Question

Sunburn Sunscreen has a zero coupon bond issue outstanding with a $12,000 face value that matures in one year. The current market value of the firm’s assets is $13,800. The standard deviation of the return on the firm’s assets is 34 percent per year, and the annual risk-free rate is 6 percent per year, compounded continuously. The firm is considering two mutually exclusive investments. Project A has an NPV of $1,500, and Project B has an NPV of $2,300. As the result of taking Project A, the standard deviation of the return on the firm’s assets will increase to 49 percent per year. If Project B is taken, the standard deviation will fall to 21 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))

  

	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	$

Answer is not

Current market value of the firm’s assets = $13,800

Total Value of Firm = $13800 a-1 NPV of Project A = $1,500 Total Value of Firm if selects Project A = Current Value + NPV of the new Project = $13800 + $1500 = $15,300 Value of debt = $12000 Value of Equity= Value of Firm -Value of Debt = $15300 - $12000 = $3300 a-2 NPV of Project B = $2300 Total Value of firm if selects project B = Current Value + NPV of the new Project = $13800 + $2300 = $16100 Value of Debt = $12000 Value of Equity = Value of Firm -Value of Debt = $16100 - $12000 = $4,100

Answer 1

15,300 =13800+1500 49% 6% 12,000 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) X 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(D2) 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 5,036.68 15 Value of debt 10,263.32 0.8633 =(LN(C2/C5)+(C4+0.5*C3^2)*C6)/(C3*C6^0.5) 0.3733 =(LN(C2/C5)+(C4-0.5*C3^2) *C6)/(C3*C6^0.5) 0.8060 =NORM.S.DIST(C7,TRUE) 0.6455 =NORM.S.DIST(C8,TRUE) 5,036.68 =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 16,100 =13800+2300 19 standard deviation of the return on assets sigma 21% 20 annual risk-free rate 6% 21 Exercise Price(Face value of debt) X 12,000 22 Time to Maturity(yrs) 23 d1 [In(So/X)+(r+.5*sigma^2) *T]/[sigma*sqrt(T)] 1.7903 =(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)] 1.5803 =(LN(C18/C21)+(C20-0.5*C19~2)*C22)/(C19*C22~0.5) | 25 N(D1) N(D1)=NORM.S.DIST(d1, TRUE) 0.9633 ENORM.S.DIST(C23, TRUE) 26 N(2) N(D2)=NORM.S.DIST(d2, TRUE) 0.9430 =NORM.S.DIST(C24,TRUE) 27 call option value on Firm's Assets SO*N(01)-X*exp(-rT)*N(02) 4,852.29 =C18*C25-C21*EXP(-C20*С22)*C26 (=Value of Equity) 29 30 Value of equity 4,852.29 31 Value of debt 11,247.71 28

a-1) Equity Debt $ 5,036.68 $ 10,263.32 a-2) Equity Debt $ 4,852.29 $11,247.71 b) Project A c) Yes

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