Question

Sunburn Sunscreen has a zero coupon bond issue outstanding with a $22,000 face value that matures in one year. The current market value of the firm’s assets is $24,600. The standard deviation of the return on the firm’s assets is 25 percent per year, and the annual risk-free rate is 4 percent per year, compounded continuously.

Based on the Black-Scholes model, what is the market value of the firm’s equity and debt? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Answer 1

Final answer:

• Market value of equity = $ 4,409.58 and
• that of debt = $ 20,190.42

Before we get into the question, let's understand the basic stuff shown below:

Assets, A = Debt, D + Equity, E

Hence, A = D + E

Hence, E = A - D

Thus, E = A - D if A > D otherwise 0

Thus E can be written as = max (A - D, 0)

This is similar to payoff from a call option = max ( S - K, 0)

Thus equity can be seen as a call option on the assets of the firm with Face value of the Debt as the strike price.

Hence, let's look at Black Scholes Model for valuing a call option:

I have used excel to solve it from here. Please see the inputs and outputs in the table below. Against each output, the excel formula has been written so as to make you understand how each value has been obtained. This will also help you understand the mathematics behind each calculation. All the financials are in $.

Hence, market value of equity = $ 4,409.58 and that of debt = $ 20,190.42