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 | ||||
| N(d2) | |||||
| 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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