78106_04_Web_Ch04A_p01-13

78106_04_Web_Ch04A_p01-13 - WEB EXTENSION The Tabular...

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WEB EXTENSION 4A The Tabular Approach I n this extension we explain how to solve time value of money problems with the tabular approach. 4.1 F UTURE V ALUE Suppose you deposit $100 in a bank that pays 5% interest each year. How much would you have at the end of 5 years? The future value of an initial lump sum at the end of N years can be found by applying Equation 4A-1: FV N ¼ PV ð 1 þ I Þ N (4A-1) The future value interest factor for I and N (FVIF I,N ) is defined as (1 + I) N , and these factors can be found by using a regular calculator (as discussed in the text) and then put into tables. Table 4A-1 is illustrative, while Table 4A-4 at the end of this extension contains FVIF I,N values for a wide range of I and N values. Equation 4A-1 can be rewritten as follows: FV N ¼ PV ð FVIF I ; N Þ (4A-1a) To illustrate, the FVIF for the 5-year, 5% interest problem can be found in Table 4A-1 by first looking down the first column to Period 5 and then looking across that row to the 5% column, where we see that FVIF 5%,5 = 1.2763. Then, the value of $100 after 5 years can be calculated. Future Value Interest Factors: FVIF I,N TABLE 4A-1 INTEREST RATE (I) PERIOD (N) 4% 5% 6% 1 1.0400 1.0500 1.0600 2 1.0816 1.1025 1.1236 3 1.1249 1.1576 1.1910 4 1.1699 1.2155 1.2625 5 1.2167 1.2763 1.3382 6 1.2653 1.3401 1.4185 1
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FV N ¼ PV ð FVIF I ; N Þ (4A-1a) ¼ $100 ð 1 : 2763 Þ¼ $127 : 63 (4A-1a) 4.2 P RESENT V ALUE If interest rates are 5%, how much must you invest today if you want $127.63 in 5 years? In general, the present value of a cash flow due N years in the future is the amount which, if it were on hand today, would grow to equal the future amount. Finding present values is called discounting, and it is simply the reverse of com- pounding: If you know the PV then you can compound to find the FV; and if you know the FV, you can discount to find the PV. We can express PV as PV ¼ FV N 1 ð 1 þ I Þ N ¼ FV N ð PVIF I ; N Þ (4A-2) The last term in Equation 4A-2 is called the present value interest factor for I and N, or PVIF I,N . Table 4A-2 at the end of this extension contains present value interest fac- tors for selected values of I and N. The value of PVIF I,N for I = 5% and N = 5 is 0.7835, so the present value of $127.63 to be received after 5 years when the appro- priate interest rate is 5% is $100: PV ¼ $127 : 63 ð PVIF 5% ; 5 $127 : 63 ð 0 : 7835 $100 4.3 S OLVING FOR I NTEREST R ATE AND T IME At this point, you should realize that compounding and discounting are related and that we have been dealing with one equation in two different forms. FV Form: FV N ¼ PV ð FVIF I ; N Þ (4A-1a) PV Form: PV ¼ FV N ð PVIF I ; N Þ (4A-2) There are four variables in these equations PV, FV, I, and N and if you know the values of any three, you can find the value of the fourth. Thus far, we have always given you the interest rate (I) and the number of years (N), plus either the PV or the FV. In many situations, though, you will need to solve for either I or N, as we discuss next.
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78106_04_Web_Ch04A_p01-13 - WEB EXTENSION The Tabular...

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