Lawler's is considering a new project. The company has a debt-equity ratio of 0.72. The company's cost of equity is 15.1 percent, and the aftertax cost of debt is 7.2 percent. The firm feels that the project is riskier than the company as a whole and that it should use an adjustment factor of +3 percent. What is the WACC it should use for the project?

Question

BlackTom AI · Accepted Answer

We begin by restating the given information and the question to set the stage for calculation:
- Debt–equity ratio D/E = 0.72
- Cost of equity Re = 15.1%
- After-tax cost of debt Rd = 7.2%
- The project is riskier than the firm, so an adjustment factor of +3 percentage points should be applied to the WACC for this project.
- We are asked: What is the WACC to use for the project?

First, compute the weights of debt and equity from the given debt–equity ratio. If D/E = 0.72, then D = 0.72 E. The total capitalization is D + E = 0.72E + E = 1.72E. The weight of debt wd is D/(D+E) = 0.72/1.72 ≈ 0.4186, and the weight of equity we is E/(D+E) = 1/1.72 ≈ 0.5814.

Next, calculate the base WACC (before the risk adjustment) using the weighted average formula:
WACC_base = wd * Rd + we * Re
Plugging in the numbers: WACC_base ≈ 0.4186 * 7.2% + 0.5814 * 15.1%.
- The debt contribution is 0.4186 × 7.2% ≈ 3.0139%
- The equity contribution is 0.5814 × 15.1% ≈ 8.7791%
Summing these gives WACC_base ≈ 11.793% (roughly 11.79%).

Apply the project risk adjustment of +3 percentage points to the base WACC: WACC_project ≈ 11.79% + 3.00% ≈ 14.79%.

Now, evaluate each answer option against this calculation:
- 12.53 percent: This is too low because it would require either a much smaller weight on debt, a much lower Rd, or no adjustment; with the given D/E and Rd, the base WACC is already around 11.79% prior to adjustment, so 12.53% is inconsistent with the data after adjustment.
- 12.98 percent: Closer than 12.53% but still inconsistent. Even without the risk adjustment, the base WACC is ~11.79%, and applying +3 percentage points yields ~14.79%, not 12.98%.
- 14.79 percent: This matches the calculated WACC after applying the +3 percentage-point risk adjustment to the base WACC derived from D/E and the given costs of equity and debt. It aligns with the step-by-step computation above.
- 15.14 percent: This is higher than the calculated 14.79% and would require a larger adjustment or different input values; with a +3 percentage-point adjustment, the base WACC would need to be about 12.14%, which is not the case here.

In summary, the correct WACC to use for the project, after incorporating the given capital structure and costs and applying the +3 percentage-point risk adjustment, is 14.79%. The other options fail to align with the weighted average of the firm's costs of capital and the specified risk adjustment because they either understate or overstate the combined effect of debt, equity, and the adjustment.

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