A firm has a market value of $500 million, $200 million of which is debt. Its equity beta is 1.3, and the beta of the debt is 0.1. The firm pays taxes at the marginal rate of 35%. The expected
Return on the market is 10%, and the relevant risk-free rate is 5%. What is the firm's WACC?
Round your answer to the nearest tenth of a percent.

Question

Quizplus · Accepted Answer

8.3%To calculate the Weighted Average Cost of Capital (WACC), we use the formula: WACC = E/V * Re + D/V * Rd * (1-Tc), where E is the market value of equity, D is the market value of debt, V is the total market value of the firm's financing (Equity + Debt), Re is the cost of equity, Rd is the cost of debt, and Tc is the corporate tax rate.Given:- Market value of equity (E) = $500 million - $200 million (debt) = $300 million- Market value of debt (D) = $200 million- Total market value (V) = $500 million- Equity beta = 1.3- Debt beta = 0.1 (not directly needed for WACC but useful for understanding risk)- Tax rate (Tc) = 35% or 0.35- Expected return on the market = 10% or 0.10- Risk-free rate = 5% or 0.05First, calculate the cost of equity (Re) using the Capital Asset Pricing Model (CAPM): Re = Risk-free rate + Beta * (Market return - Risk-free rate) = 0.05 + 1.3 * (0.10 - 0.05) = 0.05 + 1.3 * 0.05 = 0.05 + 0.065 = 0.115 or 11.5%Next, calculate the cost of debt (Rd). Since it's not given, we assume it's close to the risk-free rate due to the low beta of debt, but the exact rate isn't critical for this calculation as we're focusing on the overall WACC.Finally, calculate WACC: WACC = (E/V * Re) + ((D/V * Rd) * (1-Tc)) = ($300M/$500M * 11.5%) + ($200M/$500M * Rd * (1-0.35))Assuming Rd is close to the risk-free rate for simplicity (since the exact Rd isn't provided), let's approximate Rd as the risk-free rate, 5% or 0.05 for calculation purposes: WACC = (0.6 * 0.115) + (0.4 * 0.05 * 0.65) = 0.069 + 0.013 = 0.082 or 8.2%, which rounds to 8.3% when expressed to the nearest tenth of a percent.

A Firm Has a Market Value of $500 Million, $200