Question

I am re-posting this because I never received the correct answer.

Sunburn Sunscreen has a zero coupon bond issue outstanding with a face value of $25,000 that matures in one year. The current market value of the firm’s assets is $27,200. The standard deviation of the return on the firm’s assets is 33 percent per year, and the annual risk-free rate is 4 percent per year, compounded continuously.

  

Frostbite Thermalwear has a zero coupon bond issue outstanding with a face value of $50,000 that matures in one year. The current market value of the firm’s assets is $53,600. The standard deviation of the return on the firm’s assets is 38 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 18 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 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 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 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 answer to 2 decimal places, e.g., 32.16.)

  

Debt

$

  

c-1.	What was the gain or loss for shareholders? (A loss should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Gain / Loss

$

  

c-2.	What was the gain or loss for bondholders? (A loss should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Gain / Loss

$

Answer 1

For Sunburn

Firm assets(S) = $ 27200

Debt face value(X) = $ 25000

Standard Deviation = 33%

Risk Free rate = 4%

d1 = [ln(27200/25000) + (0.04 + 0.33^2/2)*1]/[0.33*sqrt(1)] = 0.5418

d2 = 0.5418-(0.33*sqrt(1)) = 0.2118

N(d1) = 0.7060

N(d2) = 0.5837

Equity = $27200*(0.7060) - ($25,000*exp(-0.04*1))*(0.5837) = $5179.43

Debt = $27200- $5179.43= $ 22020.57

For Frostbite

Firm assets(S) = $ 53600

Debt face value(X) = $ 50000

Standard Deviation = 38%

Risk Free rate = 4%

d1 = [ln(53600/50000) + (0.04 + 0.38^2/2)*1]/[0.38*sqrt(1)] = 0.4782

d2 = 0.4782-(0.38*sqrt(1)) = 0.0982

N(d1) = 0.6838

N(d2) = 0.5391

Equity = $53600*(0.6838) - ($50,000*exp(-0.04*1))*(0.5391) = $10750.07

Debt = $53600- $10750.07= $42849.93

a-1. Combined Equity = 10750.07+5179.43 = 15929.50

a-2. Combined debt value = 42849.93+22020.57 = 64870.50

b. Total assets = 27200+53600 = 80800

Total debt = 25000+50000 = 75000

Standard Deviation = 18%

Risk Free rate = 4%

d1 = [ln(80800/75000) + (0.04 + 0.18^2/2)*1]/[0.18*sqrt(1)] = 0.7260

d2 = 0.7260-(0.18*sqrt(1)) = 0.5460

N(d1) = 0.7661

N(d2) = 0.7075

Equity = $80800*(0.7661) - ($75,000*exp(-0.04*1))*(0.7075) = $10919.80

Debt = $80800- $110919.80= $ 69880.20

c. Gain/loss to shareholders = (10919.80-15929.50)/15929.50 = -31.45%

d. Gain/loss to bondholders = (69880.20-64870.50)/64870.50 = 7.72%