The current stock price for a company is $40 per share, and there are 3 million

Question

The current stock price for a company is $40 per share, and there are 3 million shares outstanding. The beta for this firms stock is 1.2, the risk-free rate is 4.7, and the expected market risk premium is 5.9%. This firm also has 180,000 bonds outstanding, which pay interest semiannually. These bonds have a coupon interest rate of 7%, 16 years to maturity, a face value of $1,000, and a current price of 926.36. If the corporate tax rate is 34%, 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

Total Capital of the company = ($40 x 3,000,000) + ($926.36 x 180,000) =$286,744,800

Weight of equity = ($40x3,000,000) / $286,744,800 = 0.4185 or 41.85%

So, weight of debt = 1 – 0.4185 = 0.5815 or 58.15%

Required return on equity = Rf + Beta*(Market Risk Premium) => 4.7% +1.2*(5.9%) = 11.78%

So, cost of equity = 11.78%

YTM of the bond:
Bond Value = C/2 {[1-(1+(YTM/2))-2t/(YTM/2)] + [F / (1+ (YTM/2))2t]

B0 = $926.36
C = $1,000 x 7% = $70
F = $1,000
YTM = the yield to maturity on the bond
t = 16

$926.36 = $70/2 {[1-(1+(YTM/2))-32/(YTM/2)] + [$1,000 / (1+ (YTM/2))32] = 7.81%

After tax cost of debt = 7.81% * (1 – tax rate)
=> 7.81%*(1 – 0.34) = 5.1546%

WACC = (Weight of debt x After tax cost of debt) + (Weight of equity x Cost of equity)
            = (0.5815 x0.051546) + (0.4185 x 0.1178) = 0.079273

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