A firm has 1,000,000 shares of common stock outstanding, each with a market price of $10.00 per share. It has 15,000 bonds outstanding, each selling for $900 (with a face value of $1,000). The bonds mature in 15 years, have a coupon rate of 10 percent, and pay coupons annually. The firm's equity has a beta of 1.5, and the expected market return is 20 percent. The tax rate is 21 percent and the WACC is 16 percent. What is the risk-free rate?
A) 9.16 percent
B) 11.4 percent
C) 4.8 percent
D) 16.0 percent

Question

Quizplus · Accepted Answer

The correct answer is A because the risk-free rate is 9.16 percent. This can be calculated using the following formula:Rf = YTM - (YTM x (1 - Tc) x Beta x (Rm - Rf))where:Rf = risk-free rateYTM = yield to maturity on the bondTc = tax rateBeta = beta of the equityRm = expected market returnPlugging in the given values, we get:Rf = 0.10 - (0.10 x (1 - 0.21) x 1.5 x (0.20 - Rf))Rf = 0.10 - (0.10 x 0.79 x 1.5 x (0.20 - Rf))Rf = 0.10 - (0.1878 - 0.1878Rf)Rf = 0.10 - 0.1878 + 0.1878Rf0.2878Rf = 0.0878Rf = 0.0878 / 0.2878Rf = 0.0916 or 9.16%

A Firm Has 1,000,000 Shares of Common Stock Outstanding, Each