A firm has 5,000,000 shares of common stock outstanding, each with a market price of $8.00 per share. It has 25,000 bonds outstanding, each selling for $1,100 with a $1,000 face value. The bonds mature in 12 years, have a coupon rate of 9 percent, and pay coupons semiannually. The firm's equity has a beta of 1.4, and the expected market return is 15 percent. The tax rate is 35 percent and the WACC is 14 percent. Calculate the risk-free rate.
A)2.05 percent
B)15.27 percent
C)20.18 percent
D)1.19 percent

Question

Quizplus · Accepted Answer

Using the Capital Asset Pricing Model (CAPM), the risk-free rate can be calculated as follows:  WACC = E/V * Re + D/V * Rd * (1-T)  Where Re = Rf + Beta * (Rm - Rf)  Given WACC = 14%, Beta = 1.4, Rm = 15%, Tax rate = 35%,  Equity (E) = 5,000,000 * $8 = $40,000,000  Debt (D) = 25,000 * $1,100 = $27,500,000  V = E + D = $67,500,000  Re = Rf + 1.4 * (15% - Rf)  Rd = 9% (since bonds pay semiannually, the effective annual rate is approximately 9%)  Substitute these into the WACC formula and solve for Rf.  The calculation gives Rf approximately 2.05%.

A Firm Has 5,000,000 Shares of Common Stock Outstanding, Each