same underlying variable, the rate of output. PV ( fixed cos t ) β asset = β revenue 1 + PV (asset ) Corporate Finance, 12 Cost of capital Example Consider Grand Sport, Inc., which is currently all-equity financed and has a beta of 0.90. The firm has decided to lever up to a capital structure of 1 part debt to 1 part equity. Since the firm will remain in the same industry, its asset beta should remain 0.90. However, assuming a zero beta for its debt, its equity beta would become twice as large: βAsset = 0.90 = 1 × βEquity 1+1 βEquity = 2 × 0.90 = 1.80 MBF, Corporate Finance, 2010 238 Project IRR Corporate Finance, 12 Cost of capital Capital budgeting & project risk The SML can tell us why: SML Incorrectly accepted negative NPV projects RF + βFIRM ( R M − RF ) Hurdle rate rf βFIRM Incorrectly rejected positive NPV projects Firm’s risk (beta) A firm that uses one discount rate for all projects may over time increase the risk of the firm while decreasing its value. MBF, Corporate Finance, 2010 239 Corporate Finance, 12 Cost of capital Example: capital budgeting & project risk Suppose the all-equity firm Conglomerate Company has a cost of capital, based on the CAPM, of 17%. The risk-free rate is 4%, the market risk premium is 10%, and the firm’s beta is 1.3. RS = 17% = 4% + 1.3 × 10% This is a breakdown of the company’s investment projects: 1/3 Automotive Retailer β = 2.0 1/3 Computer Hard Drive Manufacturer β = 1.3 1/3 Electric Utility β = 0.6 average β of assets = 1.3 When evaluating a new electrical generation investment, which cost of capital should be used? MBF, Corporate Finance, 2010 240 SML Project IRR Corporate Finance, 12 Cost of capital Example: capital budgeting & project risk 24% Investments in hard drives or auto retailing should have higher discount rates. 17% 10% Project’s risk (β) 0.6 1.3 2.0 R = 4% + 0.6×(14% – 4% ) = 10% 10% reflects the opportunity cost of capital on an investment in electrical generation, given the unique risk of the project. MBF, Corporate Finance, 2010 241 Corporate Finance, 12 Cost of capital The cost of capital with debt The Weighted Average Cost of Capital WACC is given by: RWACC = Equity Debt × REquity + × RDebt ×(1 – TC) Equity + Debt Equity + Debt S B RWACC = × RS + × RB ×(1 – TC) S+B S+B S = stock B = bond • Because interest expense is tax-deductible, we multiply the last term by (1 – TC). MBF, Corporate Finance, 2010 242 Example Estimating beta from the market data gives the RS or the RA for the unlevered firm. RB must be given from outstanding bonds. Given the R B, the beta of debt can be computed via the CAPM: R B = RF + betaB(risk premium). Example: RF= 6%; RM= 14%; betaS = .5; RB = 7%; B/A = .4 RS = R f + β S ( RM − RF ) = .10 = .06 + .5(14 − 6)% RB = R f + β B ( RM − RF ) = .07 = .06 + β B (.08) ⇔ β B = .125 β A = βB B S + β S = .4(.125) + .6(.5) = .35 A A RA = R f + β A ( RM − RF ) = .06 + .35(.08) = .088 alternatively RA = RB B S + RS = .4(.07) + .6(.10) = .088 A A Corporate Finance, 12 Cost of capital Example: International Paper First, we estimate the cost of equity and the cost of debt. We estimate an equity beta to estimate the cost of equity. We can often estimate the cost of debt by observing the YTM of the firm’s debt. Second, we determine the WACC by weighting these two costs appropriately. MBF, Corporate Finance, 2010 244 Corporate Finance, 12 Cost of capital Example: International Paper The industry average beta is 0.82, the risk free rate is 3%, and the market risk premium is 8.4%. Thus, the cost of equity capital is: RS = RF + βi × ( RM – RF) = 3% + 0.82×8.4% = 9.89% MBF, Corporate Finance, 2010 245 Corporate Finance, 12 Cost of capital Example: International Paper The yield on the company’s debt is 8%, and the firm has a 37% marginal tax rate. The debt to asset value ratio is 32% S B RWACC = × RS + × RB ×(1 – TC) S+B S+B = 0.68 × 9.89% + 0.32 × 8% × (1 – 0.37) = 8.34% 8.34% is International’s cost of capital. It should be used to discount any project where one believes that the project’s risk is equal to the risk of the firm as a whole and the project has the same leverage as the firm as a whole. MBF, Corporate Finance, 2010 246 Corporate Finance, 12 Cost of capital Example : if we do not know the yield of the debt, we estimate it by computing the current average yield of debt. Assume the yield on International’s debt is given in the following table. Coupon rate Maturity 3.25% 2008 7.00 % of total YTM $ 72 m 0.05 5.02% 2012 187 0.13 5.36 0.72 6.30 2018 143 0.10 6.20 0.64 7.25 2024 497 0.36 6.45 2.30 7.625 2024 200 0.14 6.41 0.92 7.60 2027 297 0.21 6.41 1.36 $1,396 1.00 Total Book value (face value) Book value weights 0.26% = 5% × 5.02% 6.19% S B RWACC = × RS + × RB ×(1 – TC) S+B S+B = 0.68 × 9.89% + 0.32 × 6.19% × (1 – 0.37) = 7.97% MBF, Corporate Finance, 2010 247 Corporate Finance, 12 Cost of capital What the Corporation can do to decrease its costs of equity Liquid stocks are less volatile The corporation has an incentive to lower trading costs since this would result in a lower cost of capital. A stock split would increase the liquidity of the shares. A stock split would also reduce the adverse selection costs, thereby lowering bid-ask spreads. This idea is a new one, and empirical evidence is not yet available. MBF, Corporate Finance, 2010 248 The Cost of Equity: A Recap Preferably, a bottom-up beta, based upon other firms in the business, and firm’s own financial leverage Cost of Equity = Riskfree Rate Has to be in the same currency as cash flows, and defined in same terms (real or nominal) as the cash flows + Beta * (Risk Premium) Historical Premium 1. Mature Equity Market Premium: Average premium earned by stocks over T.Bonds in U.S. 2. Country risk premium = Country Default Spread* ( σEquity/σCountry bond) or Implied Premium Based on how equity market is priced today and a simple valuation model Appendix: Bottom-up Betas Step 1: Find the business or businesses that your firm operates in. Possible Refinements Step 2: Find publicly traded firms in each of these businesses and obtain their regression betas. Compute the simple average across these regression betas to arrive at an average beta for these publicly traded firms. Unlever this average beta using the average debt to equity ratio across the publicly traded firms in the sample. Unlevered beta for business = Average beta across publicly traded firms/ (1 + (1- t) (Average D/E ratio across firms)) Step 3: Estimate how much value your firm derives from each of the different businesses it is in. Step 4: Compute a weighted average of the unlevered betas of the different businesses (from step 2) using the weights from step 3. Bottom-up Unlevered beta for your firm = Weighted average of the unlevered betas of the individual business Step 5: Compute a levered beta (equity beta) for your firm, using the market debt to equity ratio for your firm. Levered bottom-up beta = Unlevered beta (1+ (1-t) (Debt/Equity)) If you can, adjust this beta for differences between your firm and the comparable firms on operating leverage and product characteristics. While revenues or operating income are often used as weights, it is better to try to estimate the value of each business. If you expect the business mix of your firm to change over time, you can change the weights on a year-to-year basis. If you expect your debt to equity ratio to change over time, the levered beta will change over time. Bottom-up Beta Example: Firm in Multiple Businesses Disney in 2003 Start with the unlevered betas for the businesses usiness edia Networks arks and Resorts tudio Entertainment onsumer Products Comparable firms Radia and TV broadcasting companies Theme park & Entertainment firms Movie companies Toy and apparel retailers; Entertainment software Number of firms 24 9 11 77 Average levered beta 1.23 1.63 1.35 1.14 Median D/E Unlevered beta Cash/Firm Value Corrected for cash 20.45% 1.08 0.75% 1.0932 120.76% 0.91 2.77% 0.9364 27.96% 1.14 14.08% 1.3310 9.18% 1.07 12.08% 1.2186 Estimate the unlevered beta for Disney’s businesses Business Media Networks Parks and Resorts Studio Entertainment Consumer Products Disney Revenues in 2002 $9,733 $6,465 $6,691 $2,440 $25,329 EV/Sales 3.41 2.37 2.63 1.63 Estimated Value $33,162.67 $15,334.08 $17,618.07 $3,970.60 $70,085.42 Estimate a levered beta for Disney Market debt to equity ratio = 37.46% Marginal tax rate = 37.60% Levered beta = 1.1258 ( 1 + (1- .376) (.3746)) = 1.39 Firm Value Proportion 47.32% 21.88% 25.14% 5.67% 100.00% Unlevered beta 1.0932 0.9364 1.3310 1.2186 1.1258 Corporate Finance, 12 Cost of capital Chapter 12 - problem An all equity firm is considering the following projects: Project Beta Expected Return W 0.60 11% X 0.90 13% Y 1.20 14% Z 1.70 16% The T-Bill rate is 5%, and the expected return on the market is 12%. a. Which projects have a higher expected return than the firm’s 12% cost of capital? b. Which projects should be accepted? c. Which projects would be incorrectly accepted or rejected if the MBF, Corporate Finance, 2010 firm’s overall cost of capital were used as a hurdle rate? 252 Corporate Finance - chapter 13 - Corporate Financing Decisions & Efficient Capital Markets Corporate Finance, 13 Efficient markets Information sets and the efficient market hypothesis Strong EMH All information relevant to a stock Semi-strong EMH Information set of publicly available information Weak EMH Information set of past prices EMH : Security prices reflect all relevant information in the market MBF, Corporate Finance, 2010 254 Corporate Finance, 13 Efficient markets Empirical Challenges Limits to Arbitrage “Markets can stay irrational longer than you can stay insolvent.” John Maynard Keynes Earnings Surprises Stock prices adjust slowly to earnings announcements. Behavioralists claim that investors exhibit conservatism. Size Small cap stocks seem to outperform large cap stocks. Value versus Growth High book value-to-stock price stocks and/or high E/P stocks outperform growth stocks. Crashes On October 19, 1987, the stock market dropped between 20 and 25 percent on a Monday following a weekend during which little surprising news was released. A drop of this magnitude for no apparent reason is inconsistent with market efficiency. Bubbles Consider the tech stock bubble of the late 1990s. MBF, Corporate Finance, 2010 255 Corporate Finance, 13 Efficient markets Winner-Loser Effect Stocks whose returns have been worst over a 3-year period have outperformed the market over the subsequent 5 years by about 30%. Stocks whose returns have been best over a 3-year period have underperformed the market over the subsequent 5 years by about 10%. On a cumulative basis, losers outperform winners by about 40% over 5 years. Source: Shefrin, H., 2007, Behavioral Corporate Finance MBF, Corporate Finance, 2010 256 Corporate Finance, 13 Efficient markets Momentum A portfolio formed by holding the winners from the past 6 months, and shorting the losers from the past 6 months earned more than 10% per year. Pattern is pronounced among small cap stocks. Source: Shefrin, H., 2007, Behavioral Corporate Finance MBF, Corporate Finance, 2010 257 Experiment – the beauty contest Each student is invited to choose a number between 0 and 100. The winner is the one whose number is most closely to 2 / 3 of the average of all chosen numbers. If, for example, there are 5 listeners and the numbers 10, 20, 30, 40, 50, so the average number is 30. Therefore, the student who chose 20 (= 30×2/3) would win. Each player has an incentive to undercut the average numbers of the other players, so for the rational solution to the game each listener chooses the number zero. For most runs of the games, however, a number in the vicinity of 17 wins this game. It wins the best estimate of the magnitude of the errors of the other players. MBF, Corporate Finance, 2010 258 Corporate Finance - chapter 15 - Capital Structure Basic Concepts Corporate Finance, 15 Capital structure Capital Structure and the Pie The value of a firm is defined to be the sum of the value of the firm’s debt and the firm’s equity. V=B+S • If the goal of the firm’s management is to make the firm as valuable as possible, then the firm should pick the debt-equity ratio that makes the pie as big as possible. • What is the ratio of debt-to-equity that maximizes the shareholder’s value? MBF, Corporate Finance, 2010 SB Value of the Firm 260 Corporate Finance, 15 Capital structure Financial Leverage, EPS, and ROE Consider an all-equity firm that is contemplating going into debt. (Maybe some of the original shareholders want to cash out.) Assets Debt Equity Debt/Equity ratio Interest rate Shares outstanding Share price Current $20,000 $0 $20,000 0.00 n/a 400 $50 MBF, Corporate Finance, 2010 Proposed $20,000 $8,000 $12,000 2/3 8% 240 $50 261 Corporate Finance, 15 Capital structure EPS and ROE Under Current Structure Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest 0 0 0 Net income $1,000 $2,000 $3,000 EPS $2.50 $5.00 $7.50 ROA 5% 10% 15% ROE 5% 10% 15% Current Shares Outstanding = 400 shares, price/share = $50 MBF, Corporate Finance, 2010 262 Corporate Finance, 15 Capital structure EPS and ROE Under Proposed Structure Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest (640) (640) (640) Net income $360 $1,360 $2,360 EPS $1.50 $5.67 $9.83 ROA 1.8% 6.8% 11.8% ROE 3.0% 11.3% 19.7% Proposed Shares Outstanding = 240 shares, price/share = $50 Note: Leverage increases the risk of the firm MBF, Corporate Finance, 2010 263 12.00 Debt 10.00 8.00 EPS Corporate Finance, 15 Capital structure Financial Leverage and EPS 6.00 4.00 No Debt Advantage to debt Break-even point 2.00 0.00 1,000 (2.00) Disadvantage to debt 2,000 MBF, Corporate Finance, 2010 3,000 EBIT in dollars, no taxes 264 Corporate Finance, 15 Capital structure The WACC of the (un-)levered firm RWACC = B S × RB + × RS B+S B+S B/(B+S) = 800/2000 RB = 8% E(RS) = 11.33% (each state equiprobable) 2 3 RWACC = × 8% + ×11. 3 % = 10% 5 5 RWACC = RU = 10% Note: RWACC does not change with leverage. Without taxes RWACC = RU = return of all-equity (unlevered) firm. MBF, Corporate Finance, 2010 265 Corporate Finance, 15 Capital structure Assumptions of the M&M Model Homogeneous Expectations Homogeneous Business Risk Classes Perpetual Cash Flows Perfect Capital Markets: Perfect competition Firms and investors can borrow/lend at the same rate Equal access to all relevant information No transaction costs No taxes MBF, Corporate Finance, 2010 266 Corporate Finance, 15 Capital structure Homemade Leverage: An Example (reproduce cash flow with personal debt) We are buying 40 shares of a $50 stock, 40 × 50 = 2000, using $800 in margin. We get the same ROE as if we bought into a 2/3 levered firm. Recession Expected Expansion EPS of Unlevered Firm $2.50 $5.00 $7.50 Earnings for 40 shares $100 $200 $300 Less interest on $800 (8%) ($64) ($64) ($64) Net Profits $36 $136 $236 ROE (Net Profits / $1,200) 3.0% 11.3% 19.7% Our personal debt-equity ratio is: B $800 2 = = 3 S $1,200 MBF, Corporate Finance, 2010 267 Corporate Finance, 15 Capital structure Homemade (Un)Leverage: An Example Recession Expected Expansion EPS of Levered Firm $1.50 $5.67 $9.83 Earnings for 24 shares $36 $136 $236 Plus interest on $800 (8%) $64 $64 $64 Net Profits $100 $200 $300 ROE (Net Profits / $2,000) 5% 10% 15% Buying (by spending $2000) 24 shares ($1200) of the levered firm along with some of the firm’s debt ($800) gets us to the ROE of the unlevered firm. MBF, Corporate Finance, 2010 268 Corporate Finance, 15 Capital structure Value of the firm :MM Proposition I (no taxes) Proposition I The value of the levered firm is the same as the value of the unlevered firm; VL = VU VL is the present value of levered firm VU is the present value of unlevered firm We can create a levered or unlevered position by adjusting the trading in our own account. By homemade leverage, individuals can either replicate or undo the effects of corporate leverage. MBF, Corporate Finance, 2010 269 Corporate Finance, 15 Capital structure Expected return and leverage :MM Proposition II (no taxes) Proposition II The expected return on levered equity is Rs = RU + (B / SL) (RU - RB) RB is the interest rate (cost of debt) Rs is the return on (levered) equity (cost of equity) RU is the return on unlevered equity (cost of capital) B is the value of debt SL is the value of levered equity The required cost of equity rises with leverage because the risk to equity increases with leverage. MBF, Corporate Finance, 2010 270 Corporate Finance, 15 Capital structure MM Proposition II (No Taxes), Proof B S RWACC = × RB + × RS B+S B+S B S × RB + × RS = RU B+S B+S RWACC = RU B+S × S B+S B B+S S B+S × × RB + × × RS = RU S B+S S B+S S B B+S × RB + RS = RU S S B B × RB + RS = RU + RU S S RS = RU + MBF, Corporate Finance, 2010 B ( RU − RB ) S 271 Cost of capital: R (%) Corporate Finance, 15 Capital structure MM Proposition II (No Taxes) RU RS = RU + RWACC = B × ( RU − RB ) SL B S × RB + × RS B+S B+S RB RB Debt-to-equity Ratio B S MBF, Corporate Finance, 2010 272 Corporate Finance, 15 Capital structure Corporate taxes : Basic insight All-equity firm S Levered firm Tax S Tax B The levered firm pays less in taxes than does the all-equity firm. The tax advantage of the levered firm (disadvantage of the unlevered firm) is the tax shield. This is how slicing the pie differently can make the aftertax pie “larger.”The total cash flow to investors (bondholders and shareholders) increases, as the government takes a smaller slice of the pie! MBF, Corporate Finance, 2010 273 Corporate Finance, 15 Capital structure Example : Present value of the tax shield for Water Products Company tC = 35%, B = $4,000,000, RB = 10% EBIT Interest (RB B) EBT Taxes (tC = .35) Earnings after tax All equity $1,000,000 0 1,000,000 (350,000) 650,000 Levered $1,000,000 (400,000) 600,000 (210,000) 390,000 Total cashflow to both $ 650,000 $ 790,000 stockholders and bondholders Tax shield from debt is 140,000 = 790,000 - 650,000 = 350,000 – 210,000 = RB × B × tC = EBIT × tC – (EBIT – RB × B) tC Assuming perpetuity, the present value of the tax shield is tC B = MBF, Corporate Finance, 2010 RB × B × t C RB 274 Corporate Finance, 15 Capital structure Value of the levered firm : MM Proposition I (with taxes) Proposition I (with corporate taxes) EBIT × (1 − tC ) tC RB B VL = + = VU + tC B RU RB VL is the present value of the levered firm VU is the present value of the unlevered firm EBIT × (1-tC) is the firm cash flow after corporate tax tC is the corporate tax rate RU is the required return to an all-equity firm (aftertax cost of capital). RB is the interest rate (cost of debt) Firm value increases with leverage due to the tax shield MBF, Corporate Finance, 2010 275 Corporate Finance, 15 Capital structure MM Proposition I (with taxes); Proof • The total cash flow to bondholders and stockholders of the levered firm is CF = ( EBIT − RB B) × (1 − tC ) + RB B = EBIT × (1 − tC ) + RB B − RB B × (1 − tC ) • Assuming perpetuity of the cash flow, the present value of the levered firm is EBIT × (1 − tC ) RB B − RB B × (1 − tC ) VL = + RU RB • where RU is the cost of capital to an unlevered firm and R B the interest on the debt. • Simplifying gives VL = VU + tC B MBF, Corporate Finance, 2010 276 Corporate Finance, 15 Capital structure Expected return and leverage (with taxes) MM Proposition II (with taxes) Proposition II (with Corporate Taxes) RS = RU + (B/S)×(1-tC)×(RU - RB) RB is the interest rate (cost of debt) RS is the return on equity (cost of equity) RU is the return on unlevered equity (cost of capital) B is the value of debt S is the value of levered equity Some of the increase in equity risk and return is offset by the interest tax shield MBF, Corporate Finance, 2010 277 Corporate Finance, 15 Capital structure MM Proposition II (with taxes); Proof E[CFL] = VURU + tCBRB Start from M&M Proposition I : VL = VU + tC B Since VL = S + B E[CFL] = SRS + BRB ⇒ S + B = VU + tC B ⇔ VU = S + B (1 − tC ) The expected cash flows to s/h and b/h must equal: SRS + BRB = E [ CFL ] = VU RU + t C BRB = [ S + B (1 − tC )]RU + tC RB B B B B RS + RB = [1 + (1 − tC )]RU + tC RB S S S × 1 S B RS = RU + × (1 − tC ) × ( RU − RB ) S MBF, Corporate Finance, 2010 278 Cost of capital: R(%) Corporate Finance, 15 Capital structure The Effect of Financial Leverage RS = RU + B × ( RU − RB ) SL RS = RU + B × (1 − tC ) × ( RU − RB ) SL RU RWACC = B SL × RB × (1 − tC ) + × RS B+SL B + SL RB MBF, Corporate Finance, 2010 Debt-to-equity ratio (B/S) 279 All Equity Levered Corporate Finance, 15 Capital structure Another example: total cash flow to investors EBIT Interest EBT Taxes (tc = 35%) Total Cash Flow to S/H Recession $1,000 0 $1,000 ($350) $650 Expected $2,000 0 $2,000 ($700) $1,300 Expansion $3,000 0 $3,000 ($1,050) $1,950 EBIT Interest ($8000 @ 8% ) EBT Taxes (tc = 35%) Recession $1,000 (640) $360 ($126) Expected $2,000 (640) $1,360 ($476) Expansion $3,000 (640) $2,360 ($826) Total Cash Flow to S/H -- to both S/H & B/H: EBIT(1-tC)+tCRBB $234 $874 $650+$224 $884 $1,524 $1,300+$224 $1,534 $2,174 $1,950+$224 MBF, Corporate Finance, 2010 tax shield 280 Corporate Finance, 15 Capital structure Chapter 15 – problems Beginning with the cost of capital equation RWACC, show that the cost of equity for a levered firm can be written as follows: RS = RU + (B/S) (RU – RB) MBF, Corporate Finance, 2010 281 Corporate Finance - chapter 16 - Capital Structure Limits to the Use of Debt Corporate Finance, 16 Limits to the use of debt Costs of Financial Distress Bankruptcy risk versus bankruptcy cost The possibility of bankruptcy has a negative effect on the value of the firm. However, it is not the risk of bankruptcy itself that lowers value. Rather, it is the costs associated with bankruptcy. The stockholders bear these costs. MBF, Corporate Finance, 2010 283 Corporate Finance, 16 Limits to the use of debt Example: The Knight corp. plans a one year project. CF is forecasted at either $100 and $50 with equal probability. Previously issued debt requires payoment of $49 of interest and principal. The Day corporation has equal cash flow prospects but has a $60 of debt repayment. Knight corporation boom recession prob. : ½ ½ Cash flow $100 $50 Debt repayment $49 $49 Distribution to S/H $51 $1 Day corporation boom recession ½ ½ $100 $50 $60 $50 $40 $0 . . Compute value of equity and stock: $51 / 2 + $1 / 2 S K = $23.64 = 1.10 BK = $44.54 = VK = $68.18 $49 / 2 + $49 / 2 1.10 S D = $18.18 = BD = $50 = $40 / 2 + $0 / 2 1.10 $60 / 2 + $50 / 2 1.10 VD = $68.18 Assuming an interest rate of 10% and risk neutrality, the value of each firms is equal to $68.18. The b/h value the debt only at 50; the promised return is 20% = 60/50 – 1 (junk bond). MBF, Corporate Finance, 2010 284 Corporate Finance, 16 Limits to the use of debt Example: A more realistic cash flow scenario for Day corporation would be as follows: Day corporation boom recession prob. : ½ ½. Cash flow $100 $50 Debt repayment $60 $35 . Distribution to S/H $40 $0 S D = $18.18 = BD = $43.18 = $50 / 2 + $0 / 2 1.10 $60 / 2 + $35 / 2 1.10 VD = $61.36 Why is it more realistic that the bondholders receive only $35 in the recession? We assume that bankruptcy costs in the recession total $15. If cash flow is only 50, b/h will sue the company and the case may go to a bankruptcy court. Court and lawyer fees are paid before the b/h get paid. The possibility of bankruptcy has a negative affect on the value of the firm. However, it is not the risk of bankruptcy itself that lowers value. Rather it is the cost associated with bankruptcy that lowers value. MBF, Corporate Finance, 2010 285 Corporate Finance, 16 Limits to the use of debt Description of Financial Distress Costs Direct Costs Legal and administrative costs Indirect Costs Impaired ability to conduct business (e.g., lost sales) Agency Costs Selfish Strategy 1: Incentive to take large risks Selfish Strategy 2: Incentive toward underinvestment Selfish Strategy 3: Milking the property MBF, Corporate Finance, 2010 286 Corporate Finance, 16 Limits to the use of debt Agency costs - Selfish Strategy 1: Take Risks The firm has $200 cash, which is the principal to be paid out to the b/h in one year. It is considering to invest the money in a project. 1) the Gamble Win Big Lose Big Probability 10% 90% Payoff $1,000 $0 Cost of investment is $200; required return is 50% Expected CF from the gamble = $1000 × 0.10 + $0 = $100 $100 NPV = –$200 + (1.50) NPV = –$133 MBF, Corporate Finance, 2010 287 Corporate Finance, 16 Limits to the use of debt Selfish Strategy 1: Take Risks Expected CF from the Gamble To Bondholders = $300 × 0.10 + $0 = $30 To Stockholders = ($1000 – $300) × 0.10 + $0 = $70 PV of Bonds Without the Gamble = $200 PV of Stocks Without the Gamble = $0 • PV of Bonds With the Gamble: • PV of Stocks With the Gamble: MBF, Corporate Finance, 2010 $30 $20 = (1.50) $70 $47 = (1.50) 288 Corporate Finance, 16 Limits to the use of debt Selfish Strategy 2: Underinvestment Consider a government-sponsored project that guarantees $350 in one period. Cost of investment is $300 (the firm only has $200 now), so the stockholders will have to supply an additional $100 to finance the project. Required return is 10%. $350 NPV = –$300 + (1.10) NPV = $18.18 Should the firm accept or reject? MBF, Corporate Finance, 2010 289 Corporate Finance, 16 Limits to the use of debt Selfish Strategy 2: Underinvestment Expected CF from the government sponsored project: To Bondholder = $300 To Stockholder = ($350 – $300) = $50 PV of Bonds Without the Project = $200 PV of Stocks Without the Project = $0 PV of Bonds With the Project: $300 $272.73 = (1.10) PV of Stocks With the Project: $50 – $100 – $54.55 = (1.10) MBF, Corporate Finance, 2010 290 Corporate Finance, 16 Limits to the use of debt Selfish Strategy 3: Milking the Property Liquidating dividends Suppose our firm paid out a $200 dividend to the shareholders. This leaves the firm insolvent, with nothing for the bondholders. Such tactics often violate bond indentures. Increase perquisites to shareholders and/or management MBF, Corporate Finance, 2010 291 Corporate Finance, 16 Limits to the use of debt Can costs of bankruptcy be reduced? Protective loan covenants Limitations on the amount of dividends — No merger — No issue of debt (incl. restrictive and protective covenants) + Working capital minimum level + Periodic financial statements to the lender Debt Consolidation: Determine proper arrangement of b/h and s/h. Aligned interests, when b/h become s/h too (Japan). — MBF, Corporate Finance, 2010 292 Corporate Finance, 16 Limits to the use of debt The static trade-off theory: Tax Effects and Financial Distress There is a trade-off between the tax advantage of debt and the costs of financial distress. It is difficult to express this with a precise and rigorous formula. MBF, Corporate Finance, 2010 293 Corporate Finance, 16 Limits to the use of debt Tax Effects and Financial Distress : The static trade-off theory Value of firm (V) Value of firm under MM with corporate taxes and debt Present value of tax shield on debt VL = VU + tCB Maximum firm value Present value of financial distress costs V = Actual value of firm VU = Value of firm with no debt RU RWACC According to the static theory, the RWACC falls initially because of the tax advantage of debt. Beyond point B* it rises due to financial distress costs. 0 B* MBF, Corporate Finance, 2010 Optimal amount of debt Debt (B) 294 Corporate Finance, 16 Limits to the use of debt The Pie Model Revisited Taxes and bankruptcy costs can be viewed as just another claim on the cash flows of the firm. Let G and L stand for payments to the government (tax) and bankruptcy lawyers, respectively. VT = S + B + G + L S B VT = VM + VN = marketable + nonmarketable claims L G The essence of the MM intuition is that V T depends on the cash flow of the firm; capital structure just slices the pie. MBF, Corporate Finance, 2010 295 Corporate Finance, 16 Limits to the use of debt Signaling The firm’s capital structure is optimized where the marginal yield to debt equals the marginal cost. Investors view debt as a signal of firm value. Firms with low anticipated profits will take on a low level of debt. Firms with high anticipated profits will take on a high level of debt. A manager that takes on more debt than is optimal in order to fool investors will pay the cost in the long run. MBF, Corporate Finance, 2010 296 Corporate Finance, 16 Limits to the use of debt Agency Cost of Equity An individual will work harder for a firm if he is one of the owners than if he is just hired. While managers may have motive to partake in perquisites, they also need opportunity. Free cash flow provides this opportunity. The free cash flow hypothesis says that an increase in dividends should benefit the stockholders by reducing the ability of managers to pursue wasteful activities. The free cash flow hypothesis also argues that an increase in debt will reduce the ability of managers to pursue wasteful activities even more effectively than dividend increases. MBF, Corporate Finance, 2010 297 Corporate Finance, 16 Limits to the use of debt The Pecking-Order Theory This theory states that firms prefer to issue debt rather than equity if internal financing is insufficient. Rule 1: Use internal financing first. Rule 2: Issue debt next, new equity last. The pecking-order theory is at odds with the tradeoff theory: There is no target D/E ratio. Profitable firms use less debt. (financial slack:) Firms accumulate cash to finance profitable projects in the future. MBF, Corporate Finance, 2010 298 Corporate Finance, 16 Limits to the use of debt Growth and the Debt-Equity Ratio Theory Growth implies significant equity financing, even in a world with low bankruptcy costs. Thus, high-growth firms will have lower debt ratios than low- growth firms. MBF, Corporate Finance, 2010 299 Corporate Finance, 16 Limits to the use of debt Example: no growth Date 1 EBIT Interest Taxable income 2 3 4 $100 $100 $100 $100 ($100) ($100) ($100) ($100) 0 0 0 0 Firm has issued $1000 of debt at 10%. All EBIT are paid out as interest, and pays no taxes. Equity is worthless because s/h receive no cash-flow. Debt/value = 100% (=1000/1000) is optimal as no taxes are paid and no bankruptcy risk exists. MBF, Corporate Finance, 2010 300 Corporate Finance, 16 Limits to the use of debt Example: growth Date 0 1 2 3 $1000 $1050 $1102.5 $1157.63 New debt issued $50 $52.5 $55.13 EBIT $100 $105 $110.25 $115.76 ($100) ($105) ($110.25) ($115.76) 0 0 0 0 Debt Interest Taxable income 0 4 Assume the firm is growing at 5%/year. To eliminate taxes, the firm issues sufficient debt, such that interest = EBIT. VFirm = 100/(0.1-0.05) = 2000, VS = VFirm–VB = 1000 => B/S = 1. With growth, there is equity as well as debt. The new debt issued each year can be paid as a dividend to the s/h, thus VS = $50 /(0.10-0.05). MBF, Corporate Finance, 2010 301 Corporate Finance, 16 Limits to the use of debt How Firms Establish Capital Structure Changes in financial leverage affect firm value. Stock price increases with leverage and vice-versa; this is consistent with M&M with taxes. Another interpretation is that firms signal good news when they lever up. There are differences in capital structure across industries. Most corporations have low Debt-Asset ratios, ≤ 50%. There is evidence that firms behave as if they had a target Debt- Equity ratio. MBF, Corporate Finance, 2010 302 Corporate Finance, 16 Limits to the use of debt Factors in Target D/E Ratio Taxes Since interest is tax deductible, highly profitable firms should use more debt (i.e., greater tax benefit). Uncertainty of Operating Income Even without debt, firms with uncertain operating income have a high probability of experiencing financial distress. Pecking Order and Financial Slack Theory stating that firms prefer to issue debt rather than equity if internal financing is insufficient. MBF, Corporate Finance, 2010 303 Corporate Finance, 16 Limits to the use of debt Traditional Pecking Order Empirical Evidence When large firms engage in substantial investments, they tend to rely on debt financing. However, they do not appear to exhaust their cash reserves before undertaking debt. Therefore, managers do not behave in strict accordance with pecking order theory. FEI survey finds little evidence to suggest that executives believe that the source of the undervaluation is perceived information asymmetry. Source: Shefrin, H., 2007, Behavioral Corporate Finance MBF, Corporate Finance, 2010 304 Appendix: Estimating the Cost of Debt The cost of debt is the rate at which you can borrow at currently, It will reflect not only your default risk but also the level of interest rates in the market. The two most widely used approaches to estimating cost of debt are: Looking up the yield to maturity on a straight bond outstanding from the firm. The limitation of this approach is that very few firms have long term straight bonds that are liquid and widely traded Looking up the rating for the firm and estimating a default spread based upon the rating. While this approach is more robust, different bonds from the same firm can have different ratings. You have to use a median rating for the firm When in trouble (either because you have no ratings or multiple ratings for a firm), estimate a synthetic rating for your firm and the cost of debt based upon that rating. Appendix: Cost of Capital Cost of borrowing should be based upon (1) synthetic or actual bond rating (2) default spread Cost of Borrowing = Riskfree rate + Default spread Cost of Capital = Cost of Equity (Equity/(Debt + Equity)) Cost of equity based upon bottom-up beta + Cost of Borrowing (1-t) Marginal tax rate, reflecting tax benefits of debt (Debt/(Debt + Equity)) Weights should be market value weights Corporate Finance - chapter 17 - Valuation and Capital Budgeting for the Levered Firm Corporate Finance, 17 Levered Cap Budgeting Adjusted Present Value Approach APV = NPV + NPVF The value of a project to the firm can be thought of as the value of the project to an unlevered firm (NPV) plus the present value of the financing side effects (NPVF). There are four side effects of financing: The Tax Subsidy to Debt The Costs of Issuing New Securities The Costs of Financial Distress Subsidies to Debt Financing MBF, Corporate Finance, 2010 308 Corporate Finance, 17 Levered Cap Budgeting Example Consider a project of the P.B. Singer Company with the following characteristics : Investment Year 0 Perpetuity starting in year 1 Cash inflow $500,000 Cash costs (360,000) EBIT 140,000 Corporate tax (tC = 34%) (47,600) Unlevered CF (UCF) Initial investment 92,400 (475,000) MBF, Corporate Finance, 2010 309 Corporate Finance, 17 Levered Cap Budgeting APV Example Assume the cost of capital to an all-equity firm is RU = 20%. The NPV of the unlevered cash flow is as follows. 92,400 NPV = −13,000 = −475,000 + 0 .2 The project would be rejected by an all-equity firm: NPV < 0. MBF, Corporate Finance, 2010 310 Corporate Finance, 17 Levered Cap Budgeting APV Example Now, imagine that the firm finances the project with $126,229.50 in debt and $348,770.50 in equity, the sum of which adds up to $475T. • The net present value of the project under leverage is: APV = NPV + NPV debt tax shield = NPV + tC × B APV = −$13,000 + 0.34 × 126,229.50 APV = −$13,000 + $42,918.03 = $29,918 • So, Singer should accept the project with debt. Note that 126,229.50 × 4 = $504,918 = 29,918 + 475,000 which is the present value of the project after the initial investment has been made . Hence, the debt-value ratio is 0.25. MBF, Corporate Finance, 2010 311 Corporate Finance, 17 Levered Cap Budgeting Flow to Equity: FTE-Approach Discount the cash flow from the project to the equity holders of the levered firm at the cost of levered equity capital, Rs: There are three steps in the FTE Approach: Step One: Calculate the levered cash flow (LCFs) Step Two: Calculate Rs Step Three: Value the levered cash flow at Rs i.e., LCF / Rs MBF, Corporate Finance, 2010 312 Corporate Finance, 17 Levered Cap Budgeting APV - Example continued Step One (FTE): Levered Cash Flows Consider a project of the P.B. Singer Company with the following characteristics : Investment Year 0 Perpetuity starting in year 1 Cash inflow $500,000 Cash costs (360,000) Interest (10% × 126,229.50) (12,622.95) EBT 127,377.05 Corporate tax (tC = 34%) (43,308.20) Levered CF (LCF) Initial investment 84,068.85 (475,000) 126,229.50 debt 348,770.50 equity MBF, Corporate Finance, 2010 313 Corporate Finance, 17 Levered Cap Budgeting Step one and two (FTE) : Calculating Rs 1. Alternatively, compute LCF from UCF : (EBIT - B × RB) × (1 – tC) = EBIT (1 – tC) – B × RB × (1 – tC) = LCF = UCF LCF = UCF - B × RB × (1 – tC) = $92,400 - $8,331.15 = $84,064.85 2. Compute the equity cost of capital: B RS = RU + (1 − tC )( RU − RB ) S .25 RS = .222 = .2 + (1 − .34)(.2 − .1) .75 MBF, Corporate Finance, 2010 314 Corporate Finance, 17 Levered Cap Budgeting Steps three (FTE): Valuation 3) The present value of the project’s levered cash flows LCF is: LCF 84,068.85 = = 378,688.50 RS .222 NPV = $378,688.50 - $348,770.50 = $29,918 MBF, Corporate Finance, 2010 315 Corporate Finance, 17 Levered Cap Budgeting WACC approach To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital. RWACC S B = RS + RB (1 − tC ) S+B S+B RWACC = 0.75 × 0.222 + 0.25 × 0.1 × (1 − 0.34) = 0.183 Value of the project = UCF − initial investment RWACC = NPVWACC 92400 − 475,000 = 29,918 .183 MBF, Corporate Finance, 2010 316 Corporate Finance, 17 Levered Cap Budgeting A Comparison of the APV, FTE, and WACC Approaches All three approaches attempt the same task: valuation in the presence of debt financing. In practice they are hardly equal, because cash flows are not without error determined in advance. (To make them equal the debt-equity ratio must be rebalanced each time). Which approach is best? Use APV when the level of debt is constant Use WACC and FTE when the debt ratio is constant WACC is by far the most common FTE is a reasonable choice for a highly levered firm MBF, Corporate Finance, 2010 317 Corporate Finance, 17 Levered Cap Budgeting Capital Budgeting When the Discount Rate Must Be Estimated A scale-enhancing project is one where the project is similar to those of the existing firm. In the real world, executives would make the assumption that the business risk of the non-scale-enhancing project would be about equal to the business risk of firms already in the business. No exact formula exists for this. Some executives might select a discount rate slightly higher on the assumption that the new project is somewhat riskier since it is a new entrant. MBF, Corporate Finance, 2010 318 Corporate Finance, 17 Levered Cap Budgeting Beta and Leverage: No Corporate Taxes In a world without corporate taxes, and with riskless corporate debt (βDebt = 0), it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is: β Asset = • S × β Equity B+S In a world without corporate taxes, and with risky corporate debt, it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is: β Asset B S = × β Debt + × β Equity B+S B+S MBF, Corporate Finance, 2010 319 Corporate Finance, 17 Levered Cap Budgeting Beta and Leverage: With Corporate Taxes In a world with corporate taxes, and riskless debt, it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is: S × β Equity = β Unlevered firm S + (1 - t C ) × B (1 - t C ) × B ⇔ β Equity = β Unlevered firm × 1 + S >1 ⇒ β Equity > β Unlevered firm MBF, Corporate Finance, 2010 320 Corporate Finance, 17 Levered Cap Budgeting Beta and Leverage: With Corporate Taxes If the beta of the debt is non-zero, then: B βS = β U + (1 − tC )(β U − β B ) × S S B (1 − tC ) ⇔ βU = βS + βB B (1 − tC ) + S B (1 − tC ) + S MBF, Corporate Finance, 2010 321 Corporate Finance, 17 Levered Cap Budgeting Example 17.3 A firm is considering the following scale-enhancing project. B =100, S = 200, tC = .34, βS = 2, Rf = .1, E[RM-Rf] =.085. We look for discount rate of a all-equity firm. S 200 × β Equity = × 2 = 1.5 = β Unlevered firm S + (1 - t C ) × B 200 + (1 - .34) × 100 We calculate the discount rate from the security market line R U = R f + β Unlevered firm ( E[ RM ] − R f ) = .1 + 1.5(.085) = .2275 MBF, Corporate Finance, 2010 322 Corporate Finance, 17 Levered Cap Budgeting Example 17.4: A firm is considering $1m investment, with B/(B+S) = ½. UCF (1-tC) = $0.3m/year into perpetuity. Three competitors in the industry are unlevered with betas 1.2, 1.3 and 1.4. Assume R f = .05, E[RM-Rf] = .09 and tC = .34. What is the NPV of the project? Compute average unlevered beta of the industry : E[ β] = 1.3 = [1.2 + 1.3 + 1.4] / 3 Compute levered beta .66 ×1 / 2 (1 - t C ) × B β Equity = 2.16 = 1.3 × 1 + = β Unlevered firm × 1 + 1/ 2 S Compute the cost of levered equity from the SML: RS = Rf + βEquity E[RM-Rf] = .05 + 2.16 × .09 = .2444 Calculate the WACC for the new project: S S R WACC = .139 = .2444 / 2 + .66 × .05 / 2 = R S + (1 − t C ) × R B B+S B+S Compute the project’s NPV (perpetuity) .3 UCF NPVWACC = 1.16 = −1 = − initial investment .139 RWACC MBF, Corporate Finance, 2010 Corporate Finance, 17 Levered Cap Budgeting Summary 1. The APV formula can be written as: ∞ UCFt APV = t t = (1 + RU ) 1 Additional + effects of − debt Initial investment 2. The FTE formula can be written as: Amount Initial LCFt FTE = ∑ − t investment − borrowed t =1 (1 + RS ) ∞ 3. The WACC formula can be written as ∞ NPVWACC = ∑ t =1 Initial UCFt − (1 + RWACC ) t investment MBF, Corporate Finance, 2010 324 Corporate Finance, 17 Levered Cap Budgeting Chapter 17 – problems Recall that an asset beta would be of the form: β Asset Cov( RU , RM ) = 2 σM Redo analysis of chapter’s example with B = 278,313 (B/V = 50%) MBF, Corporate Finance, 2010 325 Appendix EQUITY VALUATION WITH DIVIDENDS Dividends Net Income * Payout Ratio = Dividends Value of Equity Dividend1 Expe ct e d Growt h Retention Ratio * Return on Equity Dividend2 Dividend3 Dividend4 Firm is in stable growth: Grows at constant rate forever Terminal Value= Dividendn+1/(ke-gn) Dividend5 Dividendn ......... Forever Discount at Cost of Equity Cost of Equit y Riskfre e Rat e : - No default risk - No reinvestment risk - In same currency and in same terms (real or nominal as cash flows + Bet a - Measures market risk X Type of Business Operating Leverage Risk Premium - Premium for average risk investment Financial Leverage Base Equity Premium Country Risk Premium Appendix EQUITY VALUATION WITH FCFE Financing Weights Debt Ratio = DR Cashflow t o Equit y Net Income - (Cap Ex - Depr) (1- DR) - Change in WC (!-DR) = FCFE Value of Equity FCFE1 Expect ed Growt h Retention Ratio * Return on Equity FCFE2 FCFE3 Firm is in stable growth: Grows at constant rate forever Terminal Value= FCFEn+1/(ke-gn) FCFE5 FCFEn ......... Forever FCFE4 Discount at Cost of Equity Cost of Equit y Riskfree Rat e: - No default risk - No reinvestment risk - In same currency and in same terms (real or nominal as cash flows + Bet a - Measures market risk X Type of Business Operating Leverage Risk Premium - Premium for average risk investment Financial Leverage Base Equity Premium Country Risk Premium Appendix VALUING A FIRM Cashflow to Firm EBIT (1-t) - (Cap Ex - Depr) - Change in WC = FCFF Value of Operating Assets + Cash & Non-op Assets = Value of Firm - Value of Debt = Value of Equity FCFF1 Discount at Cost of Equity Riskfree Rate : - No default risk - No reinvestment risk - In same currency and in same terms (real or nominal as cash flows + Expected Growth Reinvestment Rate * Return on Capital Terminal Value= FCFF n+1/(r-gn ) FCFF2 FCFF3 FCFF4 FCFF5 FCFFn ......... Forever WACC= Cost of Equity (Equity/(Debt + Equity)) + Cost of Debt (Debt/(Debt+ Equity)) Cost of Debt (Riskfree Rate + Default Spread) (1-t) Beta - Measures market risk Type of Business Firm is in stable growth: Grows at constant rate forever Operating Leverage X Weights Based on Market Value Risk Premium - Premium for average risk investment Financial Leverage Base Equity Premium Country Risk Premium Corporate Finance - chapter 18 - Dividends and Other Payouts Corporate Finance, 18 Dividends Different Types of Dividends Many companies pay a regular cash dividend. Public companies often pay quarterly. Sometimes firms will pay an extra cash dividend. The extreme case would be a liquidating dividend. Companies will often declare stock dividends. No cash leaves the firm. The firm increases the number of shares outstanding. Some companies declare a dividend in kind. Wrigley’s Gum sends a box of chewing gum. MBF, Corporate Finance, 2010 330 Corporate Finance, 18 Dividends Procedure for Cash Dividend 25 Oct. 1 Nov. 2 Nov. 5 Nov. 7 Dec. … Declaration Date ExCumdividend dividend Date Date Record Date Payment Date Declaration Date: The Board of Directors declares a payment of dividends. Cum-Dividend Date: Buyer of stock still receives the dividend. Ex-Dividend Date: Seller of the stock retains the dividend. Record Date: The corporation prepares a list of all individuals believed to be stockholders as of 5 November. MBF, Corporate Finance, 2010 331 Corporate Finance, 18 Dividends Price Behavior In a perfect world, the stock price will fall by the amount of the dividend on the ex-dividend date. -t … -2 -1 0 +1 +2 … $P $P - div The price drops Exby the amount of dividend Date the cash Taxes complicate things a bit. Empirically, the dividend. price drop is less than the dividend and occurs M first few minutes within the BF, Corporate Finance, 2010 of the ex-date. 332 Corporate Finance, 18 Dividends The Irrelevance of Dividend Policy : Homemade Dividends – example Bianchi Inc. is a $42 stock about to pay a $2 cash dividend. Bob Investor owns 80 shares and prefers a $3 dividend. Bob’s homemade dividend strategy: Sell 2 shares ex-dividend homemade dividends Cash from dividend $160 Cash from selling stock $80 Total Cash $240 Value of Stock Holdings $40 × 78 = $3,120 MBF, Corporate Finance, 2010 $3 Dividend $240 $0 $240 $39 × 80 = $3,120 333 Corporate Finance, 18 Dividends Stock Repurchase versus Dividend Consider a firm that wishes to distribute $100,000 to its shareholders. Assets A.Original balance sheet Liabilities & Equity Cash $150,000 Debt 0 Other Assets 850,000 Equity 1,000,000 Value of Firm 1,000,000 Value of Firm 1,000,000 Shares outstanding = 100,000 Price per share= $1,000,000 /100,000 = $10 MBF, Corporate Finance, 2010 334 Corporate Finance, 18 Dividends Stock Repurchase versus Dividend If they distribute the $100,000 as a cash dividend, the balance sheet will look like this: Assets Liabilities & Equity B. After $1 per share cash dividend Cash $50,000 Debt Other Assets 850,000 Equity Value of Firm 900,000 0 900,000 Value of Firm 900,000 Shares outstanding = 100,000 Price per share = $900,000/100,000 = $9 MBF, Corporate Finance, 2010 335 Corporate Finance, 18 Dividends Stock Repurchase versus Dividend If they distribute the $100,000 through a stock repurchase, the balance sheet will look like this: Assets C. After stock repurchase Liabilities & Equity Cash $50,000 Debt 0 Other Assets 850,000 Equity 900,000 Value of Firm 900,000 Value of Firm 900,000 Shares outstanding = 90,000 Price pershare = $900,000 / 90,000 = $10 MBF, Corporate Finance, 2010 336 Corporate Finance, 18 Dividends Personal Taxes and Dividends To get the result that dividend policy is irrelevant, we needed three assumptions: No taxes No transactions costs No uncertainty In the United States, both cash dividends and capital gains are taxed at a maximum rate of 15 percent. Since capital gains can be deferred, the tax rate on dividends is greater than the effective rate on capital gains. MBF, Corporate Finance, 2010 337 Corporate Finance, 18 Dividends Firms without Sufficient Cash The direct costs of stock issuance will add to this effect. Investment Bankers Cash: stock issue Firm Cash: dividends Taxes Gov. Stock Holders In a world of personal taxes, firms should not issue stock to pay a dividend. MBF, Corporate Finance, 2010 338 Corporate Finance, 18 Dividends The Clientele Effect Clienteles for various dividend payout policies are likely to form in the following way: Group Stock Type High Tax Bracket Individuals Low Tax Bracket Individuals Tax-Free Institutions Corporations Zero-to-Low payout Low-to-Medium payout Medium payout High payout MBF, Corporate Finance, 2010 339 Corporate Finance, 18 Dividends Stock Dividends Pay additional shares of stock instead of cash Increases the number of outstanding shares Does not change the par value Changes retained earnings -> Par value -> Capital in excess of par (market price – par value) Small stock dividend Less than 20 to 25% If you own 100 shares and the company declared a 10% stock dividend, you would receive an additional 10 shares. Large stock dividend – more than 20 to 25% MBF, Corporate Finance, 2010 340 Corporate Finance, 18 Dividends Stock Splits Stock splits – have the same impact as a stock dividend except it is expressed as a ratio A 2-for-1 split means that one receives for each old share an additional new share. Splits are different from dividends in accounting treatment Stock price (and par value) is reduced when the stock splits. Reverse split For example, a 1-for-2 reverse split means that 2 old shares are exchanged for 1 new share. Upcoming stock splits: http://www.stocksplits.net/ MBF, Corporate Finance, 2010 341 Corporate Finance, 18 Dividends Empirical Evidence Investors over the age of 65 concentrate their stock holdings in firms that pay high dividends, especially if the investors are retired. “Don’t dip into the principal” These investors hold over 80% of their stock portfolio in dividend paying stocks. In contrast, investors under the age of 45 hold 65% of their portfolios in dividend paying stocks. Source: Shefrin, H., 2007, Behavioral Corporate Finance MBF, Corporate Finance, 2010 342 Corporate Finance, 18 Dividends Microsoft and Con Ed Widows and Orphan Stock? March 2003, Microsoft dividend initiation. July 21, 2004 issue of The Wall Street Journal indicated that Microsoft was moving in the direction of the old AT&T model, that is a “widows and orphans” stock. Con Ed omitted dividend in 1974 to much protest. Shareholders were older, retired, and in many cases widowed, who viewed dividend income in the same way as Social Security income. Source: Shefrin, H., 2007, Behavioral Corporate Finance MBF, Corporate Finance, 2010 343 Corporate Finance, 18 Dividends Managers' Beliefs Over 80% state that there are negative consequences to reducing dividends. Over 75% believe that dividends convey information about their firm. Over 60% would rather raise funds to finance new investment projects than cut dividends. About a third believe that paying dividends, instead of plowing back earnings, makes a firm’s stock less risky. Source: Shefrin, H., 2007, Behavioral Corporate Finance MBF, Corporate Finance, 2010 344 Corporate Finance, 18 Dividends Contrast with Institutional Investors Among institutional investors, pension funds and banks find dividends attractive mainly because of stricter “prudentman” rules, rather than because of a sizeable payout. Evidence suggests that institutional investors favor repurchases over dividend payouts. When a firm increases its dividend payout, institutions tend to decrease their holdings. Source: Shefrin, H., 2007, Behavioral Corporate Finance MBF, Corporate Finance, 2010 345 Corporate Finance, 18 Dividends Repurchasing Average market response to announcement of an open market repurchase is 3.5%. Investors appear to underreact to repurchases, in that stock prices drift upwards when firms repurchase shares. Stocks of firms who repurchase shares earn four-year abnormal returns of 12.1%. 45.3% for firms with high book-to-market equity. Source: Shefrin, H., 2007, Behavioral Corporate Finance MBF, Corporate Finance, 2010 346 Corporate Finance, 18 Dividends Chapter 18 – problem You own 1000 shares of stock in corporation A. You will receive a 0.70 per share dividend in one year. In two years, A will pay a liquidating dividend of 40 per share. The required return on A stock is 15%. What is the current share price of your stock (ignoring taxes)? If you would rather have equal dividends in each of the next two years, show how you can accomplish this by creating homemade dividends. (Hint: Dividends will be in form of an annuity). MBF, Corporate Finance, 2010 347 Corporate Finance - chapter 19 - Issuing Securities to the Public Corporate Finance, 19 Public issue The Public Issue Management gets the approval of the Board. The firm prepares and files a registration statement with the SEC. The SEC studies the registration statement during the waiting period. The firm prepares and files an amended registration statement with the SEC. If everything is copasetic with the SEC, a price is set and a full-fledged selling effort gets underway. Steps in Public Offering Time . Several months 20-day waiting period Usually on the 20th day After the 20th day 30 days after offering 1. Pre-underwriting conferences 2. Registration statements 3. Pricing the issue 4. Public offering and sale 5. Market stabilization MBF, Corporate Finance, 2010 349 Corporate Finance, 19 Public issue An Example of a Tombstone MBF, Corporate Finance, 2010 350 Corporate Finance, 19 Public issue Table 19.2 - I MBF, Corporate Finance, 2010 351 Corporate Finance, 19 Public issue Table 19.2 - II MBF, Corporate Finance, 2010 352 Corporate Finance, 19 Public issue Mechanics of Rights Offerings The management of the firm must decide: The exercise price (the price existing shareholders must pay for new shares). How many rights will be required to purchase one new share of stock. These rights have value: Shareholders can either exercise their rights or sell their rights. MBF, Corporate Finance, 2010 353 Corporate Finance, 19 Public issue Rights Offering Example Popular Delusions, Inc. is proposing a rights offering. There are 200,000 shares outstanding trading at $25 each. There will be 10,000 new shares issued at a $20 subscription price. What is the new market value of the firm? What is the ex-rights price? What is the value of a right? MBF, Corporate Finance, 2010 354 Corporate Finance, 19 Public issue What is the new market value of the firm? $5,200,000 = 200,000 shares × $25 $20 + 10,000 shares × share shares There are 200,000 outstanding shares at $25 each. There will be 10,000 new shares issued at a $20 subscription price. MBF, Corporate Finance, 2010 355 Corporate Finance, 19 Public issue What Is the Ex-Rights Price? There are 210,000 outstanding shares of a firm with a market value of $5,200,000. Thus the value of an ex-rights share is: $5,200,000 = $24.76 210,000 shares MBF, Corporate Finance, 2010 356 Corporate Finance, 19 Public issue What Is the Ex-Rights Price? Thus, the value of a right is … $4.76 = ($24.76 – $20)/1 …equal to the difference between new price and subscription price /divided by the number of rights needed to buy one new share. MBF, Corporate Finance, 2010 357 Corporate Finance, 19 Public issue The Cost of New Issues Spread or underwriting discount Underpricing Green Shoe Option MBF, Corporate Finance, 2010 358 Corporate Finance, 19 Public issue The Costs of Equity Public Offerings Proceeds (in millions) 2 - 9.99 10 - 19.99 20 - 39.99 40 - 59.99 60 - 79.99 80 - 99.99 100 - 199.99 200 - 499.99 500 and up total Direct Costs SEOs IPOs 12.88% 15.36% 8.81% 11.63% 7.24% 9.81% 6.20% 9.21% 5.81% 8.65% 5.56% 8.34% 5.00% 7.67% 4.26% 6.72% 3.64% 5.15% 6.72% 10.39% MBF, Corporate Finance, 2010 Underpricing IPOs 18.18% 10.02% 17.91% 29.57% 39.20% 45.36% 37.10% 17.72% 12.19% 23.55% 359 Corporate Finance, 19 Public issue There is underpricing of IPO, but there is also long-term underperformance Comparison IPO returns and Firms Matched by Size and Book-to-Market Equity 1970-2002 18.0% 16.0% 14.0% 12.0% IPOs Matched Firms 10.0% 8.0% 6.0% 4.0% 2.0% 0.0% First 6 months Second 6 months Year 1 Year 2 Year 3 Year 4 Source: Shefrin, H., 2007, Behavioral Corporate Finance MBF, Corporate Finance, 2010 Year 5 Years 1-5 (Geometric Mean) 360 Corporate Finance, 19 Public issue Corporate Equity Security Offerings 17.7% Private Rule 144A placements 16.2% Private non-Rule 144A placements 66.1% Public equity offering Source: Jennifer E. Bethal and Erik R. Sirri, “Express Lane or Toll Booth in the Desert: The Sec of Framework for Securities Issuance,” Journal of Applied Corporate Finance (Spring 1998). MBF, Corporate Finance, 2010 361 Corporate Finance, 19 Public issue Long Lasting Effect? Empirical evidence indicates that firms issue new equity when stock prices have recently risen and market-to-book ratios are high. This suggests that managers issue equity when that equity is most likely to be overpriced. Some have concluded that this is no short-run phenomenon, that fluctuations in market value can have very long-run impacts on capital structure. MBF, Corporate Finance, 2010 362 Corporate Finance, 19 Public issue Chapter 19 – problem The MHMM Corporation wants to diversify its operations. Some recent financial information for the company is shown here: Stock price £ 98 Number of shares 14,000 Total assets £6,000,000 Total liabilities £2,400,000 Net income £630,000 MHMM is considering an investment that has the same PE ratio as the firm. The cost of the investment is £1.1M, and it will be financed with a new equity issue. The return on the investment will equal MHMM’s current ROE. What will happen to the book value per share, the market value per share, and the EPS? What is the NPV of this investment? Does dilution take place? MBF, Corporate Finance, 2010 363 Corporate Finance - chapter 20 - Long-term debt Corporate Finance, 20 Long-term debt Features of a Cisco Systems Bond Issue amount Issue date Maturity date $3 billion 2/22/06 2/22/16 Face value Coupon Coupon dates Offering price Call provision Call price $1,000 5.50 2/22, 8/22 99.543 At any time Treasury rate plus 0.20% Senior Moody's A1, S&P A+ Security Rating Bond issue total face value is $3 billion Bonds offered to the public in February 2006 Remaining principal is due February 22, 2016 Face value denomination is $1,000 per bond Annual coupons are $55.50 per bond Coupons are paid semiannually Offer price is 99.543% of face value The bonds do not have a deferred call. The bonds have a make whole call provision. Bonds are the first claim for all bondholders. Bond credit quality rated upper medium grade by Moody's and S&P's rating MBF, Corporate Finance, 2010 365 Corporate Finance, 20 Long-term debt The Public Issue of Bonds The general procedure is similar to the issuance of stock, as described in the previous chapter. The indenture lists the terms of the bond bondholder protection : negative vs positive covenants Direct placement (instead of public issues) have more restrictive covenants MBF, Corporate Finance, 2010 366 Corporate Finance, 20 Long-term debt Principal Repayment Term bonds versus serial bonds Sinking funds–how do they work? Fractional repayment each year Good news—security Bad news—unfavorable calls MBF, Corporate Finance, 2010 367 Corporate Finance, 20 Long-term debt Coupon payment Clean vs dirty price Example: A bond with 12% annual coupon, payable semiannually. Next coupon ($60) is due in 4 month. The bonds quoted (i.e., the clean) price is $1,060. Actually you pay 1,080 (i.e., the dirty price), including the accrued interest ($20) over the past two month (2month/6month × $60). MBF, Corporate Finance, 2010 368 200 Noncallable bond 175 Bond price (% of par) Corporate Finance, 20 Long-term debt Callable Bonds versus Non-callable Bonds Most bonds are callable. Some sensible reasons for call provisions include: managerial flexibility and the fact that callable bonds have less interest rate risk. 150 125 100 75 Callable bond 50 25 0 4 8 12 16 20 Yield to maturity (%) MBF, Corporate Finance, 2010 369 Corporate Finance, 20 Long-term debt Different Types of Bonds Callable Bonds Put Bonds Convertible Bonds Deep Discount Bonds Income Bonds Floating-Rate Bonds Junk Bonds Long-Term Syndicated Bank Loans MBF, Corporate Finance, 2010 370 150 140 Convertible bond price 130 Bond price (% of par) Corporate Finance, 20 Long-term debt Convertible Bond Prices 120 110 Stock price 100 90 80 Nonconvertible bond price 70 60 50 50 70 90 110 MBF, Corporate Finance, 2010 Conversion value (% of par) 130 150 371 Corporate Finance, 20 Long-term debt Bond Ratings: Investment Grade Moody's Duff & Phelps S&P's Aaa 1 AAA Aa1 Aa2 2 3 AA+ AA Aa3 A1 A2 4 5 6 AA A+ A A3 Baa1 7 8 ABBB+ Baa2 9 BBB Baa3 10 Credit Rating Description Highest credit rating, maximum safety BBB - High credit quality, investment -grade bonds Upper -medium quality, inve stment grade bonds Lower -medium quality, investment grade bonds MBF, Corporate Finance, 2010 372 Corporate Finance, 20 Long-term debt Bond Ratings: Below Investment Grade Moody's Duff & Phelps Ba1 S&P's Credit Rating Description Speculative-Grade Bond Ratings 11 BB+ Ba2 Ba3 B1 12 13 14 BB BBB+ B2 B3 15 16 B B- Low credit quality, speculative-grade bonds Very low credit quality, speculative-grade bonds Extremely Speculative-Grade Bond Ratings Caa Ca C 17 CCC + CCC CCCCC C D Extremely low credit standing, high-risk bonds Extremely speculative Bonds in default MBF, Corporate Finance, 2010 373 Corporate Finance - chapter 21 - Leasing Corporate Finance, 21 Leasing Buying versus Leasing Buy Firm U buys asset and uses asset; financed by debt and equity. Lease Lessor buys asset, Firm U leases it. Manufacturer of asset Manufacturer of asset Lessor Firm U 1. Uses asset 2. Owns asset Equity shareholders 1. Owns asset 2. Does not use asset Equity Creditors shareholders MBF, Corporate Finance, 2010 Lessee (Firm U) 1. Uses asset 2. Does not own asset Creditors 375 Corporate Finance, 21 Leasing Accounting and Leasing In the old days, leases led to off-balance-sheet financing. Today, leases are either classified as capital leases or operating leases. Operating leases do not appear on the balance sheet. Capital leases appear on the balance sheet—the present value of the lease payments appears on both sides. Taxes may be reduced by leasing. MBF, Corporate Finance, 2010 376 Corporate Finance, 21 Leasing Accounting and Leasing (Balance Sheet) Truck is purchased with debt Truck $100,000 Debt Land $100,000 Equity Total Assets $200,000 Total Debt & Equity $100,000 $100,000 $200,000 Operating Lease Truck Land Total Assets Debt $100,000 Equity $100,000 Total Debt & Equity $100,000 $100,000 Capital Lease Assets leased Land Total Assets $100,000 Obligations under capital lease $100,000 Equity $200,000 Total Debt & Equity $100,000 $100,000 $200,000 MBF, Corporate Finance, 2010 377 Corporate Finance, 21 Leasing A tax-lease example: A firm is about to acquire a delivery truck. The truck is expected to reduce costs by $4,500 per year. The truck costs $25,000 and has a useful life of 5 years. If the firm buys the truck, they will depreciate it straight-line to zero. They can lease it for 5 years from a leasing company at an annual lease payment of $6,250. Cash Flow : Buy Year : 0 1 2 3 4 5 After-tax op. savings; 4.5×(1-.34) = 2.97 2.97 2.97 2.97 2.97 Depreciation tax shield; 5 × (.34) = 1.7 1.7 1.7 1.7 1.7 4.67 4.67 2 4.67 3 4.67 4 4.67 5 Cost of truck –25 revenue less expenses Cash Flow : Lease –25 Year : 0 1 Cost of truck After-tax op. savings; 4.5×(1-.34) = 2.97 Lease tax shield; –6,250×(1-.34) = -4.125 -4.125 -4.125 -4.125 -4.125 revenue less expenses -1.155 -1.155 -1.155 -1.155 -1.155 NCF from lease : Lease - Buy 2.97 2.97 2.97 25 -5.825 -5.825 -5.825 -5.825 -5.825 MBF, Corporate Finance, 2010 IRR of NCF = 0.053 2.97 ⇒ lease is better if R > 5.3% 378 Corporate Finance, 21 Leasing Chapter 21 – problem You consider leasing a scanner. The scanner costs 3,00,000 and it would be depreciated straight-line to zero over four years. The salvage value is zero. It can be leased for 895,000. Assume the tax rate is 35%. You can borrow at 9% before taxes. Should you lease or buy? MBF, Corporate Finance, 2010 379 Corporate Finance - chapter 22 - Options and Corporate Finance al l Bu y ac ST 60 Option payoffs ($) Corporate Finance, 22 Options Call Option Payoffs 40 20 20 –20 –40 40 50 60 80 100 120 price ($) ST = stock price at expiration E = $50 = exercise price c = max(0,BF, Corporate Finance,intrinsic value of call M S – E) = 2010 T 381 60 Option profit ($) Corporate Finance, 22 Options Call Option Profits Buy a call 40 20 10 20 40 50 60 80 –10 –20 –40 100 120 Stock price ($) Exercise price = $50; option premium = $10 MBF, Corporate Finance, 2010 382 Put Option Payoffs Option payoffs ($) Corporate Finance, 22 Options 60 50 40 20 0 0 20 40 50 60 80 100 Buy a put Stock price ($) –20 –40 Exercise price = $50 MBF, Corporate Finance, 2010 383 Put Option Profits Option profit ($) Corporate Finance, 22 Options 60 40 20 10 –10 20 40 50 60 80 100 Stock price ($) Buy a put –20 –40 Exercise price = $50; option premium = $10 MBF, Corporate Finance, 2010 384 Corporate Finance, 22 Options Selling Options The seller (or writer) of an option has an obligation. The seller receives the option premium in exchange. MBF, Corporate Finance, 2010 385 Call Option Payoffs Option payoffs ($) Corporate Finance, 22 Options 60 40 20 20 40 50 60 80 100 120 Stock price ($) –20 l Se la MBF, Corporate Finance, 2010 ll Exercise price = $50 ca –40 386 Put Option Payoffs Option payoffs ($) Corporate Finance, 22 Options 40 20 0 Sell a put 0 20 40 50 60 80 100 Stock price ($) –20 –40 Exercise price = $50 –50 MBF, Corporate Finance, 2010 387 Protective Put Strategy (Profits) Corporate Finance, 22 Options Value at expiry Buy the stock at $40 $40 Profit: Protective Put strategy has downside protection and upside potential $0 -$10 -$40 $40 $50 Buy a put with exercise price of $50 for $10 Value of stock at expiry MBF, Corporate Finance, 2010 388 Covered Call Strategy Corporate Finance, 22 Options Value at expiry Buy the stock at $40 Profit: Covered Call strategy $10 $0 Value of stock at expiry $40 $50 -$30 Sell a call with exercise price of $50 for $10 -$40 MBF, Corporate Finance, 2010 389 E Portfolio value today = c0 + (1+ r)T Option payoffs ($) Corporate Finance, 22 Options Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T Portfolio payoff Call bond 25 Stock price ($) 25 Consider the payoffs from holding a portfolio consisting of a call with a strike price of $25 and a bond with a future value of $25. MBF, Corporate Finance, 2010 390 Portfolio payoff Option payoffs ($) Corporate Finance, 22 Options Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T Portfolio value today = p0 + S0 25 Stock price ($) 25 Consider the payoffs from holding a portfolio consisting of a share of stock and a put with a $25 strike. MBF, Corporate Finance, 2010 391 Corporate Finance, 22 Options Option-pricing : no-arbitrage principle Assume Call premium c = 1 Stock price today, t = 0, S0 = 20 Exercise time, T = 1 (discrete) riskless interest rate, R = 10 % Exercise price, E = 20 No dividend, Div = 0 Is there any arbitrage possible? Yes, because the call is too cheap! What must be the option premium? MBF, Corporate Finance, 2010 392 Corporate Finance, 22 Options Option Value Intrinsic Value Call: Max[ST – E, 0] Put: Max[E – ST , 0] Speculative Value The difference between the option premium and the intrinsic value of the option. Option Premium = Intrinsic Value MBF, Corporate Finance, 2010 + Speculative Value 393 Corporate Finance, 22 Options Binomial model – movement of stock price Stock price today S0 = $25 Stock price in one year ST=1 = {21.25; 28.75} S1 = $28.75 S0 = $25 S1 = $21.25 MBF, Corporate Finance, 2010 394 Corporate Finance, 22 Options Binomial model – a call option : example The call has an exercise price of E = 25 At expiry date the call is worth C(T) = max{0, ST - E} S1 = $28.75 C(1) = $3.75 S0 = $25 C(0) = ? S1 = $21.25 C(1) = $0 MBF, Corporate Finance, 2010 395 Corporate Finance, 22 Options Binomial model example: construction of a riskless portfolio Consider the following portfolio: (Buy) long ∆ units of stock (∆ S0) (Sell) short one call (–C(0)) 28.75 × ∆ – 3.75 (= ∆ × ST – 1 × C(T)) 21.25 × ∆ (= ∆ × ST – 1 × C(T)) The portfolio is riskless, if 28.75 ⋅ ∆ - 3.75 = 21.25 ⋅ ∆ , ∆ = 1/2 MBF, Corporate Finance, 2010 396 Corporate Finance, 22 Options Binomial model example: value the riskless portfolio (R = 10%) The riskless portfolio contains: Long one (delta) units of stock (∆ S) Short one call (– C(0)) Value of the portfolio at expiration (in one year): 10.63 = 28.75 × ½ – 1 × 3.75 = ST × ∆ – 1 × C(T) Present value of riskless portfolio Value of the stock position 10.63/(1.05) ∆ × S0 = 10.12= B (@5%) = 12.50 Value of the short call C(0) = 2.38 What happens to C(0) if S0 = 23 ? MBF, Corporate Finance, 2010 397 Corporate Finance, 22 Options Replicating portfolio Cash flow of long call at expiration 3.75 in the good state and 0 in the bad state The following portfolio replicates the cash flows of the call at the expiration date ½ S long ½ B x (1 + R)-1 short, where B = 21.25 No arbitrage: the cost of the replicating portfolio equals the price of the call at the initial time We can synthetically generate an option through a position in bond and stock Corporate Finance, 22 Options Option delta ∆ Delta (∆ ) is the number of shares of stock you need to construct a riskless portfolio, if you sell short one call. Delta (∆ ) varies with the assumed prices at expiration of the underlying security Delta (∆ ) is the ratio between a change in the price of the option and the change in the price of the underlying security ∆ = dC / dS In the example (∆ = ½ ), if the stock price changes by $1 the price of the call option changes by $0.50 . The swing of the call is 3.75 – 0, the swing of the stock is 7.50 = 28.75 – 21.25. The delta is ½ = 3.75/7.50. Delta (∆ ) is the sensitivity of the option to a price change in the underlying security MBF, Corporate Finance, 2010 399 Profit Option payoffs ($) Corporate Finance, 22 Options American call ST Call Market Value Time value Intrinsic value ST E Out-of-the-money loss In-the-money C0 must fall within max (S0 – E, 0) < C0 < S0. MBF, Corporate Finance, 2010 400 Corporate Finance, 22 Options Option Value Determinants Variable European C European p American c American P S0 + - + - E - + - + T ? ? + + σ + + + + r + - + - Div - + - + MBF, Corporate Finance, 2010 401 Corporate Finance, 22 Options Binomial Option Pricing Model The most important lesson (so far) from the binomial option pricing model is: the replicating portfolio intuition. Many derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the derivative securities. Corporate Finance, 22 Options The Risk-Neutral Approach S(0) is the value of the underlying asset today. q S(0), V(0) S(U), V(U) q is the risk-neutral probability of an “up” move. 1- q S(D), V(D) We could value the option, V(0), as the value of the replicating portfolio. An equivalent method is risk-neutral valuation: q × V (U ) + (1 − q ) × V ( D) V ( 0) = (1 + rf ) MBF, Corporate Finance, 2010 Corporate Finance, 22 Options The Risk-Neutral Approach The key to finding q is to note that it is already impounded into an observable security price: the value of S(0): q × S (U ) + (1 − q ) × S ( D) S ( 0) = (1 + rf ) A minor bit of algebra yields: q = MBF, Corporate Finance, 2010 (1 + rf ) × S (0) − S ( D ) S (U ) − S ( D) Corporate Finance, 22 Options Example of Risk-Neutral Valuation Suppose a stock is worth $25 today and in one period will either be worth 15% more or less. The risk-free rate is 5%. What is the value of an at-themoney call option? The binomial tree would look like this: $28.75 = $25 × (1 + .15) q $28.75,C(U) $25,C(0) $21.25 = $25 × (1 − .15) 1- q q= (1 + rf ) × S (0) − S ( D ) S (U ) − S ( D ) $21.25,C(D) (1 + .05) × 25 − 21.25 = = 2/3 28.75 − 21.25 MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Example of Risk-Neutral Valuation After that, find the value of the call in the up state and down state. C (U ) = $28.75 − $25 2/3 $28.75, $3.75 $25,C(0) = $2.38 C ( D) = max[$21.25 − $25,0] 1/3 C ( 0) = $21.25, $0 q × C (U ) + (1 − q) × C ( D) 2 / 3 × 3.75 = = 2.38 (1 + rf ) 1.05 MBF, Corporate Finance, 2010 Corporate Finance, 22 Options The Black-Scholes Model C0 = S × N(d1 ) − Ee − rT × N(d 2 ) C0 = the value of a European option at time t = 0 r = the risk-free interest rate. σ2 ln(S / E ) + (r + )T 2 d1 = σT d 2 = d1 − σ T N(d) = Probability that a standardized, normally distributed, random variable will be less than or equal to d. The Black-Scholes Model allows us to value options in the real world just as we have done in the 2-state world. MBF, Corporate Finance, 2010 Corporate Finance, 22 Options The Black-Scholes Model Find the value of a six-month call option on Microsoft with an exercise price of $150. The current value of a share of Microsoft is $160. The interest rate available in the U.S. is r = 5%. The option maturity is 6 months (half of a year). The volatility of the underlying asset is 30% per annum. Before we start, note that the intrinsic value of the option is $10—our answer must be at least that amount. MBF, Corporate Finance, 2010 Corporate Finance, 22 Options The Black-Scholes Model Let’s try our hand at using the model. If you have a calculator handy, follow along. First calculate d1 and d2 ln(S / E ) + (r + .5σ 2 )T d1 = σT ln(160 / 150) + (.05 + .5(0.30) 2 ).5 d1 = = 0.52815 0.30 .5 Then, d 2 = d1 − σ T = 0.52815 − 0.30 .5 = 0.31602 MBF, Corporate Finance, 2010 Corporate Finance, 22 Options The Black-Scholes Model C0 = S × N(d1 ) − Ee d1 = 0.52815 d 2 = 0.31602 − rT × N(d 2 ) N(d1) = N(0.52815) = 0.7013 N(d2) = N(0.31602) = 0.62401 C0 = $160 × 0.7013 − 150e −.05×.5 C0 = $20.92 MBF, Corporate Finance, 2010 × 0.62401 Corporate Finance, 22 Options 22.9 Stocks and Bonds as Options Levered equity is a call option. The underlying asset comprises the assets of the firm. The strike price is the payoff of the bond. If at the maturity of their debt, the assets of the firm are greater in value than the debt, the shareholders have an in-the-money call. They will pay the bondholders and “call in” the assets of the firm. If at the maturity of the debt the shareholders have an out-ofthe-money call, they will not pay the bondholders (i.e. the shareholders will declare bankruptcy) and let the call expire. MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Stocks and Bonds as Options Levered equity is a put option. The underlying asset comprises the assets of the firm. The strike price is the payoff of the bond. If at the maturity of their debt, the assets of the firm are less in value than the debt, shareholders have an in-the-money put. They will put the firm to the bondholders. If at the maturity of the debt the shareholders have an out-ofthe-money put, they will not exercise the option ( i.e. NOT declare bankruptcy) and let the put expire. MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Stocks and Bonds as Options It all comes down to put-call parity. c0 = S0 + p0 – Value of a call on the firm E (1+ r)T Value of a Value of = the firm + put on the – firm Stockholder’s position in terms of call options Stockholder’s position in terms of put options MBF, Corporate Finance, 2010 Value of a risk-free bond Corporate Finance, 22 Options Mergers and Diversification Diversification is a frequently mentioned reason for mergers. Diversification reduces risk and, therefore, volatility. Decreasing volatility decreases the value of an option. Assume diversification is the only benefit to a merger: Since equity can be viewed as a call option, should the merger increase or decrease the value of the equity? Since risky debt can be viewed as risk-free debt minus a put option, what happens to the value of the risky debt? Overall, what has happened with the merger and is it a good decision in view of the goal of stockholder wealth maximization? MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Example Consider the following two merger candidates. The merger is for diversification purposes only with no synergies involved. Risk-free rate is 4%. Company A Company B Market value of assets $40 million $15 million Face value of zero coupon debt $18 million $7 million 4 years 4 years 40% 50% Debt maturity Asset return standard deviation MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Example Use the Black and Scholes OPM (or an options calculator) to compute the value of the equity. Value of the debt = value of assets – value of equity Company A Company B Market Value of Equity 25.72 9.88 Market Value of Debt 14.28 5.12 MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Example The asset return standard deviation for the combined firm is 30% Market value assets (combined) = 40 + 15 = 55 Face value debt (combined) = 18 + 7 = 25 Combined Firm Market value of equity 34.18 Market value of debt 20.82 Total MV of equity of separate firms = 25.72 + 9.88 = 35.60 Wealth transfer from stockholders to bondholders = 35.60 – 34.18 = 1.42 (exact increase in MV of debt) MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Options and Capital Budgeting Stockholders may prefer low NPV projects to high NPV projects if the firm is highly leveraged and the low NPV project increases volatility. Consider a company with the following characteristics: MV assets = 40 million Face Value debt = 25 million Debt maturity = 5 years Asset return standard deviation = 40% Risk-free rate = 4% MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Example: Low NPV Current market value of equity = $22.706 million Current market value of debt = $17.294 million Project I Project II NPV $3 $1 MV of assets $43 $41 Asset return standard deviation 30% 50% MV of equity $23.831 $25.381 MV of debt $19.169 $15.169 MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Example: Low NPV Which project should management take? Even though project B has a lower NPV, it is better for stockholders. The firm has a relatively high amount of leverage: With project A, the bondholders share in the NPV because it reduces the risk of bankruptcy. With project B, the stockholders actually appropriate additional wealth from the bondholders for a larger gain in value. MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Example: Negative NPV We have seen that stockholders might prefer a low NPV to a high one, but would they ever prefer a negative NPV? Under certain circumstances, they might. If the firm is highly leveraged, stockholders have nothing to lose if a project fails, and everything to gain if it succeeds. Consequently, they may prefer a very risky project with a negative NPV but high potential rewards. MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Example: Negative NPV Consider the previous firm. They have one additional project they are considering with the following characteristics Project NPV = -$2 million MV of assets = $38 million Asset return standard deviation = 65% Estimate the value of the debt and equity MV equity = $25.453 million MV debt = $12.547 million MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Example: Negative NPV In this case, stockholders would actually prefer the negative NPV project to either of the positive NPV projects. The stockholders benefit from the increased volatility associated with the project even if the expected NPV is negative. This happens because of the large levels of leverage. MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Options and Capital Budgeting As a general rule, managers should not accept low or negative NPV projects and pass up high NPV projects. Under certain circumstances, however, this may benefit stockholders: The firm is highly leveraged The low or negative NPV project causes a substantial increase in the standard deviation of asset returns Classic NPV calculations generally ignore the flexibility that real-world firms typically have. MBF, Corporate Finance, 2010 Corporate Finance, 22 Options Chapter 22 - problems 1. Two-state option pricing model: the price of Tara Inc. stock will be either $60 or $80 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 5 percent. A. Suppose the current price of Tara stock is $70. What is the value of the call option if the exercise price is $45 per share? B. suppose the exercise price is $70 in part (a). What is the vlaue of the call option now? 2. Put-Call Parity: A put option that expires in six months with an exercise price of 5,000 sells for 489. The stock is curently priced at 5,300, and the risk-free rate is 3.6% per year, compounded continuously. What is the price of a call option with the same exercise price? MBF, Corporate Finance, 2010 425 Corporate Finance, 22 Options Chapter 22 - problems 3. AT Company has a zero coupon bond issue that matures in two years with a face value of $30,000. The current value of the company’s assets is $13,000, and the stand. Dev. of the return on assets is 60% per year. a) Assume the risk-free rate of return is 5 percent per year, compounded continuously. What is the value of a risk-free bond with the same face value and maturity as the company’s bond? b) What price would the bondholders have to pay for a put option on the firm’s assets with a strike price equal to the face value of the debt? c) Using the answers from a) and b), what is the value of the firm’s debt? What is the continuously compounded yield on the company’s debt? d) It seems likely that the company will default on its debt. Management has approached bondholders and proposed a plan whereby the company would repay the same face value of debt, but the repayment would not occur for five years. What is the value of the debt under the proposed plan? What is the new continuously compounded yield on the debt? MBF, Corporate Finance, 2010 426 Corporate Finance, 22 Options Chapter 22 - problems 4. In addition to five factors discussed in the chapter, dividends also affect the price of an option. The Black-Scholesdtoption pricing model with dividends is − − Rt C = S ×e × N (d1 ) − E × e × N (d 2 ) d1 = [ln(S / E ) + ( R − d + σ 2 / 2) × t ] /(σ × t ) d 2 = d1 − σ × t All of the variables are the same as the BS model without dividends except for the variable d, which this the continuously compounded dividend yield on the stock. a) What effect do you think the dividend yield will have on the price of a call option? b) A stock is currently priced at $84 per share, the standard deviation of its return is 50 percent per year, and the risk-free rate is 5 percent per year compounded continuously. What is the price of a call option with a strike price of $80 and a maturity of six month if the stock has a dividend yield of 2 percent per year, what if dividend is zero? MBF, Corporate Finance, 2010 427 Corporate Finance - chapter 23 - Options and Corporate Finance Extensions and Applications MBF, Corporate Finance, 2010 Corporate Finance, 23 Stock Options Executive Stock Options Executive Stock Options exist to align the interests of shareholders and managers. Executive Stock Options are call options (technically warrants) on the employer’s shares. Inalienable Typical maturity is 10 years. Typical vesting period is 3 years. Most include an implicit reset provision to preserve incentive compatibility. Executive Stock Options give executives an important tax break: grants of at-the-money options are not considered taxable income. (Taxes are due if the option is exercised.) MBF, Corporate Finance, 2010 429 Corporate Finance, 23 Stock Options Valuing Executive Compensation FASB has historically allowed firms to record zero expense for grants of at-the-money executive stock options. However, the economic value of a long-lived call option is enormous, especially given the propensity of firms to reset the exercise price after drops in the price of the stock. Due to the inalienability, the options are worth less to the executive than they cost the company. The executive can only exercise, not sell his options. Thus, he can never capture the speculative value—only the intrinsic value. This “dead weight loss” is overcome by the incentive compatibility for the grantor. MBF, Corporate Finance, 2010 430 Corporate Finance, 23 Stock Options Incentives “What a bonus plan does is communicate goals in the most effective way possible—by putting a bounty on them… When you do that you’ll get people’s attention very fast. You’ll send them a strong message. You provide them with a focus.” Jack Stack, CEO Source: Shefrin, H., 2007, Behavioral Corporate Finance MBF, Corporate Finance, 2010 431 Corporate Finance, 23 Stock Options Paying For Performance In Practice Executive compensation displays too little variability in respect to pay for performance insufficient dismissal excessive payment Directors are overconfident in their ability to structure incentives appropriately without overpaying executives. Directors' tasks are made more difficult by the overconfidence of executives. Source: Shefrin, H., 2007, Behavioral Corporate Finance MBF, Corporate Finance, 2010 432 Corporate Finance, 23 Stock Options Employee Stock By its nature, the compensation plan, and attendant communication focuses on performance for the current fiscal year. However, value creation is a multi-year proposition. Employee stock ownership serves to discourage the tendency to take decisions that improve short-term performance, but destroy value. Source: Shefrin, H., 2007, Behavioral Corporate Finance MBF, Corporate Finance, 2010 433 Corporate Finance, 23 Options 23.2 Valuing a Start-Up An important option is the option to expand. Imagine a start-up firm, Campusteria, Inc., which plans to open private dining clubs on college campuses. The test market will be your campus, and if the concept proves successful, expansion will follow nationwide. Nationwide expansion will occur in year four. The start-up cost of the test dining club is only $30,000 (this covers leaseholder improvements and other expenses for a vacant restaurant near campus). MBF, Corporate Finance, 2010 Corporate Finance, 23 Options Campusteria Pro Forma Income Statement Investment Year 0 Revenues Years 1-4 $60,000 Variable Costs ($42,000) Fixed Costs ($18,000) Depreciation ($7,500) Pretax profit ($7,500) Tax shield 34% $2,550 Net Profit Cash Flow ($4,950) -$30,000 $2,550 4 We plan to sell 25 meal plans at $200 per month with a 12-month contract. Variable costs are projected to be $3,500 per month. Fixed costs (lease payment) are projected to be $1,500 per month. We can depreciate our capitalized leaseholder improvements. $2,550 NPV = −$30,000 + ∑ = −$21,916.84 t t =1 (1.10) MBF, Corporate Finance, 2010 Corporate Finance, 23 Options Valuing a Start-Up Note that while the Campusteria test site has a negative NPV, we are close to our break-even level of sales. If we expand, we project opening 20 Campusterias in year four. The value of the project is in the option to expand. We will use the Black-Scholes option pricing model to value this option. MBF, Corporate Finance, 2010 Corporate Finance, 23 Options Valuing a Start-Up with Black-Scholes Recall the Black-Scholes Option Pricing Model C0 = S × N(d1 ) − Ee − rT × N(d 2 ) Where C0 = the value of a European option at time t = 0 r = the risk-free interest rate σ2 ln(S / E ) + (r + )T 2 d1 = σT d 2 = d1 − σ T N(d) = Probability that a standardized, normally distributed, random variable will be less than or equal to d. MBF, Corporate Finance, 2010 Corporate Finance, 23 Options Valuing a Start-Up with Black-Scholes We need to find the value of a four-year call option with an exercise price of $600,000 = $30,000×20. The interest rate available is r = 10%. The option maturity is four years. The volatility of the underlying asset is 30% per annum. The current value of the underlying assets is $110,418. 4 $2,550 20 × ∑ (1.10) t $161,663.14 t =1 = = $110,418 4 4 (1.10) (1.10) MBF, Corporate Finance, 2010 Corporate Finance, 23 Options Valuing a Start-Up with Black-Scholes Let’s try our hand again at using the model. If you have a calculator handy, follow along. ln(S / E ) + (r + .5σ 2 )T d1 = σT ln(110,418 / 600,000) + (.10 + .5(0.30) 2 )4 d1 = = −1.8544 0.30 4 Then, d 2 = d1 − σ T = −1.8544 − 0.30 4 = −2.45 MBF, Corporate Finance, 2010 Corporate Finance, 23 Options Valuing a Start-Up with Black-Scholes N(d1) = N(-1.8544) =0.032 N(d2) = N(-2.45) =0.007 C 0 = $110,418 × 0.032 − 600,000e −.10×4 × 0.007 C 0 = $718.03 The option to expand, while valuable, is not as great as the negative NPV of opening the trial Campusteria. So, we should not proceed. MBF, Corporate Finance, 2010 Corporate Finance, 23 Options 23.3 More on the Binomial Model The binomial option pricing model is an alternative to the Black-Scholes option pricing model. Find the value of a three-period at-the-money call option written on a $25 stock that can go up or down 15 percent each period when the risk-free rate is 5 percent. MBF, Corporate Finance, 2010 Three Period Binomial Process Corporate Finance, 23 Options $25.00 × (1.15)3 $25.00 × (1.15) $25.00 × (1.15) 38.02 2 2/3 33.06 $25.00 × (1.15) 2 (1 − .15) 2/3 28.75 $25.00 × (1.15)(1 − .15) 2/3 28.10 2/3 1/3 $25 24.44 2/3 1/3 21.25 $25.00 × (1 − .15) 1/3 $25.00 × (1.15) × (1 − .15) 2 1/3 $25.00 × (1. − 15) 2 1/3 18.06 20.77 2/3 $25.00 × (1 − .15) 3 1/3 MBF, Corporate Finance, 2010 15.35 Corporate Finance, 23 Options C3 (U , U , U ) = max[$38.02 − $25,0] C1 (U ) = 2 3 × $13.02 + (1 3) × $3.10 C2 (U , U ) = (1.05) 2 3 × $9.25 + (1 3) × $1.97 (1.05) 28.75 2/3 C1 ( D) = $25 4.52 1/3 6.50 33.06 2/3 9.25 1.25 2/3 C3 (U , D, U ) = C3 (U , U , D ) = 1/3 2 3 × $3.10 + (1 3) × $0 2/3 (1.05) 1/3 24.44 1.97 C 2 ( D, D ) = 1/3 18.06 0 max[$28.10 − $25,0] 28.10 3.10 C3 (U , D, D) = C3 ( D , U , D ) = C3 ( D , D , U ) = 2 3 × $0 + (1 3) × $0 2/3 (1.05) 1/3 2 3 × $6.50 + (1 3) × $1.25 C0 = (1.05) 13.02 C3 ( D , U , U ) = C2 (U , D ) = C2 ( D, U ) = 2 3 × $1.97 + (1 3) × $0 2/3 (1.05) 21.25 38.02 max[$20.77 − $25,0] 20.77 0 C3 ( D , D , D ) = max[$15.35 − $25,0] 1/3 15.35 0 MBF, Corporate Finance, 2010 Corporate Finance, 23 Options 23.4 Shutdown and Reopening Decisions Can easily be seen as options. The “Woe is Me” gold mine is currently closed. The firm is publicly held and trades under the ticker WOE. The firm has no debt and has assets of around $30 million. The market capitalization is well over $1 billion What could possibly explain why a firm with $30 million in assets and a closed gold mine that is producing no cash flow at all has this kind of market capitalization? Options. This firm has them. MBF, Corporate Finance, 2010 Corporate Finance, 23 Options Discounted Cash Flows and Options We can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project. M = NPV + OPT • A good example would be comparing the desirability of a specialized machine versus a more versatile machine. If they both cost about the same and last the same amount of time, the more versatile machine is more valuable because it comes with options. MBF, Corporate Finance, 2010 Corporate Finance, 23 Options The Option to Abandon: Example Traditional NPV analysis would indicate rejection of the project. Success: PV = $500 ½ Sit on rig; stare at empty hole: PV = $0. Drill − $300 ½ Failure Sell the rig; NPV = $0 salvage value PV = $250 The firm has two decisions to make: drill or not, abandon or stay. Do not drill MBF, Corporate Finance, 2010 Corporate Finance, 23 Options Valuation of the Option to Abandon Recall that we can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project. M = NPV + OPT $75 = -$50 + OPT OPT = $125 MBF, Corporate Finance, 2010 Corporate Finance - chapter 24 - Warrants and Convertibles MBF, Corporate Finance, 2010 Corporate Finance, 24 Warrants & Convertibles 24.1 Warrants Warrants are call options that give the holder the right, but not the obligation, to buy shares of common stock directly from a company at a fixed price for a given period of time. When a warrant is exercised, a firm must issue new shares of stock. This can have the effect of diluting the claims of existing shareholders. MBF, Corporate Finance, 2010 Corporate Finance, 24 Warrants & Convertibles 24.3 Warrant Pricing and the Black-Scholes Model Warrants are worth a bit less than calls due to the dilution. To value a warrant, value an otherwiseidentical call and multiply the call price by: n n + nw Where n = the original number of shares nw = the number of warrants MBF, Corporate Finance, 2010 Corporate Finance, 24 Warrants & Convertibles 24.4 Convertible Bonds A convertible bond is similar to a bond with warrants. The most important difference is that a bond with warrants can be separated into different securities and a convertible bond cannot. The value of a convertible bond has three components: 1. Straight bond value 2. Conversion value 3. Option value MBF, Corporate Finance, 2010 Corporate Finance, 24 Warrants & Convertibles Convertible Bond Example Litespeed, Inc., just issued a zero coupon convertible bond due in 10 years. The conversion ratio is 25 shares. The appropriate interest rate is 10%. The current stock price is $12 per share. Each convertible is trading at $400 in the market. What is the straight bond value? What is the conversion value? What is the option value of the bond? MBF, Corporate Finance, 2010 Corporate Finance, 24 Warrants & Convertibles The Value of Convertible Bonds Convertible Bond Value Convertible bond values Conversion Value floor value Straight bond value floor value = conversion ratio MBF, Corporate Finance, 2010 Option value Stock Price Corporate Finance, 24 Warrants & Convertibles 24.7 What firms issue convertibles and why? Support for these assertions is found in the fact that firms that issue convertible bonds are different from other firms: The bond ratings of firms using convertibles are lower. Convertibles tend to be used by smaller firms with high growth rates and more financial leverage. Convertibles are usually subordinated and unsecured. MBF, Corporate Finance, 2010 Corporate Finance, 24 Warrants & Convertibles 24.8 Conversion Policy Most convertible bonds are also callable. When the bond is called, bondholders have about 30 days to choose between: 1. Converting the bond to common stock at the conversion ratio. 2. Surrendering the bond and receiving the call price in cash. From the shareholder’s perspective, the optimal call policy is to call the bond when its value is equal to the call price. In the real world, most firms wait to call until the bond value is substantially above the call price. Perhaps the firm is afraid of the risk of a sharp drop in stock prices during the 30-day window. MBF, Corporate Finance, 2010 Corporate Finance - chapter 25 - Derivatives, Hedging and Risk MBF, Corporate Finance, 2010 Corporate Finance, 25 Derivatives & Hedging 25.2 Forward Contracts A forward contract specifies that a certain commodity will be exchanged at a specified time in the future at a price specified today. Its not an option: both parties are expected to hold up their end of the deal. If you have ever ordered a textbook that was not in stock, you have entered into a forward contract. Valuation of forward contracts Forward price F0 is equal to delivery price E at initiation but changes over time, so that the value of the contract changes. At initiation the value is zero. PVt = (Ft – E) e-rT MBF, Corporate Finance, 2010 Corporate Finance, 25 Derivatives & Hedging Futures Contracts Standardizing Features Contract Size Delivery Month Daily resettlement Minimizes the chance of default Initial Margin About 4% of contract value Cash or T-bills held in a street name at your brokerage MBF, Corporate Finance, 2010 Corporate Finance, 25 Derivatives & Hedging Selected Futures Contracts Contract Agricultural Contract Size Exchange Corn Wheat Cocoa OJ Metals & Petroleum Copper Gold Unleaded gasoline Financial British Pound Japanese Yen Eurodollar 5,000 bushels 5,000 bushels 10 metric tons 15,000 lbs. Chicago BOT Chicago & KC CSCE CTN 25,000 lbs. 100 troy oz. 42,000 gal. CMX CMX NYM £62,500 ¥12.5 million $1 million IMM IMM LIFFE MBF, Corporate Finance, 2010 Corporate Finance, 25 Derivatives & Hedging 25.4 Hedging Two counterparties with offsetting risks can eliminate risk. For example, if a wheat farmer and a flour mill enter into a forward contract, they can eliminate the risk each other faces regarding the future price of wheat. Hedgers can also transfer price risk to speculators, who absorb price risk from hedgers. Speculating: Long vs. Short MBF, Corporate Finance, 2010 Corporate Finance, 25 Derivatives & Hedging Hedging and Speculating: Example You speculate that copper will go up in price, so you go long 10 copper contracts for delivery in 3 months. A contract is 25,000 pounds in cents per pound and is at $0.70 per pound, or $17,500 per contract. If futures prices rise by 5 cents, you will gain: Gain = 25,000 × .05 × 10 = $12,500 If prices decrease by 5 cents, your loss is: Loss = 25,000 ×( –.05) × 10 = –$12,500 MBF, Corporate Finance, 2010 Corporate Finance, 25 Derivatives & Hedging Hedging: How many contracts? You are a farmer, and you will harvest 50,000 bushels of corn in 3 months. You want to hedge against a price decrease. Corn is quoted in cents per bushel at 5,000 bushels per contract. It is currently at $2.30 cents for a contract 3 months out, and the spot price is $2.05. To hedge, you will sell 10 corn futures contracts: 10 contracts = 50,000 bushels 5,000 bushels per contract Now you can quit worrying about the price of corn and get back to worrying about the weather. MBF, Corporate Finance, 2010 Corporate Finance, 25 Derivatives & Hedging 25.5 Interest Rate Futures Contracts Pricing of Treasury Bonds Pricing of Forward Contracts Futures Contracts Hedging in Interest Rate Futures Corporate Finance, 25 Derivatives & Hedging Pricing of Treasury Bonds Consider a Treasury bond that pays a semiannual coupon of $ C for the next T years: The yield to maturity is R C 0 C C 1 2 3 … C+F 2T Value of the T-bond under a flat term structure = PV of face value + PV of coupon payments F C 1 PV = + 1 − T (1 + R) R (1 + R)T Corporate Finance, 25 Derivatives & Hedging Pricing of Treasury Bonds If the term structure of interest rates is not flat, then we need to discount the payments at different rates depending upon maturity. C 0 C C 1 2 3 … C+F 2T = PV of face value + PV of coupon payments C C C C+F PV = + + + + 2 3 (1 + R1 ) (1 + R2 ) (1 + R3 ) (1 + R2T )T Corporate Finance, 25 Derivatives & Hedging Pricing of Forward Contracts An N-period forward contract on that T-Bond: − Pforward C C C … C+F 0 N N+1 N+2 N+3 N+2T Can be valued as the present value of the forward price. PV = Pforward (1 + RN ) N C C C C+F + + + + 2 3 (1 + RN +1 ) (1 + RN + 2 ) (1 + RN +3 ) (1 + RN + 2T )T PV = (1 + RN ) N Corporate Finance, 25 Derivatives & Hedging 25.7 Swaps Contracts In a swap, two counterparties consent to a contractual arrangement wherein they agree to exchange cash flows at periodic intervals. There are two types of interest rate swaps: Single currency interest rate swap “Plain vanilla” fixed-for-floating swaps are often just called interest rate swaps. Cross-Currency interest rate swap This is often called a currency swap; fixed for fixed rate debt service in two (or more) currencies. MBF, Corporate Finance, 2010 Corporate Finance, 25 Derivatives & Hedging The Swap Bank A swap bank is a generic term to describe a financial institution that facilitates swaps between counterparties. The swap bank can serve as either a broker or a dealer. As a broker, the swap bank matches counterparties but does not assume any of the risks of the swap. As a dealer, the swap bank stands ready to accept either side of a currency swap, and then later lay off their risk, or match it with a counterparty. MBF, Corporate Finance, 2010 Corporate Finance, 25 Derivatives & Hedging An Example of an Interest Rate Swap The borrowing COMPANY opportunities of two firms are: Fixed rate Floating rate BANK A 11.75% 10% LIBOR + .5% LIBOR Swap 10 3/8% B Bank LIBOR – 1/8% Bank A MBF, Corporate Finance, 2010 The swap bank makes this offer to Bank A: You pay LIBOR – 1/8 % per year on $10 million for 5 years, and we will pay you 10 3/8% on $10 million for 5 years Corporate Finance, 25 Derivatives & Hedging An Example of an Interest Rate Swap The swap bank makes ¼% LIBOR – 1/8 – [LIBOR – ¼ ]= 1/8 10 ½ - 10 3/8 = 1/8 Swap 10 3/8% ¼ Bank 10 ½% LIBOR – 1/8% LIBOR – ¼% Bank Company A A saves ½% B Fixed rate Floating rate COMPANY B B saves ½% BANK A 11.75% 10% LIBOR + .5% LIBOR MBF, Corporate Finance, 2010 Corporate Finance, 25 Derivatives & Hedging Pricing a Swap A swap is a derivative security, so it can be priced in terms of the underlying assets: Plain vanilla fixed for floating swap gets valued just like a bond. Corporate Finance, 25 Derivatives & Hedging 25.8 Actual Use of Derivatives Because derivatives do not appear on the balance sheet, they present a challenge to financial economists who wish to observe their use. Survey results appear to support the notion of widespread use of derivatives among large publicly traded firms. Foreign currency and interest rate derivatives are the most frequently used. MBF, Corporate Finance, 2010 Corporate Finance - chapter 26 - Short-Term Finance and Planning Corporate Finance, 26 Short-term financing Tracing Cash and Net Working Capital Current Assets are cash and other assets that are expected to be converted to cash within the year. Cash Marketable securities Accounts receivable Inventory Current Liabilities are obligations that are expected to require cash payment within the year. Accounts payable Accrued wages Taxes MBF, Corporate Finance, 2010 474 Corporate Finance, 26 Short-term financing Balance Sheet Model of the Firm Current Assets Fixed Assets 1. Tangible 2. Intangible Current Liabilities Net Working Capital How much shortterm cash flow does a company need to pay its bills? MBF, Corporate Finance, 2010 Long-Term Debt Shareholders’ Equity 475 Corporate Finance, 26 Short-term financing The Operating Cycle and the Cash Cycle Raw material purchased Finished goods sold Cash received Order Stock Placed Arrives Inventory period Accounts receivable period Time Accounts payable period Firm receives invoice Cash paid for materials Operating cycle MBF, Corporate Finance, 2010 Cash cycle Cash cycle = operating cycle – accounts payable period 476 Corporate Finance, 26 Short-term financing Carrying Costs and Shortage Costs $ Minimum point Total costs of holding current assets. Carrying costs Shortage costs CA* Investment in Current Assets ($) MBF, Corporate Finance, 2010 477 Corporate Finance, 26 Short-term financing Appropriate Flexible Policy $ Minimum point Carrying costs Total costs of holding current assets. Shortage costs CA* Investment in Current Assets ($) MBF, Corporate Finance, 2010 478 Corporate Finance, 26 Short-term financing Appropriate Restrictive Policy $ Minimum point Total costs of holding current assets. Carrying costs Shortage costs CA* Investment in Current Assets ($) MBF, Corporate Finance, 2010 479 Corporate Finance, 26 Short-term financing Cash Budgeting A cash budget is a primary tool of short-run financial planning. Cash Receipts Arise from sales, but we need to estimate when we actually collect Cash Outflow Payments of Accounts Payable Wages, Taxes, and other Expenses Capital Expenditures Long-Term Financial Planning MBF, Corporate Finance, 2010 480 Corporate Finance, 26 Short-term financing Example : cash budgeting Pet Treats Inc. specializes in gourmet pet treats and receives all income from sales Sales estimates (in millions) Q1 = 500; Q2 = 600; Q3 = 650; Q4 = 800; Q1 next year = 550 Accounts receivable Beginning receivables = $250 Average collection period = 30 days Accounts payable Purchases = 50% of next quarter’s sales Beginning payables = 125 Accounts payable period is 45 days Other expenses Wages, taxes and other expense are 30% of sales Interest and dividend payments are $50 A major capital expenditure of $200 is expected in the second quarter The initial cash balance is $80 and the company maintains a minimum balance of $50 MBF, Corporate Finance, 2010 481 Corporate Finance, 26 Short-term financing Example : cash budgeting ACP = 30 days, this implies that 2/3 of sales are collected in the quarter made, and the remaining 1/3 are collected the following quarter. Beginning receivables of $250 will be collected in the first quarter. Q1 Q2 Q3 Q4 Beginning Receivables 250 167 200 217 Sales 500 600 650 800 Cash Collections 583 567 633 750 Ending Receivables 167 200 217 267 MBF, Corporate Finance, 2010 482 Corporate Finance, 26 Short-term financing Example : cash budgeting Payables period is 45 days, so half of the purchases will be paid for each quarter, and the remaining will be paid the following quarter. Beginning payables = $125 Q1 Q2 Q3 Q4 Payment of accounts 275 313 362 338 Wages, taxes and other expenses 150 180 195 240 Capital expenditures 200 Interest and dividend payments MBF, Corporate Finance, 2010 50 50 50 475 Total cash disbursements 50 743 607 628 483 Corporate Finance, 26 Short-term financing Example : cash budgeting Q1 Q2 Q3 Q4 Total cash collections 583 567 633 750 Total cash disbursements 475 743 607 628 Net cash inflow 108 -176 26 122 80 188 12 38 Net cash inflow 108 -176 26 122 Ending cash balance 188 12 38 160 Minimum cash balance -50 -50 -50 -50 Cumulative surplus (deficit) 138 -39 -12 110 Beginning Cash Balance The company will need to access a line of credit or borrow short-term to pay for the short-fall in quarter 2, but should be able to clear up the line of credit in quarter 4. MBF, Corporate Finance, 2010 484 Corporate Finance, 26 Short-term financing Chapter 26 – problem Cash Budget: important figures from the budget of Cornell Inc. for the second quarter of 2007. April May June Credit sales 380,000 396,000 438,000 Credit purchases 147,000 175,500 200,500 Wages, taxes & expenses 39,750 48,210 50,300 Interest 11,400 11,400 11,400 Equipment purchases 83,000 91,000 0 The company predicts that 5% of its credit sales will never be collected, 35% of its sales will be collected in the month of the sale, and the remaining 60% will be collected in the following month. Credit purchases will be paid in the month following the purchase. In March 2007, credit sales were 210,000, and credit purchases were 156,000. Using this information, complete the following cash budget. April Begin cash balance May June 280,000 Cash receipts (Cash collections from credit sales, total cash available) Cash disbursements (Wages, taxes & expenses; Interest; Equipment purchases; Total) Ending cash balance MBF, Corporate Finance, 2010 485 Corporate Finance - chapter 27 - Cash Management Corporate Finance, 27 Cash management Determining the Target Cash Balance Reasons for Holding Cash Transactions motive Ability to cover normal activities of the firm Compensating balances Hold required balances with financial institutions Target Cash Balance The Baumol Model The Miller-Orr Model Other Factors Influencing the Target Cash Balance MBF, Corporate Finance, 2010 487 Corporate Finance, 27 Cash management Costs of Holding Cash Costs in dollars of holding cash Trading costs increase when the firm must sell securities to meet cash needs. Total cost of holding cash Opportunity Costs The investment income foregone when holding cash. Trading costs C* Size of cash balance MBF, Corporate Finance, 2010 488 Corporate Finance, 27 Cash management The Baumol Model F = The fixed cost of selling securities to raise cash T = The total amount of new cash needed If we start with $C, R = The opportunity cost of holding spend at a constant rate cash, a.k.a. the interest rate. each period and replace our cash with $C when we run out of cash, our average cash balance C will be – . 2 C C – 2 1 2 3 Time The opportunity cost C C of holding – is – ×R 2 2 MBF, Corporate Finance, 2010 489 Corporate Finance, 27 Cash management The Baumol Model As we transfer $C each period we incur a trading cost of F each period. C C – 2 1 2 3 If we need $T in total over the planning T period we will pay $F – C times. T The trading cost is – × F Time C MBF, Corporate Finance, 2010 490 Corporate Finance, 27 Cash management The Baumol Model C T Total cost = × R + × F 2 C Opportunity Costs C ×R 2 T Trading costs × F C C* 2T C= ×F R * Size of cash balance The optimal cash balance is found where the opportunity costs equals the trading costs MBF, Corporate Finance, 2010 491 Corporate Finance, 27 Cash management The Miller-Orr Model The firm allows its cash balance to wander randomly between upper and lower control limits. $ When the cash balance reaches the upper control limit U, cash is invested elsewhere to get us to the target cash balance Z. U Z When the cash balance reaches the lower control limit, L, investments are sold to raise cash to get us up to the target cash balance. L Time MBF, Corporate Finance, 2010 492 Corporate Finance, 27 Cash management Seasonal Cash Demands Total Financing needs Bank loans Marketable securities Short-term financing Long-term financing J F M A MBF, Corporate Finance, 2010 M Time 493 Corporate Finance, 27 Cash management Chapter 27 - problem Baumol: A corporation has determined that its target cash balance if it uses the Baumol model is 2,200. The total cash needed for the year is 21,000, and the order cost is 10. What interest rate must the corporation be using? MBF, Corporate Finance, 2010 494 Corporate Finance - chapter 28 - Credit Management Corporate Finance, 28 Credit management The Cash Flows of Granting Credit Credit sale is made Customer mails check Firm deposits check Bank credits firm’s account Time Cash collection Accounts receivable MBF, Corporate Finance, 2010 496 Corporate Finance, 28 Credit management The Interest Rate Implicit in 3/10, net 30 A firm offering credit terms of 3/10, net 30 is essentially offering their customers a 20-day loan. To see this, consider a firm that makes a $1,000 sale on day 0. • Some customers will pay on day 10 and take the discount. $970 0 • 10 30 Other customers will pay on day 30 and forgo the discount. $1,000 0 10 30 MBF, Corporate Finance, 2010 497 Corporate Finance, 28 Credit management The Interest Rate Implicit in 3/10, net 30 A customer that forgoes the 3% discount to pay on day 30 is borrowing $970 for 20 days and paying $30 interest: –$1,000 +$970 0 10 30 $1,000 $970 = (1 + R) 20 365 $1,000 R= $970 365 20 (1 + R) 20 365 $1,000 = $970 − 1 = 0.7435 = 74.35% MBF, Corporate Finance, 2010 498 Corporate Finance, 28 Credit management The Decision to Grant Credit: Risk and Information Consider a firm that is choosing between two alternative credit policies: “In God we trust—everybody else pays cash.” Offering their customers credit. • The only cash flow of the first strategy is: Q0 ×(P0 – C0) MBF, Corporate Finance, 2010 499 Corporate Finance, 28 Credit management The Decision to Grant Credit: Risk and Information The expected cash flows of the credit strategy are: h × Q′ × P0′ 0 ′ –C0 × Q0′ 0 We incur costs up front… 1 …and get paid in 1 period by h% of our customers. MBF, Corporate Finance, 2010 500 Corporate Finance, 28 Credit management The Decision to Grant Credit: Risk and Information • The NPV of the cash only strategy is: NPVcash = Q0 × (P0 – C0) • The NPV of the credit strategy is: ′ NPVcredit = –C0 × Q0′ • + h × Q′ × P0′ 0 (1 + RB) The decision to grant credit depends on four factors: The delayed revenues from granting credit: P’ 0 × Q’0 The immediate costs of granting credit: C’ 0 × Q’0 The probability of repayment: h The discount rate: RB MBF, Corporate Finance, 2010 501 Corporate Finance, 28 Credit management Example of the Decision to Grant Credit A firm currently sells 1,000 items per month on a cash basis for $500 each. If they offered terms net 30, the marketing department believes that they could sell 1,300 items per month. The collections department estimates that 5% of credit customers will default. The cost of capital is 10% per annum. MBF, Corporate Finance, 2010 502 Corporate Finance, 28 Credit management Example of the Decision to Grant Credit No Credit Net 30 Quantity sold 1,000 1,300 Selling price $500 $500 Unit cost $400 $425 Probability of payment 100% 95% 0 30 Credit period (days) Discount rate per annum 10% MBF, Corporate Finance, 2010 503 Corporate Finance, 28 Credit management Example of the Decision to Grant Credit The NPV of cash only = 1,000×($500 – $400) = $100,000 The NPV of Net 30: 1,300×$500×0.95 –1,300×$425 + = $60,181.58 30/365 (1.10) MBF, Corporate Finance, 2010 504 Corporate Finance, 28 Credit management Example of the Decision to Grant Credit How high must the credit price be to make it worthwhile for the firm to extend credit? The NPV of Net 30 must be at least as big as the NPV of cash only: 1,300 × P0' × 0.95 $100,000 = −1,300 × $425 + (1.10) 30 / 365 ($100,000 + 1,300 × $425) × (1.10) 30 / 365 = 1,300 × P0' × 0.95 ($100,000 + 1,300 × $425) × (1.10) 30 / 365 P0' = = $532.50 1,300 × 0.95 MBF, Corporate Finance, 2010 505 Corporate Finance, 28 Credit management The Value of New Information about Credit Risk The most that we should be willing to pay for new information about credit risk is the present value of the expected cost of defaults: $0 ′ NPV default = –C0 × Q0′ × (1 – h) + (1 + RB) ′ NPV default = –C0 × Q0′ × (1 – h) • In our earlier example, with a credit price of $500, we would be willing to pay $27,625 for a perfect credit screen. ′ C 0 × Q0 ′ × (1 – h) = $425×1,300×(1 – 0.95) = $27,625 MBF, Corporate Finance, 2010 506 Corporate Finance, 28 Credit management Future Sales and the Credit Decision We face a more certain credit decision with our paying customers: Information is revealed at the end of the first period: Give credit Customer pays (Probability = h) Give credit Our first decision: Customer pays h = 100% Do not give credit Customer defaults (Probability = 1– h) Do not We refuse further sales give credit to deadbeats. MBF, Corporate Finance, 2010 507 Corporate Finance, 28 Credit management Optimal Credit Policy Costs in dollars Total costs Carrying Costs Opportunity costs C* Level of credit extended At the optimal amount of credit, the incremental cash flows from increased sales are exactly equal to the carrying costs from the increase in accounts receivable. MBF, Corporate Finance, 2010 508 Corporate Finance, 28 Credit management Credit Analysis Credit Information Financial Statements Credit Reports on Customer’s Payment History with Other Firms Banks Customer’s Payment History with the Firm Credit Scoring: The traditional 5 C’s of credit Character, Capacity, Capital, Collateral, Conditions Some firms employ sophisticated statistical models MBF, Corporate Finance, 2010 509 Corporate Finance, 28 Credit management Factoring The sale of a firm’s accounts receivable to a financial institution (known as a factor) The firm and the factor agree on the basic credit terms for each customer. Customers send payment to the factor. Customer Factor The factor pays an agreedupon percentage of the accounts receivable to the firm. The factor bears the risk of nonpaying customers. Goods MBF, Corporate Finance, 2010 Firm 510 Corporate Finance, 28 Credit management Chapter 28 - problem Simba Inc. Operates a mail-order running shoe business. Management is considering dropping its policy of no credit. The credit policy under consideration is as follows Current policy New policy Price per unit £ 98 £ 98 Cost per unit £ 98 £ 98 Quantity sold 2,000 3,000 Probability of payment 100% 85% 0 1 Credit period A. if the interest rate is 3% per period, should the company offer credit to its customers? B. what must the probability of payment be before the company would adopt the policy? MBF, Corporate Finance, 2010 511 Corporate Finance - chapter 29 - Mergers and Acquisitions The Basic Forms of Acquisitions Corporate Finance, 29 M&A Merger : stockholders of both firms approve merger by vote Acquiring firm retains name and acquired firm ceases to exist Is legally simple, but must be approved by stockholders of both firms Consolidation: entirely new firm is created from merging firms Acquisition: A firm acquires another firm by purchasing voting shares Tender offer – public offer to buy shares Mostly Classifications Horizontal – both firms are in the same industry Vertical – firms are in different stages of the production process Conglomerate – firms are unrelated MBF, Corporate Finance, 2010 513 Corporate Finance, 29 M&A Varieties of Takeovers Merger Acquisition Takeovers Acquisition of Stock Proxy Contest Acquisition of Assets Going Private (LBO) MBF, Corporate Finance, 2010 514 Corporate Finance, 29 M&A Synergy Suppose firm A is contemplating acquiring firm B. The synergy from the acquisition is Synergy = VAB – (VA + VB) The synergy of an acquisition can be determined from the standard discounted cash flow model: Σ T Synergy = t=1 ∆ CFt (1 + r)t ∆ CFt = ∆ Incremen Revenuet - ∆ Costst - ∆ Taxest - ∆ Capit requirementst MBF, Corporate Finance, 2010 515 Two “Bad” Reasons for Mergers Corporate Finance, 29 M&A Earnings Growth If there are no synergies or other benefits to the merger, then the growth in EPS is just an artifact of a larger firm and is not true growth (i.e., an accounting illusion). Diversification Shareholders who wish to diversify can accomplish this at much lower cost with one phone call to their broker than can management with a takeover. The Base Case: if two all-equity firms merge, there is no transfer of synergies to bondholders, but if… Both Firms Have Debt : the value of the levered shareholder’s call option falls. Can Shareholders Reduce their Losses from the Coinsurance Effect? Retire debt pre-merger and/or increase post-merger debt usage. MBF, Corporate Finance, 2010 516 The NPV of a Merger Corporate Finance, 29 M&A The analysis is straightforward with a cash offer. The NPV of a cash acquisition is: NPV = (V + ΔV) – cash cost = V * – cash cost B B Value of the combined firm is: V AB = VA + (VB* – cash cost) Value of combined firm in stock acquisition VAB = VA + VB + ∆ V Cost of acquisition Depends on the number of shares given to the target stockholders and the price of the combined firm’s stock after the merger Considerations when choosing between cash and stock Sharing gains – target stockholders do not participate in stock price appreciation with a cash acquisition Taxes – cash acquisitionsBF, Corporate Finance, 2010 M are generally taxable 517 Control – cash acquisitions do not dilute control Corporate Finance, 29 M&A Friendly vs. Hostile Takeovers In a friendly merger, both companies’ management are receptive. In a hostile merger, the acquiring firm attempts to gain control of the target without their approval. Tender offer Proxy fight MBF, Corporate Finance, 2010 518 Corporate Finance, 29 M&A Defensive Tactics Classified board (i.e., staggered elections) Supermajority voting requirement Golden parachutes Targeted repurchase (a.k.a. greenmail) Standstill agreements Poison pills (share rights plans) Leveraged buyouts Corporate charter Poison put Crown jewel White knight Lockup Shark repellent Bear hug Fair price provision Dual class capitalization Countertender offer MBF, Corporate Finance, 2010 519 Do Mergers Add Value? Corporate Finance, 29 M&A Shareholders of target companies tend to earn excess returns in a merger: Shareholders of target companies gain more in a tender offer than in a straight merger. Target firm managers have a tendency to oppose mergers, thus driving up the tender price. Empirically, most acquisitions fail to create value for the acquirer. The main reason why they do not work, lies in failures to integrate two companies after a merger. Intellectual capital often walks out the door when acquisitions are not handled carefully. Traditionally, acquisitions deliver value when they allow for scale economies or market power, better products and services in the market, or learning from the new firms. MBF, Corporate Finance, 2010 520 Corporate Finance, 29 M&A The Tax Forms of Acquisition If it is a taxable acquisition, selling shareholders need to figure their cost basis and pay taxes on any capital gains. If it is not a taxable event, shareholders are deemed to have exchanged their old shares for new ones of equivalent value. MBF, Corporate Finance, 2010 521 Corporate Finance, 29 M&A Accounting for Acquisitions The Purchase Method Assets of the acquired firm are reported at their fair market value. Any excess payment above the fair market value is reported as “goodwill.” Historically, goodwill was amortized. Now it remains on the books until it is deemed “impaired.” MBF, Corporate Finance, 2010 522 Corporate Finance, 29 M&A Going Private and Leveraged Buyouts The existing management buys the firm from the shareholders and takes it private. If it is financed with a lot of debt, it is a leveraged buyout (LBO). The extra debt provides a tax deduction for the new owners, while at the same time turning the pervious managers into owners. This reduces the agency costs of equity. MBF, Corporate Finance, 2010 523 Corporate Finance, 29 M&A Divestitures Divestiture – company sells a piece of itself to another company Equity carve-out – company creates a new company out of a subsidiary and then sells a minority interest to the public through an IPO Spin-off – company creates a new company out of a subsidiary and distributes the shares of the new company to the parent company’s stockholders MBF, Corporate Finance, 2010 524 Corporate Finance, 29 M&A The Winner's Curse in M&A Between 1991 and 2001, shareholders of acquiring firms lost $216 billion, thereby experiencing the winner's curse. Disproportionate share traced to very large losses by a few acquirers during the period 1998 through 2001. Many of the large loss acquirers had been active acquirers prior to their large loss acquisitions, and the market values of their firms had been increasing. Source: Shefrin, H., 2007, Behavioral Corporate Finance MBF, Corporate Finance, 2010 525 Asset Writedown to reflect the decline in the value of the combined firm. In the previous 12 months, the operating profit for most AOL Time Warner businesses experienced positive growth. But its AOL business fell 30%. AOL Time Warner Market Capitalization Jan 2001 - Dec 2002 $300.00 $250.00 $200.00 $150.00 $100.00 $50.00 Date 12/12/2002 11/12/2002 10/12/2002 9/12/2002 8/12/2002 7/12/2002 MBF, Corporate Finance, 2010 6/12/2002 5/12/2002 4/12/2002 3/12/2002 2/12/2002 1/12/2002 12/12/2001 11/12/2001 10/12/2001 9/12/2001 8/12/2001 7/12/2001 6/12/2001 5/12/2001 4/12/2001 3/12/2001 2/12/2001 $0.00 1/12/2001 $ (Billions) Corporate Finance, 29 M&A In April 2002, AOL Time Warner wrote down $54 billion in goodwill, Source: Shefrin, H., 2007, Behavioral Corporate Finance 526 $2.5bn Net Synergies After-Tax Net Synergies (26% tax rate) Future Value of Net Synergies at 20x P/E Present Value of Net Synergies at 20x P/E $2.0bn Synergies Impact of Revenue Loss $1.5bn $29.4bn $21.2bn ($0.5)bn Cumulative Returns H-P, IBM, Dell, S&P 500 May 2002 - January 2005 1.8 Dell 1.6 1.4 1.2 1 $ 0.8 S&P 500 H-P 0.6 IBM 0.4 0.2 Jan-05 Dec-04 Oct-04 Nov-04 Sep-04 Jul-04 Aug-04 Jun-04 Apr-04 May-04 Mar-04 Jan-04 Feb-04 Dec-03 Oct-03 Nov-03 Sep-03 Jul-03 Aug-03 Jun-03 Apr-03 May-03 Mar-03 Jan-03 Feb-03 Dec-02 Oct-02 Nov-02 Sep-02 Jul-02 Aug-02 Jun-02 0 May-02 Corporate Finance, 29 M&A Valuation Before and After Date MBF, Corporate Finance, 2010 Source: Shefrin, H., 2007, Behavioral Corporate Finance 527 Chapter 29 – problem Corporate Finance, 29 M&A Plant is considering making an offer to purchase Palmer. Plant’s vice president of finance has collected the following information: Plant Palmer P/E ratio 550,000 $2,000,000 $580,000 Dividends 1,000,000 Earnings 9 Shares outstanding 12.5 $600,000 $290,000 Plant expects earnings and dividends of Palmer to grow 5% per year, an acquisition by Plant increases this growth rate to 7%. A. What is the value of Palmer to Plant? B. What would Plant’s gain be from this acquisition? C. if Plant offers $18 in cash per share of Palmer, what is the NPV of the acquisition? D. what is th emost Plant should be willing to pay in cash per share for the stock of Palmer? E. if Plant offers 110,000 shares in exchange for Palmer outstanding stock, what is the NPV? F. shoud the acquisition be attempted? If so, should it be as in (C) or as in (E)? G. If Plant’s growth perspectives of Palmer decrease from 7% to 6%. What is the effect on (F)? MBF, Corporate Finance, 2010 528 Corporate Finance - chapter 30 - Financial Distress Corporate Finance, 30 Financial Distress What Is Financial Distress? Financial distress is a situation where a firm’s operating cash flows are not sufficient to satisfy current obligations, and the firm is forced to take corrective action. Financial distress may lead a firm to default on a contract, and it may involve financial restructuring between the firm, its creditors, and its equity investors. MBF, Corporate Finance, 2010 530 Corporate Finance, 30 Financial Distress Insolvency Stock-base insolvency: the value of the firm’s assets is less than the value of the debt. Solvent firm Insolvent firm Debt Assets Assets Debt Equity Debt Equity Note the negative equity MBF, Corporate Finance, 2010 531 Corporate Finance, 30 Financial Distress Insolvency Flow-base insolvency occurs when the firms cash flows are insufficient to cover contractually required payments. $ Cash flow shortfall Contractual obligations Firm cash flow Insolvency MBF, Corporate Finance, 2010 time 532 Corporate Finance, 30 Financial Distress Largest U.S. Bankruptcies Firm Liabilities (in $ mio) Conseco Inc. $56,639.30 December 2002 Worldcom Inc. 45,984.00 July 2002 Enron Corp. 31,237.00 December 2001 Delta Air Lines 28,546.00 September 2005 Pacific Gas & Electric Co. 25,717.00 April 2001 MBF, Corporate Finance, 2010 Date 533 Corporate Finance, 30 Financial Distress What Happens in Financial Distress? No financial restructuring 49% Private workout Financial distress 51% 47% Financial restructuring 53% Reorganize and emerge 83% Legal bankruptcy Chapter 11 7% Merge with another firm 10% Source: Karen H. Wruck, “Financial Distress: Reorganization and Organizational Efficiency,” Journal of Financial Economics MBF,(1990), Figure 2010 27 Corporate Finance, 2. Liquidation 534 Corporate Finance, 30 Financial Distress Responses to Financial Distress Think of the two sides of the balance sheet. Asset Restructuring: Selling major assets Merging with another firm Reducing capital spending and R&D spending Financial Restructuring: Issuing new securities Negotiating with banks and other creditors Exchanging debt for equity Filing for bankruptcy MBF, Corporate Finance, 2010 535 Corporate Finance, 30 Financial Distress Bankruptcy Liquidation and Reorganization Firms that cannot meet their obligations have two choices: liquidation or reorganization. Liquidation (Chapter 7) means termination of the firm as a going concern. It involves selling the assets of the firm for salvage value. The proceeds, net of transactions costs, are distributed to creditors in order of priority. Reorganization (Chapter 11) is the option of keeping the firm a going concern. Reorganization sometimes involves issuing new securities to replace old ones. MBF, Corporate Finance, 2010 536 Corporate Finance, 30 Financial Distress Bankruptcy Liquidation: Priority of Claims Liquidation proceeds are distributed in order of priority: 1. Administration expenses associated with liquidation 2. Unsecured claims arising after the filing of an involuntary bankruptcy petition 3. Wages earned within 90 days before the filing date, not to exceed $2,000 per claimant 4. Contributions to employee benefit plans arising with 180 days before the filing date 5. Consumer claims, not exceeding $900 6. Tax claims 7. Secured and unsecured creditors’ claims 8. Preferred stockholders’ claims 9. Common stockholders’ claims MBF, Corporate Finance, 2010 537 Corporate Finance, 30 Financial Distress Absolute Priority Rule in Practice The APR states that senior claims are fully satisfied before junior claims receive anything. Deviations from APR Equityholders Unsecured creditors Secured creditors Expectation: No payout Reality: Payout in 81% of cases Expectation: Full payout after secured creditors Reality: Violation in 78% of cases Expectation: Full payout Reality: Full payout in 92% of cases MBF, Corporate Finance, 2010 538 Corporate Finance, 30 Financial Distress Bankruptcy Reorganization: Chapter 11 A typical sequence: 1. A voluntary petition or an involuntary petition is filed. 2. A federal judge either approves or denies the petition. 3. In most cases the debtor continues to run the business. 4. The firm is given 120 days to submit a reorganization plan. 5. Creditors and shareholders are divided into classes. Requires only approval by 1/2 of creditors owning 2/3 of outstanding debt. 6. After acceptance by the creditors, the plan is confirmed by the court. 7. Payments in cash, property, and securities are made to creditors and shareholders. MBF, Corporate Finance, 2010 539 Corporate Finance - chapter 31 - International Corporate Finance Corporate Finance, 31 International CF Terminology American Depository Receipt (ADR): a security issued in the U.S. to represent shares of a foreign stock Cross rate: the exchange rate between two foreign currencies, e.g., the exchange rate between £ and ¥ Eurobonds: bonds denominated in a particular currency and issued simultaneously in the bond markets of several countries Eurocurrency: money deposited in a financial center outside the home country. Eurodollars are dollar deposits held outside the U.S.; Euroyen are yen denominated deposits held outside Japan. Foreign bonds: bonds issued in another nation’s capital market by a foreign borrower Gilts: British and Irish government securities LIBOR: the London Interbank Offer Rate is the rate most international banks charge one another for loans of Eurodollars overnight in the London market MBF, Corporate Finance, 2010 541 Corporate Finance, 31 International CF Foreign Exchange Markets Participants Without a doubt, the foreign exchange market is the world’s largest financial market. The FOREX market is a two-tiered market: Interbank Market (Wholesale) About 700 banks worldwide stand ready to make a market in Foreign exchange. Nonbank dealers account for about 20% of the market. There are FX brokers who match buy and sell orders but do not carry inventory and FX specialists. Client Market (Retail) Market participants include international banks, their customers, nonbank dealers, FOREX brokers, and central banks. MBF, Corporate Finance, 2010 542 Corporate Finance, 31 International CF Exchange Rates The price of one country’s currency in terms of another. Most currency is quoted in terms of dollars. Consider the following quote: (2008-11-28) Euro 1.2692 .7879 The two numbers are reciprocals of each other (1€/1.2692$ = .7879) http://pacific.commerce.ubc.ca/datacentre.html MBF, Corporate Finance, 2010 543 Corporate Finance, 31 International CF Cross Rates Suppose that S£(0) = 2 i.e., $2 = £1 in the spot market and that S¥(0) = 100 i.e., $1 = ¥100 What must the £/¥ cross rate be? £$£ since = × , ¥¥$ £ $1 £1 £1 = × = = ¥ ¥100 $2 ¥200 ⇒ S £ / ¥ (0) = .005 or £1 = ¥200 MBF, Corporate Finance, 2010 544 Corporate Finance, 31 International CF Triangular Arbitrage Suppose we observe these banks posting these exchange rates. First calculate the implied cross rates to see if an arbitrage exists. The implied S(¥/£) cross rate is S(¥/£) = 80 £1.50 $1 £1 × = $1 ¥120 ¥80 How can we make money? $ Barclays S¥(0) = 120 Credit Lyonnais S£(0) = 1.50 ¥ £ Credit Agricole S¥/£(0) = 85 MBF, Corporate Finance, 2010 545 Corporate Finance, 31 International CF Absolute Purchasing Power Parity Price of an item is the same regardless of the currency used to purchase it. Requirements for absolute PPP to hold: Transaction costs are zero No barriers to trade (no taxes, tariffs, etc.) No difference in the commodity between locations For most goods, Absolute PPP rarely holds in practice. MBF, Corporate Finance, 2010 546 Corporate Finance, 31 International CF Relative Purchasing Power Parity Provides information about what causes changes in exchange rates. The basic result is that exchange rates depend on relative inflation between countries: E(St ) = S0[1 + (hFC – hUS)]t Because absolute PPP does not hold for many goods, we will focus on relative PPP from here on out. MBF, Corporate Finance, 2010 547 Corporate Finance, 31 International CF Example : Relative PPP Suppose the Canadian spot exchange rate is 1.18 Canadian dollars per U.S. dollar. U.S. inflation is expected to be 3% per year, and Canadian inflation is expected to be 2%. Do you expect the U.S. dollar to appreciate or depreciate relative to the Canadian dollar? Since inflation is higher in the U.S., we would expect the U.S. dollar to depreciate relative to the Canadian dollar. What is the expected exchange rate in one year? E(S ) = 1.18[1 + (.02 - .03)]1 = 1.1682 1 MBF, Corporate Finance, 2010 548 Corporate Finance, 31 International CF Interest Rate Parity IRP is an arbitrage condition. If IRP did not hold, then it would be possible for an astute trader to make unlimited amounts of money exploiting the arbitrage opportunity. Since we do not typically observe persistent arbitrage conditions, we may assume that IRP holds. MBF, Corporate Finance, 2010 549 Corporate Finance, 31 International CF IRP and Covered Interest Arbitrage A trader with $1,000 to invest could invest in the U.S., in one year his investment will be worth $1,071 = $1,000× (1+ i$) = $1,000× (1.071) Alternatively, this trader could: 1. exchange $1,000 for £800 at the prevailing spot rate, (note that £800 = $1,000÷$1.25/£) 2. invest £800 at i£ = 11.56% for one year to achieve £892.48. 3. Translate £892.48 back into dollars at F£(360) = $1.20/£, the £892.48 will be exactly $1,071. MBF, Corporate Finance, 2010 550 Corporate Finance, 31 International CF IRP and Covered Interest Arbitrage A trader with $1,000 to invest: Can invest in the U.S. In one year his investment will be worth $1,071 = $1,000× (1.071) = $1,000× (1+ i$) MBF, Corporate Finance, 2010 551 Corporate Finance, 31 International CF IRP and Covered Interest Arbitrage $1.25 £800= $1,000× £1 $1,000 Domestic FV = $1,071 and British FV = $1,071 £800 Invest £800 at i£ = 11.56% In one year £800 will be worth £892.48 = $1,000× (1+ i£) Bring it on back to the U.S.A. $1.20 $1,071 = £892.48 × £1 MBF, Corporate Finance, 2010 552 Corporate Finance, 31 International CF Reasons for Deviations from IRP Transactions Costs The interest rate available to an arbitrageur for borrowing, ib,may exceed the rate he can lend at, il. There may be bid-ask spreads to overcome, Fb/Sa < F/S Thus (Fb/Sa)(1 + i¥l) − (1 + i¥ b) ≤ 0 Capital Controls Governments sometimes restrict import and export of money through taxes or outright bans. MBF, Corporate Finance, 2010 553 Corporate Finance, 31 International CF International Fisher Effect The International Fisher Effect (h is the inflation rate): Rhome currency – hhc = Rforeign currency – hfc The International Fisher Effect tells us that the real rate of return must be equal across countries. If it is not, investors will move their money to the country with the higher real rate of return. MBF, Corporate Finance, 2010 554 Corporate Finance, 31 International CF International Capital Budgeting Home Currency Approach Estimate cash flows in foreign currency Estimate future exchange rates using UIP Uncovered Interest Parity: E[St] = [1 + (Rforeign + Rhome) ]t Convert future cash flows to dollars Discount using domestic required return Foreign Currency Approach Estimate cash flows in foreign currency Use the IFE to convert domestic required return to foreign required return Discount using foreign required return Convert NPV to dollars using current spot rate MBF, Corporate Finance, 2010 555 Corporate Finance, 31 International CF Home Currency Approach Your company is looking at a new project in Mexico. The project will cost 9 million pesos. The cash flows are expected to be 2.25 million pesos per year for 5 years. The current spot exchange rate is 9.08 pesos per dollar. The risk-free rate in the US is 4%, and the risk-free rate in Mexico 8%. The dollar required return is 15%. Should the company make the investment? MBF, Corporate Finance, 2010 556 Corporate Finance, 31 International CF Foreign Currency Approach Use the same information as the previous example to estimate the NPV using the Foreign Currency Approach Mexican inflation rate from the International Fisher Effect is 8% - 4% = 4% Required Return = 15% + 4% = 19% PV of future cash flows = 6,879,679 NPV = 6,879,679 – 9,000,000 = -2,120,321 pesos NPV = -2,120,321 / 9.08 = -233,516 MBF, Corporate Finance, 2010 557 Corporate Finance, 31 International CF Chapter 31 – problems 1: You observe that the inflation rate in the US is 3.5% per year and that T-bills currently yield 3.9% annually. What do you estimate the inflation rate to be in A. Australia if short-term Australian government securities yield 5% per year? B. Canada if short-term Canadian government securities yield 7% per year? C. Taiwan if short-term Taiwanese government securities yield 10% per year? 2: LE Inc has an investment opportunity in Europe. The project costs €12 million and is expected to produce cash flows of €2.7 million in year 1, €3.5 million in year 2, and €3.3 million in year 3. The current spot exchange rate is $1.22/€ and the current risk-free rate in the US is 4.8%, compared to that in Europe of 4.1%. The appropriate discount rate for the project is estimated to be 13%, the US cost of capital for the company. In addition, the subsidiary can be sold at the end of three years for an estimated €7.4 million. What is the NPV of the project? MBF, Corporate Finance, 2010 558 ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online