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# Sources of Capital; Present Value Concept

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For each of the following situations, the present value concept should be applied;

1. Your wealthy aunt has just established a trust fund for you that will accumulate to a total of \$100,000 in 12 years. Interest on the trust fund is compounded annually at an 8% interest rate. How much is your trust fund today?

2. On January 1, you will purchase a new car. The car dealer will allow you to make increasing annual December 31 payments over the following four years. The amounts of these payments are \$4,000, \$4,500, \$5,000, \$6,000. On this same January 1, your mother will lend you just enough money to enable you to meet these payments. Interest rates are expected to be 8% for the next five years. Assuming that you can earn annual compounding interest by depositing the loan from your mother in a bank, what is the minimum amount your mother must loan you to enable you to meet the car payments?

3. In settlement of a claim for your recently wrecked car, your insurance company will pay you either a lump sum today or three annual payments of #3,100 starting one year from now. Interest rates are expected to be 6 percent for the next five years. What is the least amount of money that you should be willing to accept today?

4. What is the present value of #3,000 a year to be received in years 3-11, assuming a 12% discount rate?

#### Solution Preview

For each of the following situations, the present value concept should be applied;

1. Your wealthy aunt has just established a trust fund for you that will accumulate to a total of \$100,000 in 12 years. Interest on the trust fund is compounded annually at an 8% interest rate. How much is your trust fund today?

PV = FV/(1 + i)n where PV is the present value
FV is the future value
i is the interest rate
n is the period
PV = 100,000/(1.08)12
PV = 39,710

2. On January 1, you will ...

#### Solution Summary

This solution is comprised of a detailed calculation to calculate how much is your trust fund today, what is the minimum amount your mother must loan you to enable you to meet the car payments, what is the least amount of money that you should be willing to accept today, and what is the present value of #3,000 a year to be received in years 3-11, assuming a 12% discount rate.

\$2.19

## What is Time Value of Money (TVM) and how is it used in managerial decision making?

You are considering expanding your line of equipment and apparel for high school athletic teams to include soccer teams. Based on research conducted by the Marketing department, you estimate an increase in sales for your division of \$150,000 per year the first two years, then \$250,000 per year over the following three years. In order to manufacture the necessary equipment, you will need to invest in some new manufacturing equipment that you estimate will cost \$300,000. You figure that you will be able to manufacture the equipment and apparel utilizing your existing manufacturing staff and will not need to hire additional workers.

After gathering the information, you arranged a meeting with the Chief Financial Officer (CFO), Don Morgan. During the meeting Don listened to your proposal, reviewed your information, and stated that he would need to do some additional calculations to see if the capital project would fit into the firm's financial plan. Don used some terminology that you didn't quite understand. For example, he mentioned the time value of money, the company's cost of capital, market risk, weighted average cost of capital, and marginal cost of capital.

Dazed and confused, you walk back to the manufacturing plant in search of other division managers to find out what these terms mean. Discuss the following questions with the other managers:

What is the time value of money and how does it apply to this situation? How might you (as division managers) use the time value of money to make managerial decisions?
What is weighted average cost of capital and how does it impact the decision to expand your division?
What is marginal cost of capital and how does it impact the decision to expand your division?

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