The first table gives the present value of $1 at the end of different time perio

Question

The first table gives the present value of $1 at the end of different time periods, given different interest rates. For example, at an interest rate of 10%, the present value of $1 to be paid in 20 years is $0.149. At 10% interest, the present value of $1,000 to be paid in 20 years equals $1,000 times 0.149, or $149. The second table gives the present value of a stream of payments of $1 to be made at the end of each period for a given number of periods. For example, at 10% interest, the present value of a series of $1 payments, made at the end of each year for the next 10 years, is $6.145. Using that same interest rate, the present value of a series of 10 payments of $1,000 each is $1,000 times 6.145, or $6,145.

Table 13.3 Present Value of $1 to Be Received at the End of a Given Number of Periods

Table 13.4 Present Value of $1 to Be Received at the End of Each Period for a Given Number of Periods

Question Your Uncle Arthur, not to be outdone by Aunt Carmen, offers you a choice. You can have $10,000 now or $30,000 in 15 years. If you took the payment now, you could put it in a bond fund or bank account earning 8% interest. Use present value analysis to determine which alternative is better.

Percent Interest Period 2 4 6 8 10 12 14 16 18 20 1 0.980 0.962 0.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 2 0.961 0.925 0.890 0.857 0.826 0.797 0.769 0.743 0.718 0.694 3 0.942 0.889 0.840 0.794 0.751 0.712 0.675 0.641 0.609 0.579 4 0.924 0.855 0.792 0.735 0.683 0.636 0.592 0.552 0.515 0.442 5 0.906 0.822 0.747 0.681 0.621 0.567 0.519 0.476 0.437 0.402 10 0.820 0.676 0.558 0.463 0.386 0.322 0.270 0.227 0.191 0.162 15 0.743 0.555 0.417 0.315 0.239 0.183 0.140 0.180 0.084 0.065 20 0.673 0.456 0.312 0.215 0.149 0.104 0.073 0.051 0.037 0.026 25 0.610 0.375 0.233 0.146 0.092 0.059 0.038 0.024 0.016 0.010 40 0.453 0.208 0.097 0.046 0.022 0.011 0.005 0.003 0.001 0.001 50 0.372 0.141 0.054 0.021 0.009 0.003 0.001 0.001 0 0

Explanation / Answer

Present value (PV) of $30,000 at current period ($) = 30,000 x PVIF(8%, 15) = 30,000 x 0.315 = 9,450

Since $10,000 now is of higher PV, taking the payment now is the better option.

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