Please show your work for each question rather than simply providing an answer.
ID: 2701698 • Letter: P
Question
Please show your work for each question rather than simply providing an answer.
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Q2 (15 points): SFE 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's the cost of equity?
d) What's the after-tax WACC?
Q1 (5 points): What 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?Q2 (15 points): SFE 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's the cost of equity?
d) What's the after-tax WACC?
Explanation / Answer
Q1 What 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?
We have Krf = 4%, Beta = 1.5, Yield =Ks =16%
We have Yield Ks = Krf + Beta*MRP
So MRP = (Ks-Krf)/beta = (16%-4%)/1.5 = 8.00%
So Risk Prem is 8.00%
Q2 (15 points): SFE 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?
Total Firm Value = Equity + Debt
= 1M*$50 + 1.10*$10M
= $50M + $11M
= $61M
SO Ratio of Debt to Firm value = $11/$61 = 0.1803 or 18.03%
b) What is the after-tax cost of debt?
We have Face value of Debt = FV = $10M
Current price = 110%*FV = 1.10*10 = $11M
Coupon = 10.5%. So PMT = 10.5%*FV = 10.5%*10M = 1.05M
No of periods = 5 Yrs = 5
So Return on Bond Kd = Rate(nper,pmt,pv,fv)
= Rate(5,1.05,-11,10)
so Kd = 8.00%
SO AFter Tax cost fo debt = Kd*(1-t) = 8%*(1-35%) = 5.20%
c) What's the cost of equity?
Cost of Equity Ks = Krf + Beta*MRP
= 4%+ 1.2*8% = 13.60%
d) What's the after-tax WACC?
The WACC formula states that:
WACC = kd * wd * (1 - t) + ke * we
Where:
kd = cost of debt=8%
wd = % debt =18.03%
t = tax rate=35%
ke = cost of common equity = 13.60%
we = % common equity==50/61 =81.97%
So WACC = 8%*18.03%*(1-35%) + 13.6%*81.97% = 12.09%