Question

Sunburn Sunscreen has a zero coupon bond issue outstanding with a $10,000 face value that matures in one year. The current market value of the firm's assets is $11,900. The standard deviation of the return on the firm's assets is 28 percent per year. Frostbite Thermalwear has a zero coupon bond issue outstanding with a face value of $44,000 that matures in one year. The current market value of the firm's assets is $47,600. The standard deviation of the return on the firm's assets is 34 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, and the annual risk-free rate is 4 percent per year, compounded continuously. 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

(a) Firm 1:

Value of Asset = S = $ 11900, Face Value of Debt = K = $ 10000, Standard Deviation = s = 28%, Debt Tenure = t =1 year, Risk Free Interest Rate = r = 4% compounded continuosly.

The Equity Value of this firm will be equal to a call option with a strike price equal to the debt's face value and spot price equal to the firm's asset value. Hence, the BSM formula would be used to calculate the firm's equity value.

Using an online calculator to solve the BSM we get:

Equity Value = E1 = Call Price = $ 2673.15

Debt Value = D1 = Firm's Asset Value - E1 = 11900 - 2673.15 = $ 9226.85

Firm 2:

Value of Asset = S = $ 47600, Face Value of Debt = K = $ 44000, Standard Deviation = s = 34%, Debt Tenure = t =1 year, Risk Free Interest Rate = r = 4% compounded continuosly.

The Equity Value of this firm will be equal to a call option with a strike price equal to the debt's face value and spot price equal to the firm's asset value. Hence, the BSM formula would be used to calculate the firm's equity value.

Using an online calculator to solve the BSM we get:

Equity Value = Call Price = E2 = $ 9090.31

Debt value = Firm's Asset Value - E2 = D2 = 47600 - 9090.31 = $ 38509.69

Therefore, combined equity value = E1 + E2 = 2673.15 + 9090.31 = $ 11763.46

(a2) Combined Debt Value = D1 + D2 = 9226.85 + 38509.69 = $ 47736.54

(b1) Post Merger:

Face Value of Firm's Debt = 10000 + 44000 = $ 54000, Debt Tenure = 1 Year

Market Value of Firm's Assets = 11900 + 47600 = $ 59500

Standard Deviation = s = 18% and Risk Free Rate = 4 % per annum C.C

Using the BSM to value the firm's equity:

Equity Value = E = Call Price = $ 8901.24

(b2) New Firm's Debt = Combined Firm's Market Value - E = 59500 - 8901.24 = $ 50598.76

NOTE: Please raise separate queries for solutions to the remaining sub-parts.