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]Single choice
A
A. 8.00%
B
B. 9.00%
C
C. 10.00%
D
D. 11.00%
E
E. 24.00%

Question

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]Single choice

A

A. 8.00%

B

B. 9.00%

C

C. 10.00%

D

D. 11.00%

E

E. 24.00%

BlackTom AI · Accepted Answer

WACC equals the weighted average of the after-tax cost of debt and the cost of equity, weighted by their proportions in the firm’s capital structure.

1) Relevant concepts
- Weight of debt (wd) and equity (we): based on market (here given) values.  
- After-tax cost of debt = pre-tax cost of debt × (1 − corporate tax rate) because interest is tax-deductible.  
- WACC formula: WACC = we × Re + wd × Rd × (1 − Tc).

2) Step-by-step reasoning
- Total capital = Debt + Equity = $40m + $60m = $100m.  
- Weight of debt, wd = 40 / 100 = 0.40.  
- Weight of equity, we = 60 / 100 = 0.60.  
- Pre-tax cost of debt, Rd = 6% = 0.06.  
- Corporate tax rate, Tc = 30% = 0.30.  
- Cost of equity, Re = 12% = 0.12.

3) Intermediate calculations
- After-tax cost of debt = Rd × (1 − Tc) = 0.06 × (1 − 0.30) = 0.06 × 0.70 = 0.042 = 4.20%.  
- Contribution of equity to WACC = we × Re = 0.60 × 0.12 = 0.072 = 7.20%.  
- Contribution of debt to WACC = wd × Rd × (1 − Tc) = 0.40 × 0.06 × 0.70 = 0.40 × 0.042 = 0.0168 = 1.68%.  
- WACC = 7.20% + 1.68% = 8.88%.

4) Why the correct answer is correct
- After-tax debt cost lowers the effective cost of borrowing; including the tax shield gives WACC = 8.88%, which when rounded to the nearest percentage point is 9.00%.

5) Why other options are incorrect
- A (8.00%): too low; understates either equity or debt contribution.  
- C (10.00%): equals the WACC if one ignored the tax shield on debt (0.60×12% + 0.40×6% = 9.6% → 10% rounded) — incorrect because interest is tax-deductible.  
- D (11.00%): much higher than computed WACC; would require much higher equity cost or different weights.  
- E (24.00%): far off; implies a massively higher cost of capital.