Question

Frostbite Thermalwear has a zero coupon bond issue outstanding with a face value of $46,000 that matures in one year. The current market value of the firm’s assets is $49,600. The standard deviation of the return on the firm’s assets is 36 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? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

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(49600/46000) + (.05 + (.36^2)/2)* 1)/.36 *1

= .52819

d2 = d1 - stadev*root(t)

= .16819

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

N(d1) = .70132

N(d2) = .56678

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

= $ 9984.81

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

= $49600 - $9984.81 = $39615.19

Ans b) 39615.19*e^(r*t) = 46000

where t =1

and r is a continuous compounded rate

r = 14.94%