Question

Gary Levin is the chief executive officer of Mountainbrook Trading Company. The board of directors has just granted Mr. Levin 48,000 at-the-money European call options on the company's stock, which is currently trading at $35 per share. The stock pays no dividends. The options will expire in five years and the standard deviation of the returns on the stock is 56 percent. Treasury bills that mature in five years currently yield a continuously compounded interest rate of 5.5 percent. a. Use the Black-Scholes model to calculate the value of the stock options. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value of option grant

Answer 1

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*r^(-r*t)
Where
S = Current price =		35
t = time to expiry =		5
K = Strike price =		35
r = Risk free rate =		5.5%				1.0%
q = Dividend Yield =		0%
σ = Std dev =		56%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(35/35)+(0.055-0+0.56^2/2)*5)/(0.56*5^(1/2))
d1 = 0.845713
d2 = d1-σ*t^(1/2)
d2 =0.845713-0.56*5^(1/2)
d2 = -0.406485
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.801144
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.342193
Value of call= 35*0.801144-0.342193*35*e^(-0.055*5)
Value of call= 18.94

Value of grant = option price*number of options = 18.942831*48000=909255.89