Frostbite Thermalwear has a zero coupon bond issue outstanding with a face value

Question

Frostbite Thermalwear has a zero coupon bond issue outstanding with a face value of $35,000 that matures in one year. The current market value of the firm’s assets is $40,300. The standard deviation of the return on the firm’s assets is 47 percent per year, and the annual risk-free rate is 4 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 and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Cost of debt

Explanation / Answer

Black-Scholes model can be used to value the equity of a firm:

Asset - $40,300

FV of Zero coupon bonds - $35,000

Risk Free Rate = 4% compounded continuously

S.D. on assets = 47%

Time = 1 year

Let’s calculate N (d1) & N(d2) first:

d1 = ln($40,300/$35,000) + [0.04 + (0.47)^2 / 2) *1] / (0.47 * 1^-1) = 0.61999

d2 = 0.61999 – (0.47 *1^-1) = 0.15322

N(d1) = N(0.61999) = 0.732367815

N(d2) = N(0.15322) = 0.560887607

By putting these values into the Black-Scholes model, equity value is:

Equity = $40,300 * (0.7324) – ($35,000 * e^(–0.04*1) * (0.5609)

= 29514.42 - 18861.32

= 10653.1

Value of Equity = $10,653.1

Thus Value of Debt = Value of asset – Value of equity = $40,300 - $10,653.1 = $29,646.9

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