A firm's capital structure includes debt, 60% common stock, and no preferred stock. The after-tax cost of debt is 5%, and the cost of equity is 10%. What is the WACC?

Question

BlackTom AI · Accepted Answer

We start by identifying the capital structure weights and the corresponding costs given in the problem. The firm has debt and 60% common stock, with no preferred stock, which implies the equity weight is 60% and the debt weight is 40% (since 100% - 60% = 40%). The after-tax cost of debt is 5% and the cost of equity is 10%. The formula for WACC is: WACC = wd * rd(1 - T) + we * re, where wd is the weight of debt, rd is the cost of debt, T is the tax rate, we is the weight of equity, and re is the cost of equity.

Option by option analysis:
- Option 6.00%: If we compute using the given numbers, 0.40 * 0.05 = 0.02 (2%), and 0.60 * 0.10 = 0.06 (6%), summing to 0.08 (8%). Therefore, 6.00% would be too low because it omits the equity contribution entirely, which is 6 percentage points in this calculation.

- Option 8.00%: This matches the calculated WACC using wd = 0.40, rd = 0.05, we = 0.60, re = 0.10: 0.40 * 0.05 = 0.02, and 0.60 * 0.10 = 0.06; total = 0.08 or 8%. This is consistent with the standard WACC formula.

- Option 7.00%: This would arise if one of the components were misvalued. For example, using 0.40 * 0.05 = 0.02 and 0.60 * 0.10 = 0.05 would yield 0.07, but the cost of equity is stated as 10%, not 8% or 5%, so 7.00% ignores part of the equity contribution.

- Option 9.00%: This would occur if the debt portion were weighted more heavily or if both costs were attributed differently. However, with debt at 40% carrying 5% after-tax cost and equity at 60% carrying 10%, the sum cannot exceed 8% under the given inputs, making 9.00% inconsistent with the data.

In summary, the WACC derived from the provided capital structure and costs is 8%, since the debt contribution is 2 percentage points and the equity contribution is 6 percentage points, totaling 8%.

A firm's capital structure includes debt, 60% common stock, and no preferred stock. The after-tax cost of debt is 5%, and the cost of equity is 10%. What is the WACC?单项选择题

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