Frostbite Thermalwear has a zero coupon bond issue outstanding with a face value of $31,000 that matures in one year. The current market value of the firm’s assets is $34,400. The standard deviation of the return on the firm’s assets is 39 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.) |
Market value | |
Equity | $ |
Debt | $ |
b. |
What is the firm's continuously compounded cost of debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) |
Cost of debt | % |
Black Scholes model is an option pricing technique which can also be used to value equity. The basic idea is that because of limited liability, shareholders can walk away from a company when the debt exceeds the asset value. However, when the assets exceed the debts, those shareholders will keep running the business, in order to collect the surplus.
Therefore, the value of shares can be seen as a call option owned by shareholders and we can use Black-Scholes to value such an option.
Value of assets (Strike price in terms of option) = 34,400
Face Value of O/S debt (exercise price in terms of option) = 31,000
Time of Debt (Life of option) = 1 year
Variance in the value of firm = SD*2 = .(39)2 = 0.1521
Risk less rate = 5%
The formula for BSM is:
Price =S*N(d1)−Ke−rtN(d2)
where:d1= [ln(S/K) + (r+ ((SD*2)/2)t / (σv2) t]
and d2=d1−σ* under root(t)
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