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]Single choice
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]Single choice

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.

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