A firm has zero debt in its capital structure and has an overall cost of capital of 14 percent. The firm is considering a new capital structure with 30 percent debt at an interest rate of 8 percent. Assuming there are no taxes or other imperfections, what would be the cost of equity with the new capital structure?

Question

BlackTom AI · Accepted Answer

Modigliani-Miller without taxes implies the unlevered firm’s cost of capital (ru) remains the overall WACC and leverage increases equity cost according to re = ru + (ru − rd)·(D/E).

Relevant concepts:
- ru (unlevered cost of capital) = 14% (the firm initially has zero debt).
- rd (cost of debt) = 8%.
- Target capital structure: D/V = 30% so E/V = 70%.
- Debt-to-equity ratio D/E = (D/V) / (E/V) = 0.30 / 0.70.

Step-by-step calculation:
1. Compute D/E:
   D/E = 0.30 / 0.70 = 3/7 ≈ 0.428571.
2. Compute the spread (ru − rd):
   ru − rd = 0.14 − 0.08 = 0.06 (6 percentage points).
3. Multiply the spread by D/E:
   0.06 × 0.428571 ≈ 0.0257143 (≈ 2.5714 percentage points).
4. Add this to ru to get re:
   re = 0.14 + 0.0257143 = 0.1657143 ≈ 16.57143%.

Rounded to one decimal place this is 16.6 percent.

Alternative verification using WACC decomposition:
WACC = ru = re·(E/V) + rd·(D/V). Solve for re:
re = (ru − rd·(D/V)) / (E/V) = (0.14 − 0.08·0.30) / 0.70 = (0.14 − 0.024) / 0.70 = 0.116 / 0.70 = 0.1657143 → 16.6%.

Why the correct answer is correct:
Leverage raises equity risk and thus equity required return; the numeric application of MM (no taxes) yields 16.571% ≈ 16.6%.

Why other options are incorrect:
- 14.0%: This is the unlevered cost; with debt added equity must earn more than ru.
- 12.2%: Lower than ru, impossible here because leverage increases equity risk.
- 14.7%: Does not result from the correct D/E adjustment; it understates the levering effect.

Final confirmation: The correct cost of equity under the new structure is 16.6 percent, matching the provided answer.

类似问题

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Calculate the company’s cost of equity if the company’s stock beta is 1.8, the risk-free rate is 5% and the expected market return is 13%. If the answer is 10.4567%, write 0.1046.

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