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FIN374 Ch 29

# FIN374 Ch 29 - 19878_29W_p001-034.qxd 4:30 PM Page 1 Basic...

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29 CHAPTER 29W-1 Basic Financial Tools: A Review IMAGE: © GETTY IMAGES, INC., PHOTODISC COLLECTION The building blocks of finance include the time value of money, risk and its relationship with rates of return, and stock and bond valuation models. These topics are covered in introductory finance courses, but because of their fundamental importance, we review them in this Web chapter. 1 TIME VALUE OF MONEY Time value concepts, or discounted cash flow analysis, underlie virtually all the important topics in financial management, including stock and bond valuation, capital budgeting, cost of capital, and the analysis of financing vehicles such as convertibles and leasing. Therefore, an understanding of time value concepts is essential to anyone studying financial management. Future Values An investment of PV dollars today at an interest rate of i percent for n periods will grow over time to some future value (FV). The following time line shows how this growth occurs: 1 This review is limited to material that is necessary to understand the chapters in the main text. For a more detailed treatment of risk, return, and valuation models, see Chapters 2 through 5. For a more detailed review of time value of money concepts, see Web Chapter 28. = FV 2 (1 + i) = FV 1 (1 + i) = PV(1 + i) 0i %1 n – 1 PV FV 1 FV 2 FV 3 FV n – 1 FV n n = FV n – 2 (1 + i) = FV n – 1 (1 + i) 2 3 19878_29W_p001-034.qxd 3/14/06 4:30 PM Page 1

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29W-2 Web Chapter 29 Basic Financial Tools: A Review 2 See the Web Extension to Chapter 5 for a derivation of the sum of a geometric series. 3 An annuity in which payments are made at the start of the period is called an annuity due. The future value interest factor of an annuity due is (1 ± i)FVIFA i,n . This process is called compounding, and it can be expressed with the following equation: FV n ² PV(1 ± i) n ² PV(FVIF i,n ) | 29-1 | The term FVIF i,n is called the future value interest factor. The future value of a series of cash flows is the sum of the future values of the individual cash flows. An ordinary annuity has equal payments, with symbol PMT, that occur at the end of each period, and its future value (FVA n ) is found as follows: 01 n – 1 n 2 PMT PMT PMT PMT PMT 3 | 29-2 | ² PMT(FVIFA i,n ) The second and third forms of Equation 29-2 represent more convenient ways to solve the equation set forth in the first row. 2 The term FVIFA i,n is called the future value interest factor for an annuity at i percent for n periods. 3 Here are some applications of these concepts. First, consider a single payment, or lump sum, of \$500 made today. It will earn 7 percent per year for 25 years. This \$500 present value will grow to \$2,713.72 after 25 years: Future value ² \$500(1 ± 0.07) 25 ² \$500(5.42743) ² \$2,713.72 | 29-1a | Now suppose we have an annuity with 25 annual payments of \$500 each, starting a year from now, and the interest rate is 7 percent per year. The future value of the annuity is \$31,624.52: | 29-2a | A financial calculator could be used to solve this problem. On most calcula- tors, the N button is for the number of periods. We recommend setting the calcu- lator to one period per year, with payments occurring at the end of the year. The I
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FIN374 Ch 29 - 19878_29W_p001-034.qxd 4:30 PM Page 1 Basic...

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