Question

Sunburn Sunscreen has a zero coupon bond issue outstanding with a $25,000 face value 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 35 percent per year, and the annual risk-free rate is 5 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 final answers to 2 decimal places (e.g., 32.16).)

Market value

Equity $ ????

Debt $ ????

Answer 1

We can use black scholes formula to find this.

d1 = (ln(Vt/K) + ((r + stadev^2/2)*t))/(root(t)*stadev)

where Vt is current market value of the firm's asset

k is face value of zero counpon bond

r is interest rate

t is time period

d1 = (ln(27200/25000) + (.05 + (.35^2)/2)* 1)/.35 *1

= .55883

d2 = d1 - stadev*root(t)

= .20883

With the help of z-table we will find the value of n(d1) and n(d2)

N(d1) = .71186

N(d2) = .58271

Market value of the firm's equity = Vt * N(d1) - K*e^(-r*t)*N(d2)

= $ 5505.36

Market value of debt = market value of firm's asset - market value of equity

= $27200 - $5505.26 = $21694.74