Question

Sunburn Sunscreen has a zero coupon bond issue outstanding with a $30,000 face value that matures in one year. The current market value of the firm’s assets is $31,800. The standard deviation of the return on the firm’s assets is 34 percent per year, and the annual risk-free rate is 4 percent per year, compounded continuously. The firm is considering two mutually exclusive investments. Project A has an NPV of $2,100, and Project B has an NPV of $3,000. As the result of taking Project A, the standard deviation of the return on the firm’s assets will increase to 48 percent per year. If Project B is taken, the standard deviation will fall to 29 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 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 answers to 2 decimal places, e.g., 32.16.)

  

	Market value
Equity	$
Debt	$

Answer 1

NOTE: Equity of the firm would have a payoff structure equivalent to a call option. Therefore, the equity would be valued as a call option using the Black Scholes Formula(BSM). The formula would be applied using an online BSM calculator.

(a) Face Value of Debt = Strike Price of Call Option = $ 30000, Firm's Asset Value = $ 31800

NPV of Project A = $ 2100, Total Asset Value = 31800 + 2100 = $ 33900

Risk Free Rate = 4 % C.C and Debt Tenure = 1 year. Standard Deviation = 48%

Using the online calculator, Equity Value would be :

Equity Value = Call Price = E1 = $ 8815.73

Debt Value = Total Asset Value - E1 = 33900 - 8815.73 = $ 25084.27

(b) Face Value of Debt = Strike Price of Call Option = $ 30000, Firm's Asset Value = $ 31800

NPV of Project B = $ 2100, Total Asset Value = 31800 + 3000 = $ 34800

Risk Free Rate = 4 % C.C and Debt Tenure = 1 year. Standard Deviation = 29%

Using the online calculator, Equity Value would be :

Equity Value = Call Price = E2 = $ 7395.76

Debt Value = Total Asset Value - E2 = 34800 - 7395.76 = $ 27404.24