1%u3002What is the expected return on the market portfolio at a time when the ri

Question

1%u3002What is the expected return on the market portfolio at a time when the risk free rate (e.g., T-Bill rate) is 4% and a stock with a beta of 1.5 is expected to yield 16%? What%u2019s the risk premium for this stock?

2%u3002SFE Inc. has 1 million shares of common stock outstanding at a book value of $40 per share. The stock trades for $50 per share. It also has $10 million in face value of debt (corporate bonds of 5 years with coupon rate 10.5%) that trades at 110% of face value. The company%u2019s equity beta is 1.2. The risk-free rate is 4% and the market risk premium is 8%. The corporate tax rate for SFE is 35%.

a)      What is its ratio of debt to total firm value?

b)      What is the after-tax cost of debt?

c)      What%u2019s the cost of equity?

d)     What%u2019s the after-tax WACC?

Explanation / Answer

First problem

Stock return = 16% = risk free rate + beta * risk premium = 4% + 1.5* premium, which means risk premium = 8%

Market return = risk free rate + risk premium = 4%+8% = 12%

Second problem

Market value of equity = 1 million shares * $50/share = $50 million

Market value of debt = $10 million * 110% = $11 million

So firm value = $50 + $11 = $61 million

a. Ratio of debt to firm value = 11/61 = 0.1803

b. Yield of the bond is calculated in Excel as =RATE(5,10.5,-110,100,0). This is equal to 8%, which is the pretax cost of debt.

After tax cost of debt = 8%*(1-tax rate) = 8%*(1-35%) = 5.2%

c. Cost of equity = risk free + beta *risk premium = 4%+1.2*8% = 13.6%

d. WACC = (11/61)*5.2% + (50/61)*13.6% = 12.08%

Hope this helped ! Let me know in case of any queries.

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