The Two Dollar Store has a cost of equity of 12.7 percent, the YTM on the company's bonds is 5.4 percent, and the tax rate is 21 percent. If the company's debt-equity ratio is .62, what is the weighted average cost of capital?

Question

BlackTom AI · Accepted Answer

WACC = (E/V)·Re + (D/V)·Rd·(1 − Tc).

Relevant concepts: The weighted average cost of capital (WACC) combines the cost of equity (Re) and the after-tax cost of debt (Rd(1−Tc)) using weights based on the market-value debt-to-equity structure. Given a debt-equity ratio (D/E), weights are D/(D+E) and E/(D+E).

Step-by-step calculation:
1. Let E = 1 (for relative weights). D = 0.62 (since D/E = 0.62). Total value V = D + E = 1 + 0.62 = 1.62.
2. Equity weight: E/V = 1 / 1.62 = 0.6172839506172839.
   Debt weight: D/V = 0.62 / 1.62 = 0.38271604938271606.
3. After-tax cost of debt: Rd(1 − Tc) = 5.4% × (1 − 0.21) = 0.054 × 0.79 = 0.04266 (4.266%).
4. Equity contribution: (E/V)·Re = 0.6172839506172839 × 0.127 = 0.07839506172839506 (7.839506172839506%).
5. Debt contribution: (D/V)·Rd(1 − Tc) = 0.38271604938271606 × 0.04266 = 0.016326666666666665 (1.6326666666666665%).
6. WACC = 0.07839506172839506 + 0.016326666666666665 = 0.09472172839506173 ≈ 0.0947 or 9.47%.

Why this is correct: The formula properly weights equity and the after-tax cost of debt. Using the debt-equity ratio to derive weights and applying the tax shield to debt are standard and necessary; the arithmetic above yields 9.472% which rounds to 9.47%.

Why other approaches would be wrong: (a) Using Rd without the (1 − Tc) tax adjustment overstates the cost from debt and gives a higher WACC. (b) Using raw D or E (instead of D/(D+E) and E/(D+E)) for weights misallocates proportions and produces an incorrect WACC. (c) Swapping D and E in weights would also be incorrect.

Conclusion: The weighted average cost of capital is 9.47%, which matches the provided answer.

The Two Dollar Store has a cost of equity of 12.7 percent, the YTM on the company's bonds is 5.4 percent, and the tax rate is 21 percent. If the company's debt-equity ratio is .62, what is the weighted average cost of capital?单项选择题

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