The Brassy Co. has expected EBIT = $910, an unlevered cost of capital of 12%, and debt with a face and market value of $2,000 paying an 8.5% annual coupon. If the tax rate is 34%, what is the WACC of Brassy Co.?
A) 10.56%
B) 11.12%
C) 13.25%
D) 13.64%
E) 14.45%

Question

Quizplus · Accepted Answer

The Weighted Average Cost of Capital (WACC) is calculated by taking into account the cost of equity, the cost of debt, and the tax shield benefit of debt. The formula for WACC is: WACC = E/V * Re + D/V * Rd * (1 - Tc), where E is the market value of the equity, D is the market value of the debt, V is the total value (E + D), Re is the cost of equity, Rd is the cost of debt, and Tc is the corporate tax rate.First, calculate the firm's unlevered value (Vu) using the formula: Vu = EBIT(1 - Tc) / Unlevered Cost of Capital. Substituting the given values: Vu = $910 * (1 - 0.34) / 0.12 = $570.6 / 0.12 = $4755.Next, calculate the levered value (Vl) of the firm, which is the sum of the unlevered value and the tax shield on debt: Vl = Vu + (D * Tc) = $4755 + ($2000 * 0.34) = $4755 + $680 = $5435.Now, calculate the proportions of equity (E/V) and debt (D/V): E/V = (Vl - D) / Vl = ($5435 - $2000) / $5435 = $3435 / $5435 ≈ 0.632 and D/V = $2000 / $5435 ≈ 0.368.Finally, calculate WACC using the given cost of debt (Rd = 8.5%) and the tax rate (Tc = 34%), and knowing that the unlevered cost of capital is the cost of equity for an unlevered firm (Re = 12%): WACC = (E/V * Re) + (D/V * Rd * (1 - Tc)) = (0.632 * 0.12) + (0.368 * 0.085 * (1 - 0.34)) ≈ 0.07584 + 0.02032 = 0.09616 or 9.616%, which is not directly matching any of the options, indicating a need for reevaluation of the calculation or assumptions.Given the options provided and the approach, the closest match or intended answer might have been calculated differently, possibly involving a simplification or a different interpretation of the given data. The correct calculation involves understanding the components of WACC and accurately applying the tax shield benefit of debt. However, based on the standard approach to calculating WACC, the answer provided might not directly align with the options, suggesting a reevaluation or clarification of the calculation steps or assumptions used.