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FM11_Ch_02_Study_Guide

# FM11_Ch_02_Study_Guide - CHAPTER 2 TIME VALUE OF MONEY...

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C HAPTER 2 T IME V ALUE OF M ONEY OVERVIEW A dollar in the hand today is worth more than a dollar to be received in the future because, if you had it now, you could invest that dollar and earn interest. Of all the techniques used in finance, none is more important than the concept of time value of money, also called discounted cash flow (DCF) analysis. Future value and present value techniques can be ap- plied to a single cash flow (lump sum), ordin- ary annuities, annuities due, and uneven cash flow streams. Future and present values can be calculated using, a regular calculator, a cal- culator with financial functions, or a spread- sheet program. When compounding occurs more frequently than once a year, the effect- ive rate of interest is greater than the quoted rate. OUTLINE Time lines are used to help visualize what is happening in time value of money problems. Cash flows are placed directly below the tick marks, and interest rates are shown directly above the time line; unknown cash flows are indicated by a symbol for the particular item that is missing. Thus, to find the future value of \$100 after 5 years at 5 percent interest, the following time line can be set up: Time: 0 5% 1 2 3 4 5 | | | | | | Cash flows: -100 FV 5 = ? Finding the future value (FV), or compounding, is the process of going from today's values (or present values) to future amounts (or future values). It can be calculated as FV n = PV(1 + i) n = PV(FVIF i,n ), where PV = present value, or beginning amount; i = interest rate per year; and n = number of periods involved in the analysis. FVIF i,n , the Future Value Interest Factor, is a short- hand way of writing the equation. This equation can be solved in one of three ways: nu- merically with a regular calculator, with a financial calculator, or with a spreadsheet pro-

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TIME VALUE OF MONEY 2 - 2 gram. For calculations, assume the following data that were presented in the time line above: present value (PV) = \$100, interest rate (i) = 5%, and number of years (n) = 5. To solve numerically, use a regular calculator to find 1 + i = 1.05 raised to the fifth power, which equals 1.2763. Multiply this figure by PV = \$100 to get the final answer of FV = \$127.63 5 . With a financial calculator, the future value can be found by using the time value of money input keys, where N = number of periods, I = interest rate per period, PV = present value, PMT = payment, and FV = future value. By entering N = 5, I = 5, PV = -100, and PMT = 0, and then pressing the FV key, the answer 127.63 is displayed. Some financial calculators require that all cash flows be designated as either in- flows or outflows, thus an outflow must be entered as a negative number (for ex- ample, PV = -100 instead of PV = 100). Some calculators require you to press a “Compute” key before pressing the FV
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FM11_Ch_02_Study_Guide - CHAPTER 2 TIME VALUE OF MONEY...

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