Module 8: Numeric Questions

For students

Last updated: 10/11/2025 12:23

The questions are based on or inspired by the following references:

• Berk & DeMarzo, Corporate Finance, 5th ed. (2020)
  
• Brealey & Myers, Principles of Corporate Finance, 13th ed. (2020)

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💡 You can also press Ctrl + P (or Cmd + P on Mac) to print or save your responses as a .pdf file.

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⚠️ These exercises are powered by AI-assisted technologies and may contain occasional formatting or logic errors. Please report any issues you encounter so I can improve the experience.

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📙 Part 2 (Midterm to Final)

Module	Chapter	Slides	T/F	MCQ	Numeric	Long	Self-quiz
8	ch15	🎞️	✅	❓	🔢	📝	🧪

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Answer the following questions based on the discussions in class.

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Q1.

WACC and Firm Value (with growth)

Solar Technologies expects to generate free cash flow of 8.03 million over the next year. Free cash flow is expected to grow at a constant rate of 3% per year. The cost of equity is 13.07%, cost of debt is 6.91%, and the corporate tax rate is 35%. Assuming a debt-to-equity ratio of 0.5, compute:

• 1. the pre-tax WACC (in %)
• 2. the value of the unlevered firm (in million dollars)
• 3. the after-tax WACC (in %)
• 4. the value of the levered firm (in million dollars)

a. Pre-tax WACC (%):

✅ \(WACC = w_D r_D + w_E r_E =\) 11.02%.

b. \(V_U\) (millions):

✅ \(V_U = \dfrac{FCF_1}{WACC_{pre-tax} - g} = \dfrac{8.03}{0.1102 - 0.03} =\) 100 million.

c. After-tax WACC (%):

✅ \(WACC_{after-tax} = w_E r_E + w_D r_D(1 - T_c) =\) 10.21%.

d. \(V_L\) (millions):

✅ \(V_L = \dfrac{FCF_1}{WACC_{after-tax} - g} = \dfrac{8.03}{0.1021 - 0.03} =\) 111 million.

Q2.

Aurora Technologies — Adjusting WACC for Corporate Taxes

Solar Technologies currently has a pre-tax WACC of 13.7%. The corporate tax rate is 25%, and the pre-tax cost of debt is 6.9%. If the company issues enough debt to reach a debt-to-value ratio of 0.55, compute the after-tax WACC (in %).

After-tax WACC (%):

✅ \(WACC_{after} = w_E r_E + w_D r_D(1 - T_c)= w_E r_E + w_D r_D - w_D r_D T_c\)
Since \(WACC_{pre} = w_E r_E + w_D r_D = 13.7\%\), then
\(WACC_{after} = 13.7\% - (0.55 \times 6.9\% \times 0.25) = \mathbf{12.75\%}.\)

Q3.

Debt, Taxes, and Firm Value (MM with Corporate Taxes)

Aurora Technologies is currently unlevered and is considering adopting a permanent debt policy. The following information applies:

• Unlevered firm value: 545 million
• Unlevered cost of capital: 10.34%
• Corporate tax rate: 25%
• Proposed permanent debt: 325.5 million at 6.36%

Compute:

• 1. the present value of the interest tax shield (in million dollars)
• 2. the levered firm value \(V_L\) (in million dollars)
• 3. the equity value \(E\) (in million dollars)
• 4. the levered cost of equity \(r_E\) (in %)
• 5. the after-tax WACC (in %)

a. PV of interest tax shield (millions):

✅ $ = T_c D = 0.25 \(\times\) 325.5 = 81.4 million.

b. \(V_L\) (millions):

✅ $V_L = V_U + = 545 + 81.4 = 626.4 million.

c. \(E\) (millions):

✅ $E = V_L - D = 626.4 - 325.5 = 300.9 million.

d. \(r_E\) (%):

✅ \(r_E = r_U + \frac{D}{E}(1 - T_c)(r_U - r_D)\) = 13.57%.

e. After-tax WACC (%):

✅ \(WACC_{after} = \frac{E}{D+E}r_E + \frac{D}{D+E}r_D(1 - T_c)\)
\(= \frac{300.9}{626.4}r_E + \frac{325.5}{626.4}r_D(1 - T_c) = \mathbf{9}\%.\)