Omega limited has market values of loans, market values of bonds, market values of preference shares and market values of common shares of $384 million, $83 million, $360 million, and $236 million respectively. The pre-tax cost of loan is 3%, the yield to maturity is 7%, the cost of preference shares is 13%, the cost of common shares is 18%, and the tax rate is 30%.

Calculate the post-tax WACC.

If the answer is 10.4567%, write 0.1046.

Question

Omega limited has market values of loans, market values of bonds, market values of preference shares and market values of common shares of $384 million, $83 million, $360 million, and $236 million respectively. The pre-tax cost of loan is 3%, the yield to maturity is 7%, the cost of preference shares is 13%, the cost of common shares is 18%, 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 equals the weighted average of the after‑tax costs of debt plus the costs of preference and common equity, each weighted by their market value proportions.

1) Relevant concepts
- Use market-value weights: weight = market value of component / total market value.
- Debt interest is tax-deductible, so use after‑tax cost of debt = pre‑tax cost × (1 − tax rate).
- Preference shares and common equity costs are not tax-deductible, so use their stated costs.

2) Step‑by‑step reasoning and intermediate calculations
- Total market value = 384 + 83 + 360 + 236 = 1,063 (million).
- After‑tax cost of loans = 3% × (1 − 0.30) = 0.03 × 0.70 = 0.0210 (2.10%).
- After‑tax cost of bonds = 7% × (1 − 0.30) = 0.07 × 0.70 = 0.0490 (4.90%).
- Cost of preference shares = 13% = 0.13.
- Cost of common shares = 18% = 0.18.

Compute weighted contributions (market value × cost):
- Loans: 384 × 0.0210 = 8.064
- Bonds: 83 × 0.0490 = 4.067
- Preference shares: 360 × 0.13 = 46.8
- Common shares: 236 × 0.18 = 42.48

Sum of weighted costs = 8.064 + 4.067 + 46.8 + 42.48 = 101.411

Divide by total market value to get WACC:
WACC = 101.411 / 1,063 = 0.095389... ≈ 0.0954 (rounded to 4 decimal places)

3) Why this answer is correct
Each component’s cost was correctly adjusted for taxes where applicable (both loan and bond debt), weights were based on market values, and the weighted sum was normalized by total market value. The arithmetic yields 0.095389, which rounded to four decimals is 0.0954.

4) Common incorrect approaches (why other answers would be wrong)
- Forgetting to apply the (1 − tax rate) to debt costs (would overstate WACC).
- Treating preference shares as tax-deductible (would understate WACC).
- Using book values instead of market values (would change weights and give a different result).

Conclusion: The calculated post‑tax WACC is 0.0954, which matches the provided 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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