Question

Sunburn Sunscreen has a zero coupon bond issue outstanding with a $24,000 face value that matures in one year. The current market value of the firm’s assets is $24,900. The standard deviation of the return on the firm’s assets is 34 percent per year, and the annual risk-free rate is 5 percent per year, compounded continuously. The firm is considering two mutually exclusive investments. Project A has an NPV of $2,200, and Project B has an NPV of $3,000. As the result of taking Project A, the standard deviation of the return on the firm’s assets will increase to 47 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? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

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))

b. Which project would the stockholders prefer?

Suppose the stockholders and bondholders are in fact the same group of investors. Would this affect your answer to (b)?

Answer 1

SO 27,100 =24900+2200 47% 5% 24,000 1 BSM Call Option Pricing Model 2 Current value of the company's assets 3 Standard deviation of the return on assets sigma 4 Annual risk-free rate 5 Exercise Price(Face value of debt) 6 Time to Maturity lyrs) 7 d1 [In(So/X)+(r+.5*sigma^2) *T]/[sigma*sqrt(T)] 8 d2 [In(So/X)+(r-.5*sigma^2) *T]/[sigma*sqrt(T)] 9 N(d1) N(D1)=NORM.S.DIST(d1, TRUE) 10 N(D2) N(02)=NORM.S.DIST(02,TRUE) 11 call option value on Firm's Assets SO*N(d1)-x*exp(-rT)*N(2) 0.5999 LN(C2/C5)+(C4+0.5*C3^2)*C6)/(C3*C6^0.5) 0.1299 =(LN(C2/C5)+(C4-0.5*C3^2) *C6)/(C3*C6^0.5) 0.7257 ENORM.S.DIST(C7, TRUE) 0.5517 ENORM.S.DIST(C8, TRUE) $ 7,072.32 =C2*C9-C5*EXP(-C4*C6)*C10 (=Value of Equity) 12 13 14 Value of equity 15 Value of debt $ 7,072.32 20,027.68 16 27,900 =24900+3000 29% 5% 24,000 17 BSM Call Option Pricing Model 18 current value of the company's assets 19 standard deviation of the return on assets sigma 20 annual risk-free rate 21 Exercise Price(Face value of debt) 22 Time to Maturity lyrs) 23 d1 [In(So/X)+(r+.5*sigma^2) *T]/[sigma*sqrt(T)] 24 d2 [In(So/X)+(r-.5*sigma^2) *T]/[sigma*sqrt(T)] N(D1)=NORM.S.DIST(d1, TRUE) 26 N(D2) N(02)=NORM.S.DIST(02,TRUE) 27 call option value on Firm's Assets SO*N(d1)-x*exp(-rT)*N(2) 25 Nd1) 0.8366 =(LN(C18/C21)+(C20+0.5*C19^2)*C22)/(C19*C22~0.5) 0.5466 =(LN(C18/C21)+(C20-0.5*C19^2)*C22)/(C19*C22~0.5) 0.7986 ENORM.S.DIST(C23, TRUE) 0.7077 =NORM.S.DIST(C24,TRUE) $ 6,124.87 |=C18*C25-C21*EXP(-C20*С22)*C26 (=Value of Equity) 29 30 Value of equity 31 Value of debt 6,124.87 21,775.13

a-1) Equity Debt $ 7,072.32 $ 20,027.68 a-2) Equity Debt $ 6,124.87 $ 21,775.13 b) Project A c) Yes

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