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# Five Finance Problems

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1. Firm A's capital structure contains 20 percent debt and 80 percent equity. Firm B's capital structure contains 50 percent debt and 50 percent equity. Both firms pay 7 percent annual interest on their debt. The stock of firm A has a beta of 1.0 and the stock of firm B has a 1.375 beta. The risk free rate of interest equals 4 percent and the expected return on the market portfolio equals 12 percent.
a. Calculate the WACC for each firm assuming there are no taxes.
b. Recalculate the WACC figures assuming that the firms face a marginal tax rate of 34 percent.

2. A firm has a capital structure containing 60 percent debt and 40 percent common stock equity. Its outstanding bonds offer investors a 6.5 percent yield to maturity. The risk free rate currently equals 5 percent and the expected risk premium on the market portfolio equals 6 percent. The forms common stock beta is 1.2
a. What is the firms required return on equity
b. Ignoring taxes, use your findings in part (a) to calculate the firms WACC
c. Assuming a 40 percent marginal tax rate, recalculate the firms WACC found in part (b).

3. JK's marketing department believes that the firm can sell the product for \$500 per unit, but feels that if the initial market response is weak, the price may have to be 20% lower in order to be competitive with existing products. The firms best estimates of its costs are fixed cost of \$3.6 million and variable cost of \$325 per unit. Although the firm expects this cost to be \$325 per unit it could be as much as 8 percent above that value. The firm expects to sell about 50,000 units per year.
a. Calculate the firms volume breakeven point (BEP) assuming its initial estimates are accurate.
b. Perform a sensitivity analysis by calculating the breakeven point for all combinations of the sale price per unit and variable cost per unit. (hint: there are four combinations)
c. In the best case, how many units will the firm need to sell to break even
d. In the worst case how many units will the firm need to sell to break even
e. If each of the possible price/variable cost combinations is equally probable, what is the firms expected breakeven point

4. A project has the following stream of cash flows:
Year Cash Flows
0 \$17,500
1 - 80,500
2 138,425
3 -105,455
4 30,030
a. What are the projects IRR's (4 of them)

5. Initial cash outflow is \$20,000 and a project is expected to yield cash inflows of \$4,400 per year for 7 years, the firm has a 10 percent cost of capital.
a. Determine the NVP for the project
b. Determine the IRR for the project

#### Solution Preview

1. Firm A's capital structure contains 20 percent debt and 80 percent equity. Firm B's capital structure contains 50 percent debt and 50 percent equity. Both firms pay 7 percent annual interest on their debt. The stock of firm A has a beta of 1.0 and the stock of firm B has a 1.375 beta. The risk free rate of interest equals 4 percent and the expected return on the market portfolio equals 12 percent.
a. Calculate the WACC for each firm assuming there are no taxes.

First, you need to find the cost of equity for each firm by using the formula as follows: -

rs = rf + (rm - rf)b where rs is the stock's cost of equity
rm is the market required rate of return
rf is the risk free rate
b is the beta

For Stock A, the cost of equity is

k = 4% + (12% - 4%)1.0
k = 12%

For Stock B, the cost of equity is

k = 4% + (12% - 4%)1.375
k = 15%

WACC is the weighted average cost of capital whereby the target proportions of debt and equity along with the component costs of capital are used to calculate. The equation can be summarized as follows: -

WACC = WdKd(1 - T) + WcKs where Wd is the weight of debt
Kd is the cost of debt
T is the tax rate
Wc is the weight of common stock
Ks is the cost of common stock

Stock A

WACC = 0.20(0.07)(1 - 0) + 0.80(0.12)
WACC = 0.014 + 0.096
WACC = 0.11 or 11%

Stock B

WACC = 0.50(0.07)(1 - 0) + 0.50(0.15)
WACC = 0.035 + 0.075
WACC = 0.11 or 11%

b. Recalculate the WACC figures assuming that the firms face a marginal tax rate of 34 percent.

Stock A

WACC = 0.20(0.07)(1 - 0.34) + 0.80(0.12)
WACC = 0.00924 + 0.096
WACC = 0.10524 or 10.524%

Stock B

WACC = 0.50(0.07)(1 - 0.34) + 0.50(0.15)
WACC = 0.0231 + 0.075
WACC = 0.0981 or 9.81%

2. A firm has a capital structure containing 60 percent debt and 40 percent common stock equity. Its outstanding bonds offer investors a 6.5 percent yield to maturity. The risk free rate currently equals 5 percent and the expected risk premium on the market portfolio equals 6 percent. The firm's common stock beta is 1.2
a. What is the firms required return on ...

#### Solution Summary

This solution is comprised of a detailed explanation and calculation to answer the finance problems in both text and Excel files.

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