Review Problem 1: Basic Present Value

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.

You may also be interested in other articles from “capital budgeting decisions” chapter:

  1. Capital Budgeting – Definition and Explanation
  2. Typical Capital Budgeting Decisions
  3. Time Value of Money
  4. Screening and Preference Decisions
  5. Present Value and Future Value – Explanation of the Concept
  6. Net Present Value (NPV) Method in Capital Budgeting Decisions
  7. Internal Rate of Return (IRR) Method – Definition and Explanation
  8. Net Present Value (NPV) Method Vs Internal Rate of Return (IRR) Method
  9. Net Present Value (NPV) Method – Comparing the Competing Investment Projects
  10. Least Cost Decisions
  11. Capital Budgeting Decisions With Uncertain Cash Flows
  12. Ranking Investment Projects
  13. Payback Period Method for Capital Budgeting Decisions
  14. Simple rate of Return Method
  15. Post Audit of Investment Projects

  16. Inflation and Capital Budgeting Analysis
  17. Income Taxes in Capital Budgeting Decisions
  18. Review Problem 1: Basic Present Value Computations
  19. Review Problem 2: Comparison of Capital Budgeting Methods
  20. Future Value and Present Value Tables


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