Shim Interiors has a target debt-equity ratio of .40. Its cost of equity is 13.5 percent and its pretax cost of debt is 5.5 percent. Its tax rate is 21 percent. What is the company's WACC?

Question

BlackTom AI · Accepted Answer

WACC is the weighted average of the after-tax cost of debt and the cost of equity, so we must (1) derive the capital weights from the debt-equity ratio, (2) compute the after-tax cost of debt, and (3) combine using the WACC formula.

1) Relevant knowledge points and concepts
- Debt-equity ratio D/E = 0.40 means D = 0.40·E.
- Weights: w_D = D/(D+E), w_E = E/(D+E).
- After-tax cost of debt = r_D · (1 − Tax rate).
- WACC = w_E·r_E + w_D·r_D·(1 − T_c).

2) Step-by-step reasoning and 3) intermediate calculations
- Let E = 1 (unit of equity). Then D = 0.40.
- Total capital = D + E = 0.40 + 1 = 1.40.
- Equity weight: w_E = E/(D+E) = 1 / 1.40 = 0.7142857 (71.42857%).
- Debt weight: w_D = D/(D+E) = 0.40 / 1.40 = 0.2857143 (28.57143%).

- Given r_E = 13.5% = 0.135; r_D (pretax) = 5.5% = 0.055; tax rate T_c = 21% = 0.21.
- After-tax cost of debt: r_D(1 − T_c) = 0.055 × (1 − 0.21) = 0.055 × 0.79 = 0.04345 (4.345%).

- Compute WACC:
  w_E·r_E = 0.7142857 × 0.135 = 0.09642857 (9.642857%).
  w_D·r_D(1 − T_c) = 0.2857143 × 0.04345 = 0.01241429 (1.241429%).
  WACC = 0.09642857 + 0.01241429 = 0.10884286 = 10.884286% ≈ 10.88%.

4) Why the correct answer is correct
The calculation uses the correct interpretation of the D/E ratio to derive weights, applies the corporate tax shield to the debt cost, and then forms the weighted average. Each arithmetic step above leads directly to 10.8843%, which rounds to 10.88%.

5) Why the other choices are incorrect
- 11.21% (choice A) equals the WACC if you incorrectly use the pretax debt cost (0.055) instead of after-tax (0.04345); that overstates WACC.
- 6.96% (choice B) results if the debt and equity weights are swapped (using w_E = 0.2857 and w_D = 0.7143), which misapplies the D/E ratio.
- 9.97% (choice D) and 5.10% (choice E) come from other misinterpretations or arithmetic mistakes (e.g., treating D/E = 0.40 as D/(D+E)=0.40 without consistent application, or ignoring equity cost entirely), so they do not follow the correct weighting and after-tax debt adjustment.

6) Conclusion / confirmation
Following the correct weight derivation and after-tax debt adjustment produces WACC = 10.8843%, which rounds to 10.88%. This matches the provided correct answer: 10.88%.

Shim Interiors has a target debt-equity ratio of .40. Its cost of equity is 13.5 percent and its pretax cost of debt is 5.5 percent. Its tax rate is 21 percent. What is the company's WACC?单项选择题

类似问题

A firm has the following capital structure: Debt = $40 million; Equity = $60 million; Pre-tax cost of debt = 6%; Cost of equity = 12%; and Corporate tax rate = 30%. What is the firm’s weighted average cost of capital (WACC) to the nearest percentage?[Fill in the blank]

A firm has 250M shares trading at $20, debt of $5,000M with a pre-tax cost of debt of 8%, equity β = 1.50, risk-free rate = 4%, ERP = 6%, and tax rate = 30%. Compute WACC. (Answer in percent, 2 decimals.)

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单