Question

Sunburn Sunscreen has a zero coupon bond issue outstanding with a $15,000 face value that matures in one year. The current market value of the firm’s assets is $16,400. The standard deviation of the return on the firm’s assets is 43 percent per year, and the annual risk-free rate is 6 percent per year, compounded continuously.

  

Frostbite Thermalwear has a zero coupon bond issue outstanding with a face value of $39,000 that matures in one year. The current market value of the firm’s assets is $42,400. The standard deviation of the return on the firm’s assets is 40 percent per year.

   

Suppose 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 19 percent per year.

  

a-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

$

  

a-2.	What is the combined value of debt in the two existing companies? (Do not round 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-2.	What is the value of the new firm’s debt? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

  

Debt

$

  

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

$

  

c-2.	What was the gain or loss for bondholders? (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

$

Answer 1

1 BSM Call Option Pricing Model 2 current value of the company's assets SO 16,400 3 standard deviation of the return on assets sigma 43% 4 annual risk-free rate 6% 5 Exercise Price(Face value of debt) 15,000 6 Time to Maturitylyrs) 7 d1 [In(So/X)+(r+.5*sigma^2) *T]/[sigma*sqrt(T)] 0.5620 =(LN(C2/C5)+(C4+0.5*C3^2) *C6)/(C3*C6^0.5) 8 d2 [In(So/X)+(r-.5*sigma^2) *T]/[sigma*sqrt(T)] 0.1320 =(LN(C2/C5)+(C4-0.5*C3^2)*C6)/(C3*C6^0.5) 9 N(d1) N(D1)=NORM.S.DIST(d1,TRUE) 0.7130 ENORM.S.DIST(C7,TRUE) 10 N(D2) Nd2)=NORM.S.DIST(d2,TRUE) 0.5525 =NORM.S.DIST(C8, TRUE) 11 call option value on Firm's Assets SO*N(01)-X*exp(-rT)*N(02) $ 3,887.26 =C2*C9-C5*EXP(-C4*C6)*C10 12 (=Value of Equity) 13 14 Value of equity 3,887.26 15 Value of debt 12,512.74 16 17 BSM Call Option Pricing Model 18 current value of the company's assets SO 42,400 19 standard deviation of the return on assets sigma 20 annual risk-free rate 6% 21 Exercise Price(Face value of debt) 39,000 22 Time to Maturitylyrs) 23 d1 [In(So/X)+(r+.5*sigma^2) *T]/[sigma*sqrt(T)] 0.5590 =(LN(C18/C21)+(C20+0.5*C1942)*C22)/(C19*C2240.5) [In(So/X)+(r-.5*sigma^2) *T]/[sigma*sqrt(T)] 0.1590 I=(LN(C18/C21)+(C20-0.5*C19^2)*C22)/(C19*C22~0.5) 25 N(d1) N(D1)=NORM.S.DIST(d1,TRUE) 0.7119 =NORM.S.DIST(C23, TRUE) 26 N(02) Nd2)=NORM.S.DIST(d2,TRUE) 0.5632 =NORM.S.DIST(C24,TRUE) 27 call option value on Firm's Assets SO*N(01)-X*exp(-rT)*N(02) $ 9,500.97 |=C18*C25-C21*EXP(-C20*С22)*C26 28 |(=Value of Equity) 29 30 Value of equity 9,500.97 31 Value of debt 32,899.03 40% 24 d2

x А B 33 BSM Call Option Pricing Model 34 current value of the company's assets SO 58,800 35 standard deviation of the return on assets sigma 19% 36 annual risk-free rate 6% 37 Exercise Price(Face value of debt) 54,000 38 Time to Maturity(yrs) T 39 d1 [In(So/X)+(r+.5*sigma^2) *T]/[sigma*sqrt(T)] || 0.8590 =(LN(C34/C37)+(C36+0.5*C35^2)*C38)/(C35*C38^0.5) 40 d2 [In(S0/X)+(r-.5*sigma^2) *T]/[sigma*sqrt(T)] 0.6690 =(LN(C34/C37)+(C36-0.5*C35^2)*C38)/(C35*C38^0.5) 41 N(d1) N(D1)=NORM.S.DIST(d1, TRUE) 0.8048 =NORM.S.DIST(C39,TRUE) 42 N(d2) N(D2)=NORM.S.DIST(d2,TRUE) 0.7482 ENORM.S.DIST(C40,TRUE) 43 call option value on Firm's Assets SO*N(1)-X*exp(-rT)*N(02) $ 9,271.41 |=C34*C41-C37*EXP(-C36*C38) *C42 (=Value of Equity) 45 46 Value of equity 9,271.41 47 Value of debt 49,528.59 44

a-1) Equity a-2) Debt b-1) Equity b-2) Debt b-1) Gain/Loss b-2) Gain/Loss $ 13,388.23 $ 45,411.77 $ 9,271.41 $ 49,528.59 -$4,116.82 $4,116.82

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