Question

Sunburn Sunscreen has a zero coupon bond issue outstanding with a $25,000 face value that matures in one year. The current market value of the firm’s assets is $27,200. The standard deviation of the return on the firm’s 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 $2,300, and Project B has an NPV of $3,100. 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 29 percent per year. a-1. What is the value of the firm’s equity and debt if Project A is undertaken? Equity = ?? Debt = ?? a-2. What is the value of the firm’s equity and debt if Project B is undertaken? Equity = ?? Debt = ??

Answer 1

Firm assets(S) = $ 27200

Debt face value(X) = $ 25000

Standard Deviation = 34%

Risk Free rate = 4%

a) For Project A, standard deviation = 48% and NPV = 2300, so firm value becomes = 27200+2300 = 29500
d1 = [ln(29500/25000) + (0.04 + 0.48^2/2)*1]/[0.48*sqrt(1)] = 0.6682

d2 = 0.6682-(0.48*sqrt(1)) = 0.1882

N(d1) = 0.7480

N(d2) = 0.5746

Equity = $29500*(0.7480) - ($25,000*exp(-0.04*1))*(0.5746) = $ 8263.21

Debt = $29500- $8263.21= $ 21236.79

b) For Project B, standard deviation = 29% and NPV = 3100, so firm value becomes = 27200+3100 = $30300
d1 = [ln(30300/25000) + (0.04 + 0.29^2/2)*1]/[0.29*sqrt(1)] = 0.9459

d2 = 0.9459-(0.29*sqrt(1)) = 0.6559

N(d1) = 0.8279

N(d2) = 0.7441

Equity = $30300*(0.8279) - ($25,000*exp(-0.04*1))*(0.7441) = $ 7213.35

Debt = $30300- $7213.35= $ 23086.65