Module 7: Numeric Questions

For students

Last updated: 10/11/2025 10:25

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
7	ch14	🎞️	✅	❓	🔢	📝	🧪

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Answer the following questions based on the discussions in class.

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Q1.

Leverage Effect — Compute \(r_E\) (no taxes)

A firm has an unlevered cost of capital of r_U = 8.75% and a cost of debt of r_D = 3.97%.
The firm’s debt-to-equity ratio is D/E = 0.74. Compute the firm’s equity cost of capital r_E (in %).

r_E (%):

✅
r_E = r_U + (D/E)(r_U − r_D) = 8.75% + 0.74×(4.78%) = 12.29%.

Q2.

Expected Return without Leverage

A company has no debt. Its assets will be worth 606.6 million in one year if the economy is strong, but only 299.5 million if the economy is weak. Both events are equally likely. The current market value of the company’s assets is 399.4 million. Compute the expected return without leverage (in %).

Expected return (%):

✅ Expected return = (453 − 399.4) ÷ 399.4 = 13.4%.

Q3.

Deleveraging and Share Issuance

Company Y has 50 million shares outstanding and a market capitalization of 2 billion. It also has 756 million in debt outstanding. The company plans to delever completely by issuing new equity and repaying all outstanding debt. Assume perfect capital markets. How many new shares must the company issue (in million)?

New shares to issue (millions):

✅ New shares = Debt ÷ Price = 756 ÷ 40 = 18.9 million.

Q4.

Stock Price under MM Proposition I

Consider two firms, Leverage and NonLeverage, that have identical assets and generate identical cash flows. NonLeverage is an all-equity firm with 1.93 million shares outstanding trading at 22.74 per share. Leverage has 2 million shares outstanding and 26 million in debt, with an interest rate of 5%. Under Modigliani–Miller Proposition I (no taxes), compute the stock price for Leverage (in $).

Leverage stock price ($):

✅ By MM I (no taxes): firm value unchanged. Equity value = Total assets − Debt = 43.89 − 26 = 17.89; Stock price = 17.89 ÷ 2 = 8.94.

Q5.

MM I — WACC and Value (no taxes)

A firm operates in a perfect capital market (no taxes) with perpetual free cash flow to the firm (FCFF) of 39.53 million per year. Its unlevered cost of capital is r_U = 7.44%, the cost of debt is r_D = 4.07%, and the target leverage is D/E = 1.16. Compute: (a) the levered cost of equity r_E (in %); (b) the WACC (in %); and (c) the levered firm value V_L (in millions).

2a. r_E (%):

✅ \(r_E = r_U + \frac{D}{E}(r_U - r_D) =\) 11.35%.

2b. WACC (%):

✅ \(WACC = \frac{E}{V}r_E + \frac{D}{V}r_D =\) 7.44%.

2c. V_L (millions):

✅ By MM I (no taxes), \(V_L = V_U = \frac{FCFF}{r_U} =\) 531.32 (millions).

Q6.

Deleveraging — Shares to Issue to Repay Debt

Company Y has 50 million shares outstanding and a market capitalization of 2 billion. It also has 756 million in debt outstanding. The company plans to delever by issuing new equity and completely repaying all the debt. Assume perfect capital markets.

1. What is the current share price (in R$)?

2. How many new shares must be issued (in millions)?

1) Share price:

✅ Share price = Market Cap (million R$) / Shares Outstanding (million) = 40 .

2) New shares to issue:

✅ New Shares = Debt / Share Price = 18.9 million.