Problem
16. The market value of $A B C^{\prime}$ s bonds is $\$ 10$ million while the market value of its common stock is $\$ 20$ million, resulting in a debt/equity ratio of 0.33 . The cost of common stock equity is estimated to be $17 \%$ using the DGM and $19 \%$ using the CAPM. The bond coupon rate and YTM are both $11 \%$ per year. The income tax rate is $40 \%$. Assuming that only debt and common equity financing exist, what is the firm's weighted-average cost of capital? (Use several decimals to reduce any rounding error.) a. $15.5 \%$ b. $12.9 \%$ c. $14.2 \%$ d.15.7\% e. None of the other statements is true.
Solution
Step 1 ：Calculate the total value of the firm (V) by adding the market value of debt (D) and equity (E): \(V = D + E = 10,000,000 + 20,000,000 = 30,000,000\)
Step 2 ：Calculate the average cost of equity (Re) using the DGM and CAPM estimates: \(Re = \frac{DGM + CAPM}{2} = \frac{0.17 + 0.19}{2} = 0.18\)
Step 3 ：Calculate the weighted-average cost of capital (WACC) using the formula: \(WACC = \frac{E}{V} \times Re + \frac{D}{V} \times Rd \times (1 - Tc)\)
Step 4 ：Plug in the values and calculate WACC: \(WACC = \frac{20,000,000}{30,000,000} \times 0.18 + \frac{10,000,000}{30,000,000} \times 0.11 \times (1 - 0.4) = 0.142\)
Step 5 ：\(\boxed{WACC = 14.2\%}\)
