Question

Frostbite Thermalwear has a zero coupon bond issue outstanding with a face value of $37,000 that matures in one year. The current market value of the firm’s assets is $40,400. The standard deviation of the return on the firm’s assets is 44 percent per year, and the annual risk-free rate is 5 percent per year, compounded continuously.

A:

Based on the Black–Scholes model, what is the market value of the firm's equity and debt? B: What is the firm's continuously compounded cost of debt?

Answer 1

Ans a) 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(40400/37000) + (.05 + (.44^2)/2)* 1)/.44 *1

= .53344

d2 = d1 - stadev*root(t)

= .09344

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

N(d1) = .70313

N(d2) = .53722

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

= $ 9498.85

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

= $40400 - $9498.85 = $30901.15

Ans b) 30901.15*e^(r*t) = 37000

where t =1

and r is a continuous compounded rate

r = 18.0125%