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.)

Question

BlackTom AI · Accepted Answer

WACC = w_E·r_E + w_D·r_D·(1 − T_c).

1) Relevant concepts:
- Market-value weights: use market value of equity and debt to compute weights.
- Cost of equity via CAPM: r_E = r_f + β·ERP.
- After‑tax cost of debt: interest is tax-deductible, so use r_D·(1 − T_c).
- WACC is the weighted average of after‑tax cost of capital.

2) Step-by-step calculations:
- Market value of equity (E): 250 million shares × $20/share = $5,000 million.
- Market value of debt (D): given = $5,000 million.
- Total firm value (V) = E + D = $5,000M + $5,000M = $10,000M.
- Equity weight w_E = E / V = $5,000M / $10,000M = 0.5.
- Debt weight w_D = D / V = $5,000M / $10,000M = 0.5.

- Cost of equity r_E (CAPM):
  r_E = r_f + β·ERP = 4% + 1.50 × 6% = 4% + 9% = 13.0%.

- After-tax cost of debt:
  r_D·(1 − T_c) = 8% × (1 − 0.30) = 8% × 0.70 = 5.6%.

3) Compute WACC with intermediate arithmetic:
- Contribution from equity = w_E × r_E = 0.5 × 13.0% = 6.5%.
- Contribution from debt = w_D × r_D·(1 − T_c) = 0.5 × 5.6% = 2.8%.
- WACC = 6.5% + 2.8% = 9.3%.

4) Why this is correct:
- Uses market values for weights, CAPM for r_E, and the tax-adjusted cost of debt; all standard inputs and formulas applied correctly produce 9.30%.

5) Why common alternative approaches are incorrect:
- Using book values instead of market values changes weights and yields a different WACC.
- Using pre-tax r_D (8%) instead of after-tax (5.6%) overstates WACC.
- Miscomputing r_E (e.g., omitting beta or ERP) yields incorrect equity cost and thus wrong WACC.

6) Conclusion:
Final WACC = 9.30%, which matches the provided answer.

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.)数值题

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