Question

Sunburn Sunscreen has a zero coupon bond issue outstanding with a $21,000 face value that matures in one year. The current market value of the firm’s assets is $22,800. The standard deviation of the return on the firm’s assets is 34 percent per year, and the annual risk-free rate is 5 percent per year, compounded continuously. The firm is considering two mutually exclusive investments. Project A has an NPV of $1,900, and Project B has an NPV of $2,700. As the result of taking Project A, the standard deviation of the return on the firm’s assets will increase to 44 percent per year. If Project B is taken, the standard deviation will fall to 26 percent per year.

What is the value of the firm’s equity and debt if Project A is undertaken?

Equity =

Debt =

What is the value of the firm’s equity and debt if Project B is undertaken?

Equity =

Debt =

Answer 1

1). Using Black-Scholes option pricing model for Project A:

Vaue of the underlying asset (S) = market value of assets + Project A NPV = 22,800 + 1,900 = 24,700

Strike price (K) = face value of debt = 21,000

Volatility of the assets (s) = 44%

Time to expiry of option (t) = 1 year

Risk-free rate (r) = 5%

Formulas:

Output:

Value of equity = 6,686.72

Value of debt = Asset value - equity = 24,700 - 6,686.72 = 18,013.28

2). Using Black-Scholes option pricing model for Project B:

Vaue of the underlying asset (S) = market value of assets + Project A NPV = 22,800 + 2,700 = 25,500

Strike price (K) = face value of debt = 21,000

Volatility of the assets (s) = 26%

Time to expiry of option (t) = 1 year

Risk-free rate (r) = 5%

Formulas:

Output:

Value of equity = 6,069.63

Value of debt = Asset value - equity = 25,500 - 6,069.63 = 19,430.37