QUESTION 40 The current stock price for a company is $34 per share, and there ar
ID: 2800959 • Letter: Q
Question
QUESTION 40 The current stock price for a company is $34 per share, and there are 8 million shares outstanding. The beta for this firms stock is 1.6, the risk-free rate is 4.8, and the expected market risk premium is 5.8%. This firm also has 200,000 bonds outstanding, which pay interest semiannually. These bonds have a coupon interest rate of 8%, 24 years to maturity, a face value of $1,000, and a current price of 1,029.96. If the corporate tax rate is 33%, what is the Weighted Average Cost of Capital (WACC) for this firm? (Answer to the nearest hundredth of a percent, but do not use a percent sign).
Explanation / Answer
Current price of stock, P0 = $34
Number of shares outstanding = 8 Million
Total market value of equity = 8 M shares * $34 Per share
= $272 Million
Beta of stock = 1.6
Risk free rate, Rf = 4.8%
Market risk premium, Rm - Rf = 5.8%
Cost of equity, Ke = Rf + Beta*(Rm - Rf)
= 4.8% + 1.6 * 5.8%
= 14.08%
Number of bonds = 200,000
Current price of bond, P = $1,029.96
Face value of bond(Maturity value),M = $1,000
Total market value of bonds = 200,000 *$1,029.96
= $205,992,000 = $205.992 M
Coupon rate = 8% *6/12 = 4% Per period
Coupon amount,C=Face value*Coupon rate=$1,000*4% = $40
Term,n = 24 Years *2 = 48 Periods
YTM = [ C + (M - P)/n] / [ (P + M)/2]
= [$40+($1,000 - $1,029.96)/48]/[($1,029.96+$1,000)/2]
= $39.375833 / $1,014.98
= 0.0387946886
= 3.88% Per period
YTM = 3.88% Per period * 2 = 7.76% Per annum
After tax cost of debt , Kd = YTM*(1 - Tax rate)
= 7.76%*( 1 - 33%)
= 5.1992% Per annum
Total value of firm = Debt + Equity
= $205.992 M + $272 M
= $477.992 Million
Weight of debt, Wd = Debt / Value of firm
= $205.992 M / $477.992 M
= 0.4309528193 = 0.431
Weight of equity, We = 1 - 0.431 = 0.569
WACC = Wd * Kd + We * Ke
= 0.431 * 5.1992% + 0.569 * 14.08%
= 2.2408552% + 8.01152%
= 10.2523752%
= 10.25% (Rounded)
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