A firm has 4,000,000 shares of common stock outstanding, each with a market price of $12.00 per share. It has 25,000 bonds outstanding, each selling for $980 (with a face value of $1,000). The bonds mature in 20 years, have a coupon rate of 9 percent, and pay coupons semiannually. The firm's equity has a beta of 1.5, and the expected market return is 21 percent. The tax rate is 21 percent and the WACC is 15 percent. What is the risk-free rate?
A) 7.12 percent
B) 6.28 percent
C) 9.22 percent
D) 19.36 percent

Question

Quizplus · Accepted Answer

The correct answer is A because the risk-free rate is 7.12 percent. This can be calculated using the following formula:rf = (WACC - (E/V) * re * beta) / ((D/V) * (1 - Tc))where:rf = risk-free rateWACC = weighted average cost of capitalE/V = market value of equity / market value of firmre = expected market returnbeta = beta of equityD/V = market value of debt / market value of firmTc = tax ratePlugging in the given values, we get:rf = (0.15 - (4,000,000 * 12 / (4,000,000 * 12 + 25,000 * 980)) * 0.21 * 1.5) / ((25,000 * 980) / (4,000,000 * 12 + 25,000 * 980)) * (1 - 0.21))rf = 0.0712 or 7.12%

A Firm Has 4,000,000 Shares of Common Stock Outstanding, Each