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 $26,100. The standard deviation of the return on the firm's assets is 41 percent per year, and the annual risk-free rate is 5 percent per year, compounded continuously. Frostbite Thermalwear has a zero coupon bond Issue outstanding with a face value of $37,000 that matures in one year. The current market value of the firm's assets Is $40,400. The standard deviation of the return on the firm's assets is 44 percent per year. Sunce Sunburn Sunscreen and Frostbite Thermalwear have decided to merge. Because the two companies have seasonal sales, the combined firm's return on assets will have a standard deviation of 21 percent per year. 6-1. What is the combined value of equity in the two existing companies? (Do not round Intermediate calculations and round your final answer to 2 decimal places. (e.g. 32.16)) Equity $D - What is the combined value of debt in the two existing companies? (Do not round 2. Intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Debt $ b-1. What is the value of the new firm's equity? (Do not round Intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Equity b. What is the value of the new firm's debt? (Do not round Intermediate calculations 2. and round your final answer to 2 decimal places. (e.g., 32.16)) Debt $D c.1. What was the gain or loss for shareholders? (Loss amount should be indicated by a minus sign. Do not round Intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Gain / Loss $D c. What was the gain or loss for bondholders? (Loss amount should be indicated by a 2. minus sign. Do not round Intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Gain / Loss

Answer 1

В D 1 BSM Call Option Pricing Model current value of the company's assets 3 standard deviation of the return on assets sigma $ S0 26,100 41% 5% 4 annual risk-free rate 5 Exercise Price (Face value of debt) 6 Time to Maturity(yrs) 7 d1 8 d2 $ X 25,000 1 [In(So/X)+(r+.5*sigma^2)*T]/[sigma*sqrt(T)] [In(So/X)+(r.5*sigma^2)*T]/[sigma*sqrt(T) N(d1) NORM.S.DIST(d1,TRUE) N(d2) NORM.S.DIST(d2,TRU E) SO*N(d1)-X*exp(-rT)*N(d2) 0.4320(LN(C2/C5)+(C4+0.5*C3^2)*C6)/(C3*C6^0.5) 0.0220 (LN(C2/C5)+(C4-0.5*C3^2)*C6)/(C3*C6^0.5) 0.6671 NORM.S.DIST(C7,TRUE) 0.5088NORM.S.DIST(C8,TRUE) 5,313.01C2*C9-C5*EXP(-C4*C6)*C10 9 N(d1) 10 N(d2) $ (=Value of Equity 11 call option value on Firm's Assets 12 13 14 Value of equity 15 Value of debt $ 5,313.01 $ 20,786.99 16 17 BSM Call Option Pricing Model 18 current value of the company's assets 19 standard deviation of the return on assets sigma $ SO 40,400 44% 5% 20 annual risk-free rate 21 Exercise Price(Face value of debt) 22 Time to Maturity(yrs) $ X 37,000 1 [In(So/X)+(r+.5*sigma^2)*T]/[sigma*sqrt(T)] [In(So/X)+(r-.5*sigma^2)*T]/[sigma*sqrt(T)] N(d1)-NORM.S.DIST(d 1,TRUE) N(d2) NORM.S.DIST(d2,TRU E) SO*N(d1)-X*exp(-rT)*N(d2) 0.5334 (LN(C18/C21)+(C20+0.5*C19^2)*C22)/(C19*C22^0.5) 0.0934 (LN(C18/C21)+(C20-0.5*C19^2)*C22)/(C19*C22^0.5) 0.7031 NORM.S.DIST(C23,TRUE) 0.5372 NORM.S.DIST(C24,TRUE) 9,498.85 C18*C25-C21*EXP (-C20*C22)*C26 23 d1 24 d2 25 N(d1) 26 N(d2) 27 call option value on Firm's Assets $ (=Value of Equity) 28 29 30 Value of equity 9,498.85 31 Value of debt $ 30,901.15

A В C D 33 BSM Call Option Pricing Model 34 current value of the company's assets 35 standard deviation of the return on assets sigma 36 annual risk-free rate 37 Exercise Price (Face value of debt) $ 66,500 S0 21% 5% r $ X 62,000 38 Time to Maturity(yrs) 39 d1 T 1 [In(So/X)+(r+.5*sigma^2)*T]/[sigma*sqrt(T) [In(So/X)+(r-.5*sigma^2)*T]/[sigma*sqrt(T)] N(d1) NORM.S.DIST(d 1,TRU E) N(d2)-NORM.S.DIST(d2,TRUE) SO*N(d1)-X*exp(-rT)*N(d2) 0.6768 (LN(C34/C37)+(C36+0.5*C35^2)*C38)/(C35*C38^0.5) 0.4668 (LN(C34/C37)+(C36-0.5*C35^2)*C38)/(C35*C38^0.5) 0.7507NORM.S.DIST(C39,TRUE) 0.6797 NORM.S.DIST(C40,TRUE) 9,838.91 C34*C41-C37*EXP(-C36*C38)*C42 40 d2 41 N(d1) 42 N(d2) 43 call option value on Firm's Assets $ (=Value of Equity) 44 45 46 Value of equity 9,838.91 47 Value of debt 56,661.09

$14,811.85 a-1) Equity a-2) Debt b-1) Equity b-2) Debt b-1) Gain/Loss b-2) Gain/Loss 51,688.15 $9,838.91 56,661.09 -$4,972.94 $4,972.94|

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