1. E nployee Stock Options Gary Levin is the chief executive officer of Mountain
ID: 2799744 • Letter: 1
Question
1. E nployee Stock Options Gary Levin is the chief executive officer of Mountainbrook Trading Company. The board of directors has just granted Mr. Levin 25,000 at-the- money European call options on the company's stock, which is currently trading at $55 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 61 percent. Treasury bills that mature in five years currently yield a continuously compounded interest rate of 6 percent. a. Use the Black-Scholes model to calculate the value of the stock options. b. You are Mr. Levin's financial adviser. He must choose between the previously men- tioned stock option package and an immediate $750,000 bonus. If he is risk-neutral, which would you recommend? c. How would your answer to (b) change if Mr. Levin were risk-averse and he could not sell the options prior to expiration?Explanation / Answer
a.) Given that, Current Stock Price, S0=55,
Strike Price, K=55 (At the money option is carrying same strike price as current price)
Risk Free Rate, r=0.06,
Volatility, =0.61,
Time to Maturity, T=5 years
Continuously Compounded Dividend Yield, q = 0
Using relation, d1 = ln (S0/K) + (r+2/2) x T
T
= ln (55/55) + (0.06 + 0.612/2) x 5
0.615
= 0.00 + 1.23025
1.3640
= 0.9019
Now, d2 = d1 - T
= 0.9019 - 0.615
= 0.9019 - 1.3640
= -0.4621
European Call Price as per Black-Scholes Merton,
= S0 x N(d1) - {Ke-rT x N(d2)}
= 55 x N(0.9019) - {55e-0.06 x 5 x N(-0.4621)}
= 55 x 0.8164 - {55e-0.30 x 0.3220}
= 44.902 - 13.1199
= 31.78
Number of Options offered = 25,000
Value of Options offered =$31.78 x 25,000 =$794,500
b.) Immediate Bonus Offered =$750,000
Value of Options offered =$31.78 x 25,000 =$794,500
Since Mr. Levin, is risk-neutral, he will prefer the alternative with a higher payoff i.e. he will prefer going with options.
c.) If Mr. Levin is risk-averse and if the options cannot be sold prior to 5 years holding, the bonus of $750,000 will be preferrred alternative as it is paid immediately and is a more predictable alternative. He can then invest the proceeds in risk-free treasury bills to generate returns rather than remain locked for the next 5 years.
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