Question

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 semi-annually. 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. Group of answer choices 2.05 percent 1.19 percent 20.18 percent 15.27 percent

Answer 1

2.05 percent

Step-by-step explanation:

WACC is given by:

= weight of equity*cost of equity + weight of debt*cost of debt

total = $67500000

weight of equity is given by:

= $40000000/(5000000*$8.00 + 25000*$1100)

= ($40000000/$67500000)*100

= 59.26%

weight of debt = ($27500000/$67500000)*100

= 40.74%

after tax cost of debt = cost of debt(1 - tax rate)

= 0.09(1 - 0.35)

= 5.85%

WACC = (0.5926*cost of equity) + (0.4074*5.85%)

0.14 = (0.5926*cost of equity) + 0.0238329

cost of equity = 0.14 - 0.0238329 /0.5926

= 19.60%

cost of equity = risk free rate + beta(market return - risk free rate)

19.60% = risk free rate + 1.4(15% - risk free rate)

19.60% = risk free rate +21% - 1.4*risk free rate

0.4*risk free rate = 1.40%

risk free rate = 1.40%/0.4

risk free rate = 2.05%

Therefore, The risk-free rate is 2.05%