Sigma Limited has market values of debt, market values of preference shares, and market values of common shares of $81 million, $22 million, and $187 million respectively. The pre-tax cost of debt is 4%, the cost of preference shares is 10%, the cost of common shares is 20%, and the tax rate is 30%.

Calculate the post-tax WACC.

If the answer is 10.4567%, write 0.1046.

Question

Sigma Limited has market values of debt, market values of preference shares, and market values of common shares of $81 million, $22 million, and $187 million respectively. The pre-tax cost of debt is 4%, the cost of preference shares is 10%, the cost of common shares is 20%, and the tax rate is 30%.

Calculate the post-tax WACC.

If the answer is 10.4567%, write 0.1046.

BlackTom AI · Accepted Answer

WACC is the weighted average cost of capital: a firm’s after‑tax cost of debt and the costs of preference and common equity weighted by their market value proportions.

1. Relevant concepts
- Use market values to compute weights: wd = D/V, wp = P/V, we = E/V where V = D+P+E.
- Interest on debt is tax‑deductible, so use post‑tax cost of debt = kd × (1 − T).
- WACC = wd × kd_posttax + wp × kp + we × ke.

2. Step‑by‑step reasoning
- Compute total market value V.
- Compute weights wd, wp, we.
- Convert pre‑tax debt cost to post‑tax.
- Multiply each cost by its weight and sum.

3. Calculations (all intermediate steps)
- Given: D = 81, P = 22, E = 187 → V = 81 + 22 + 187 = 290.
- Weights:
  wd = 81 / 290 = 0.2793103448
  wp = 22 / 290 = 0.0758620690
  we = 187 / 290 = 0.6448275862
- Post‑tax cost of debt: kd_posttax = 0.04 × (1 − 0.30) = 0.04 × 0.70 = 0.0280 (2.80%).
- Weighted components:
  Debt: 0.2793103448 × 0.0280 = 0.0078206497
  Preference: 0.0758620690 × 0.10 = 0.0075862069
  Equity: 0.6448275862 × 0.20 = 0.1289655172
- Sum WACC = 0.0078206497 + 0.0075862069 + 0.1289655172 = 0.1443723738 ≈ 0.1444

4. Why this is correct
- Market‑value weights correctly reflect investors’ required returns.
- The tax shield on debt reduces the effective cost of debt to 2.8%, which lowers WACC relative to using the pre‑tax debt rate.
- All components are combined as a weighted average, producing 14.437% (0.1444).

5. Why other approaches are wrong
- Using pre‑tax debt (4%) ignores the tax deductibility of interest and overstates WACC (would give ≈0.1477).
- Using book values instead of market values gives incorrect weights.
- Omitting any component (e.g., preference shares) misstates the weighted average.

6. Conclusion
The computed post‑tax WACC is 0.1444, which matches the provided correct answer.

类似问题

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?

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.)

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