Question

Gary Levin is the chief executive officer of Mountainbrook Trading Company. The board of directors has just granted Mr. Levin 50,000 at-the-money European call options on the company’s stock, which is currently trading at $30 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 4.2 percent.

  

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.)

What is the value of the option grant?

Answer 1

Black scholes model formula for value of call option is -

Where, C = value of call option, S₀ = Stock price, X = Strike price, r = continuous compounded rate of return, t = time to maturity

Sigma = Standard deviation

Since option is at the money, stock price = strike price = $30

Here is the solution using excel. We start with the calculation of d1 and then d2 and move on from there -

Formulae -

Therefore, value of one call option = $15.727656995

Value of option grant = 50,000 x $15.727656995 = $786,382.84975 or $786,382.85