Practice Problem – Cost of Capital

Practice Question

Intro to Finance
Weighted Average Cost of Capital (WACC)
Cost of Capital
Short Answer

AMC’s pre-tax cost of debt is 8%, its cost of equity is 12%, and it is subject to a 40% corporate income tax rate. The firm’s debt-to-equity ratio (D/E) is 2/3. What is the firm’s WACC?

Answer +
9.12%
Explanation +

Step 1: Identify the Given Variables

  • Pre-tax cost of debt \( K_d = 8\% \)
  • Cost of equity \( K_e = 12\% \)
  • Corporate tax rate \( T = 40\% \)
  • Debt-to-equity ratio \( D/E = \frac{2}{3} \)

Step 2: Calculate Capital Structure Weights

Let equity \( E = 1 \), then debt \( D = \frac{2}{3} \). Total capital \( = D + E = \frac{5}{3} \).

Proportion of debt: \[ w_d = \frac{D}{D + E} = \frac{2/3}{5/3} = \frac{2}{5} = 0.4 \] Proportion of equity: \[ w_e = \frac{E}{D + E} = \frac{1}{5/3} = \frac{3}{5} = 0.6 \]

Step 3: Calculate After-Tax Cost of Debt

\[ K_d \times (1 - T) = 0.08 \times (1 - 0.40) = 0.08 \times 0.60 = 0.048 \text{ or } 4.8\% \]

Step 4: Apply the WACC Formula

\[ WACC = w_d \times K_d \times (1 - T) + w_e \times K_e \] \[ WACC = 0.4 \times 0.048 + 0.6 \times 0.12 = 0.0192 + 0.072 = 0.0912 \text{ or } 9.12\% \]

Conclusion:
The Weighted Average Cost of Capital (WACC) for AMC is approximately 9.12%. This reflects the firm’s blended cost of capital, accounting for its capital structure and tax shield from debt.