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**Unformatted text preview: **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 the time value of money , or discounted cash flow (DCF) analysis. The principles of time value analysis that are developed in this chapter have many applications, ranging from setting up schedules for paying off loans to decisions about whether to acquire new equipment. Future value and present value techniques can be applied to a single cash flow (lump sum), ordinary annuities, annuities due, and uneven cash flow streams. Future and present values can be calculated using a regular calculator or a calculator with financial functions. When compounding occurs more frequently than once a year, the effective rate of interest is greater than the quoted rate. The cash flow time line is one of the most important tools in time value of money analysis. Cash flow time lines help to visualize what is happening in a particular problem. 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 question marks. Thus, to find the future value of $100 after 5 years at 5 percent interest, the following cash flow time line can be set up: Time: 1 2 3 4 5 | | | | | | Cash flows:-100 FV 5 = ? A cash outflow is a payment, or disbursement, of cash for expenses, investments, and so on. A cash inflow is a receipt of cash from an investment, an employer, or other sources. Compounding is the process of determining the value of a cash flow or series of cash flows some time in the future when compound interest is applied. The future value is the amount C HAPTER 3 T HE T IME V ALUE OF M ONEY OUTLINE 5% CHAPTER 3: THE TIME VALUE OF MONEY 40 to which a cash flow or series of cash flows will grow over a given period of time when compounded at a given interest rate. The future value can be calculated as FV n = PV(1 + k) n , where PV = present value, or beginning amount; k = interest rate per period; and n = number of periods involved in the analysis. This equation can be solved in one of two ways: numerically or with a financial calculator. For calculations, assume the following data that were presented in the time line above: present value (PV) = $100, interest rate (k) = 5%, and number of years (n) = 5. Compounded interest is interest earned on interest. To solve numerically, use a regular calculator to find 1 + k = 1.05 raised to the fifth power, which equals 1.2763. Multiply this figure by PV = $100 to get the final answer of FV 5 = $127.63....

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