Problem set

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Please use Excel formulas to show your calculations.  If you don’t use excel functions, you will need to include your calculation details in the file for full credit.

Problem 1

Reacher Technology has consulted with investment bankers and determined the interest rate it would pay for different capital structures, as shown below. Data for the risk-free rate, the market risk premium, an estimate of Reacher’s unlevered beta, and the tax rate are also shown below. Based on this information, what is the firm’s optimal capital structure and what is the weighted average cost of capital at the optimal structure?
Percent Financed with Debt (wd) Before-tax Cost Debt (rd) Input Data
Risk-free rate 4.5%
Market risk premium 5.5%
Unlevered beta 0.8
0% 6.0% Tax rate 40.0%
10% 6.1%
20% 7.0%
30% 8.0%
40% 10.0%
50% 12.5%
60% 15.5%
70% 18.0%
Fill in formulas in the yellow cells to find the optimum capital structure.
Debt/Value Equity/Value Debt/Equity A-T Cost of Levered Cost of
Ratio (wd) Ratio (ws) Ratio (wd/ws) Debt (rd) Beta Equity WACC
0% 1.0 0.00

Author: After tax cost of debt.

10% 0.9 0.11
20% 0.8 0.25
30% 0.7 0.43
40% 0.6 0.67
50% 0.5 1.00
60% 0.4 1.50
70% 0.3 2.33
WACC at optimum debt ratio =
Optimum debt ratio =

Problem 2

Higgs Bassoon Corporation is a custom manufacturer of bassoons and other wind instruments. Its current value of operations, which is also its value of debt plus equity, is estimated to be $200 million. Higgs has $110 million face value, zero coupon debt that is due in 3 years. The risk-free rate is 5%, and the standard deviation of returns for similar companies is 60%. The owners of Higgs Bassoon view their equity investment as an option and would like to know the value of their investment.
a. Using the Black-Scholes Option Pricing Model, how much is the equity worth?
Black-Scholes Option Pricing Model
Total Value of Firm this is the current value of operations
Face Value of Debt
Risk Free rate
Maturity of debt (years)
Standard Dev. this is sigma–also known as volatility
d1 use the formula from the text
d2 use the formula from the text
N(d1) use the Normsdist function in the function wizard
Call Price = Equity Value million
b. How much is the debt worth today? What is its yield?
Debt value = Total Value – Equity Value = million
Debt yield =
c. How much would the equity value and the yield on the debt change if Fethe’s management were able to use risk management techniques to reduce its volatility to 45 percent? Can you explain this?
Equity value at 60% volatility million
Equity value at 45% volatility million
Percent change million

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