You are considering two identical firms one levered the other not. Both firms have expected EBIT of $600. The value of the unlevered firm (Vu) is $2000. The corporate tax rate is 30%. The cost of debt is 10%, and the ratio of debt to equity is 1.00 for the levered firm. Use MM propositions to calculate the cost of equity (to the nearest percentage) for the levered firm.[Fill in the blank]单项选择题
A
1. 10.00%
B
2. 11.00%
C
3. 28.00%
D
4. 29.00%
E
5. 30.00%

Question

You are considering two identical firms one levered the other not. Both firms have expected EBIT of $600. The value of the unlevered firm (Vu) is $2000. The corporate tax rate is 30%. The cost of debt is 10%, and the ratio of debt to equity is 1.00 for the levered firm. Use MM propositions to calculate the cost of equity (to the nearest percentage) for the levered firm.[Fill in the blank]单项选择题

A

1. 10.00%

B

2. 11.00%

C

3. 28.00%

D

4. 29.00%

E

5. 30.00%

BlackTom AI · Accepted Answer

Unlevered cost of capital ru = NOPAT / Vu. NOPAT = EBIT*(1 − Tc) = 600*(1 − 0.30) = 420. So ru = 420 / 2000 = 0.21 = 21%.

MM with corporate taxes gives the levered cost of equity:
re = ru + (D/E) * (ru − rd) * (1 − Tc).

Given D/E = 1.00, rd = 10% = 0.10, ru = 21% = 0.21, Tc = 30% = 0.30:
Compute the spread: ru − rd = 0.21 − 0.10 = 0.11.
Tax-adjusted spread: (ru − rd)*(1 − Tc) = 0.11 * 0.70 = 0.077.
Add to ru: re = 0.21 + 1 * 0.077 = 0.287 = 28.7%.

Rounded to the nearest percentage gives 29.00%.

Alternate verification (value approach):
Under MM with taxes VL = Vu + Tc * D. With D/E = 1, VL = D + E = 2E, so D = VL/2.
Solve VL = Vu + Tc*(VL/2) => VL*(1 − Tc/2) = Vu => VL = 2000 / (1 − 0.15) = 2000 / 0.85 = 2352.94.
Then D = E = 1176.47. Interest = rd * D = 0.10 * 1176.47 = 117.65.
Equity cash to shareholders (after tax) = (EBIT − Interest)*(1 − Tc) = (600 − 117.65)*0.70 = 337.65.
re = 337.65 / 1176.47 = 0.287 = 28.7% → rounds to 29.00%.

Why other choices are wrong:
- 10.00% is the cost of debt, not equity.
- 11.00% is the unadjusted ru − rd spread, not equity cost.
- 28.00% is slightly below the correct rounded value (28.7% rounds to 29%).
- 30.00% is too high relative to the computed 28.7%.

Therefore, the cost of equity for the levered firm, rounded to the nearest percent, is 29.00%, matching the provided answer.

类似问题

The following data are available for Halcyon Industries at several capital structures. Based on this information, what is the firm's optimal capital structure? Debt Equity EPS Stock Price 20% 80% $2.40 $24.00 30% 70% $2.68 $25.80 40% 60% $2.95 $27.10 50% 50% $3.20 $26.50 60% 40% $3.44 $25.20

According to Modigliani and Miller, in a world with no corporate taxes a firm cannot change its total value by altering the proportions of debt and equity in its capital structure.

Which of the following statements best describes the optimal capital structure? The optimal capital structure is the mix of debt, equity, and preferred stock that maximizes the company's ____.

Modigliani and Miller (MM) won Nobel Prizes for their work on capital structure theory.

According to M&M Proposition 2, the cost of a company's equity[Fill in the blank]

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