Question

The current stock price for a company is $47 per share, and there are 8 million shares outstanding. The beta for this firms stock is 1, the risk-free rate is 4.5, and the expected market risk premium is 5.9%. This firm also has 250,000 bonds outstanding, which pay interest semiannually. These bonds have a coupon interest rate of 9%, 23 years to maturity, a face value of $1,000, and an annual yield to maturity of 8.2%. If the corporate tax rate is 32%, 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). Selected Answer: Incorrect 8.3 Correct Answer: Correct 8.38 ± 0.04

Answer 1

Required return on equity= Risk free rate + Market risk premium*beta

= 4.5 + 5.9*1

= 10.4%

Price of stock =$47

Number of shares outstanding = 8 million

Total market value= $47*8 million = $376 million

Price of bond = Coupon amount* PVAF(r%, n) + Redemption amount PVIF(r%,n)

Given coupon rate = 9% semi annually that is 4.5% every six months

time to maturity= 23 years which is 46 periods of six months each.

Face value= $1,000

Annual YTM = 8.2% that is 4.1% every six month period)

Price = $1,000*4.5%*PVAF(4.1%,46)+$1,000*PVIF(4.1%,46)

= $ 45 * 20.5489 + $ 1,000 * 0.1575

= $(924.7+157.5)

= $1,082.2

Number of outstanding bonds = 2,50,000

Market value of bonds = $ 1,082.2 * 2,50,000 = $ 270.55 million

Tax rate = 32%

Post tax cost of debt = Yield to maturity(1-tax rate) = 8.2(1-0.32) = 5.576%

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

Weight of equity = 376/(376+270.55) = 0.58 so weight of debt is 0.42.

Thus WACC = 10.4 * 0.58 + 5.576 * 0.42 = 6.032 + 2.34192 = 8.36192 or 8.36