To illustrate, assume that a company must repay a 6% loan with a $5,000 payment at each year-end for the next four years. This loan amount equals the present value of the four payments discounted at 6%. Exhibit 14A.5 shows how to compute this loan’s present value of $17,326 by multiplying each payment by its matching present value factor taken from Exhibit 14A.3.
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However, the series of $5,000 payments is an annuity, so we can compute its present value with either of two shortcuts. First, the third column of Exhibit 14A.5 shows that the sum of the present values of 1 at 6% for periods 1 through 4 equals 3.4651. One shortcut is to multiply this total of 3.4651 by the $5,000 annual payment to get the combined present value of $17,326. It requires one multiplication instead of four.
The second shortcut uses an annuity table such as the one shown in Exhibit 14A.6, which is drawn from the more complete Table B.3 in Appendix B. We go directly to the annuity table to get the present value factor for a specific number of payments and interest rate. We then multiply this factor by the amount of the payment to find the present value of the annuity. Specifically, find the row for four periods and go across to the 6% column, where the factor is 3.4651. This factor equals the present value of an annuity with four payments of 1, discounted at 6%. We then multiply 3.4651 by $5,000 to get the $17,326 present value of the annuity.
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Example: Use Exhibit 14A.6 to find the present value of an annuity of eight $15,000 payments with an 8% interest rate. Answer: $15,000 × 5.7466 = $86,199
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