Question

Sunburn Sunscreen has a zero coupon bond issue outstanding with a $14,000 face value that matures in one year. The current market value of the firm’s assets is $15,300. 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 $2,900, and Project B has an NPV of $3,800. 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 20 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 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 answers to 2 decimal places, e.g., 32.16.)

  

	Market value
Equity	$
Debt	$

  

b.	Which project would the stockholders prefer?
	Project A Project B

  

c.	Suppose the stockholders and bondholders are in fact the same group of investors. Would this affect your answer to (b)?
	No Yes

Answer 1

18,200 =15300+2900 47% 5% 14,000 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 Maturitylyrs) 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(dl) N(D1)=NORM.S.DIST(d1, TRUE) 10 N(02) N(D2)=NORM.S.DIST(d2, TRUE) 11 call option value on Firm's Assets SO*N(01)-X*exp(-rT)*N(02) 12 13 14 Value of equity 5,975.49 15 Value of debt 12,224.51 0.8996 =(LN(C2/C5)+(C4+0.5*C3^2) *C6)/(C3*C6^0.5) 0.4296 =(LN(C2/C5)+(C4-0.5*C3^2) *C6)/(C3*C6^0.5) 0.8158 ENORM.S.DIST(C7,TRUE) 0.6663 =NORM.S.DIST(C8, TRUE) 5,975.49 =C2*C9-C5*EXP(-C4*C6)*C10 (=Value of Equity) 16 17 BSM Call Option Pricing Model 18 current value of the company's assets SO 15,600 =15300+300 19 standard deviation of the return on assets sigma 20% 20 annual risk-free rate 5% 21 Exercise Price(Face value of debt) X 14,000 22 Time to Maturity(yrs) 23 d1 [In(So/X)+(r+.5*sigma^2) *T]/[sigma*sqrt(T)] 0.8911 =(LN(C18/C21)+(C20+0.5*C19^2) *C22)/(C19*C22~0.5) 24 d2 [In(So/X)+(r-.5*sigma^2) *T]/[sigma*sqrt(T)] 0.6911 =(LN(C18/C21)+(C20-0.5*C19^2)*C22)/(C19*C22~0.5) 25 N(d1) N(D1)=NORM.S.DIST(d1, TRUE) 0.8136 =NORM.S.DIST(C23, TRUE) 26 N(2) N(D2)=NORM.S.DIST(d2, TRUE) 0.7552 =NORM.S.DIST(C24, TRUE) 27 call option value on Firm's Assets SO*N(01)-X*exp(-rT)*N(02) : 2,633.76 |=C18*C25-C21*EXP(-C20*С22)*C26 (=Value of Equity) 29 30 Value of equity 2,633.76 31 Value of debt 12,966.24 28

a-1) Equity Debt $ 5,975.49 $ 12,224.51 a-2) Equity Debt $ 2,633.76 $ 12,966.24 b) Project A c) Yes

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