Sunburn Sunscreen has a zero coupon bond issue outstanding with a $13,000 face v

Question

Sunburn Sunscreen has a zero coupon bond issue outstanding with a $13,000 face value that matures in one year. The current market value of the firm's assets is $13,200. The standard deviation of the return on the firms assets is 34 percent per year, and the annual risk-free rate is 4 percent per year, compounded continuously. The firm is considering two mutually exclusive investments. Project A has an NPV of $1,400, and Project B has an NPV of $2,200. As the result of taking Project A, the standard deviation of the return on the firm's assets will increase to 48 percent per year. If Project B is taken, the standard deviation will fall to 22 percent per year a-1. What is the value of the firms equity and debt if Project A is undertaken? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)) Market value Equity Debt a-2. What is the value of the firm's equity and debt if Project B is undertaken? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)) Market value Equity Debt

Explanation / Answer

We can find the value of equity using the Black Scholes Model We would use asset value of ($13200+$1400) = $14600 as the stock price and face value of of debt $ 13000 as the exercise price, if project A is undertaken the value of debt and equity would be as follows We will calculate value of N(d1) and N(d2) Equity(A) = Stock Price*N(d1) - Debt e^(-r)N(d2) d1 =(In($14600/$13000) + (0.04 + (0.48^2)/2*1)/(0.48*1^0.50) d1 = ((In 1.123077) + 0.1552)/0.48 Solving above we get, d1 as 0.5652 Using normal distribution, we get N(d1) as 0.714 d2 = 0.5652 - (0.48^(1^0.50) d2 = 0.0852 0.5339 N(d2) = 0.5339 Equity (A) = 14600*0.714 - 13000e^(-0.04)*0.5339 Equity (A) = $ 10424.40 - $ 6668.9144 Equity (A) = 3755.69 Debt = $14600 - $3755.69 Debt = $ 10844.31 Market Value Equity $ 3755.69 Debt $ 10844.31 a-2 If Project B is undertaken, the asset value is ($13000 + $2200) = $15200 and value of debt is $13000 Equity(A) = Stock Price*N(d1) - Debt e^(-r)N(d2) d1 =(In($15200/$13000) + (0.04 + (0.22^2)/2*1)/(0.22*1^0.50) d1 = ((In 1.169231) + 0.0642)/0.22 Solving above we get, d1 as 1.0025 Using normal distribution, we get N(d1) as 0.8419 d2 = 1.0025 - (0.22^(1^0.50) d2 = 0.7825 0.5339 N(d2) = 0.7830 Equity (A) = 15200*0.8419 - 13000e^(-0.04)*0.7830 Equity (A) = $ 12796.88 - $ 9779.876 Equity (A) = $ 3017.25 Debt = $15200 - $3017.25 Debt = $ 12182.75 Market Value Equity $ 3017.25 Debt $ 12182.75

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