# Review Problem 1: Basic Present Value Computations:

For each of the following situations is independent. Workout your own solution to each situation, and then check it against the solution:

### Situation 1:

John has reached age 58. In 12 years, he plans to retire. Upon retiring, he would like to take an extended vacation, which he expects will cost at least \$4,000. What lump-sum amount must he invest now to have the needed \$4,000 at the end of 12 years if the rate of return is:
(a). Eight percent?
(b). Twelve percent?

### Situation 2:

The Morgans would like to send their daughter to an expensive music camp at the end of each of the next five years. The camp cost \$1,000 a year. What lump-sum amount would have to invested now to have the \$1,000 at the end of each year if the rate of return is:
(a). Eight percent?
(b). Twelve percent?

### Situation 3:

You have just received an inheritance from a relative. You can invest the money and either receive a \$20,000 lump-sum amount at the end of 10 years or receive \$1,400 at the end of each year for the next 10 years. If your minimum desired rate of return is 12%, which alternative would you prefer?

## Solution to Review Problem 1:

### Situation 1:

(a). The amount that must be invested now would be the present of the \$4,000, using a discount rate of 8%. From Future Value and Present Value Tables Page Table-3, the factor for a discount rate of 8% for 12 periods is 0.397. Multiplying this discount factor by the \$4,000 × 0.397 = \$1.588.

(b). We will proceed as we did in (a) above, but this time we will use a discount rate of 12%. From  Future Value and Present Value Tables Page Table-3, the factor for a discount rate of 12% for 12 periods is 0.257. Multiplying this discount factor by the \$4,000 needed in 12 years will give the amount of the present investment required: \$4,000 × 0.257 = \$1,028.
Notice that as the discount rate (desired rate of return) increases, the present value decreases.

### Situation 2:

This part differs from (1) above in that we are now dealing with an annuity rather than a single future sum. The amount that must be invested now to have \$1,000 available at the end of each year for five years. Since we are dealing with an annuity, or a series of annual cash flows, we must refer to Table-4 (see Future Value and Present Value Tables Page, Table-4)

(a). From Table-4 (see Future Value and Present Value Tables Page, Table-4) the discount factor for 12% for five periods is 3.993. Therefore, the amount that must be invested now to have \$1,000 available at the end of each year for five years is \$1,000 × 3.993 = \$3,993.

(b). From Table-4 (see Future Value and Present Value Tables Page, Table-4) the discount factor for 12% for five periods is 3.605. Therefore, the amount that must be invested now to have \$1,000 available at the end of each five years is \$1,000 × 3.605 = \$3,605.

### Situation 3:

For this part, we will need to refer to both Table-3 and Table-4 (see Future Value and Present Value Tables Page, Table-3 and Table-4)

From Table-3 we will need to find the discount factor for 12% for 10 periods, then apply it to the \$20,000 lump sum to be received in 10 years. From Table-4, we will need to find the discount factor for 12% for 10 periods, then apply it to the series of \$1,400 payments to be received over the 10-year period. Whichever alternative has the higher present value is the one that should be selected.

\$2,000 × 0.332 = \$6,440
\$1,400 × 5.650 = \$7,910

Thus you would prefer to receive the \$1,400 per year for 10 years rather than the \$20,000 lump sum.