Question

Jared Lazarus has just been named the new chief executive officer of BluBell Fitness Centers, Inc. In addition to an annual salary of $655,000, his three-year contract states that his compensation will include 17,750 at-the-money European call options on the company’s stock that expire in three years. The current stock price is $62 per share and the standard deviation of the returns on the firm’s stock is 65 percent. The company does not pay a dividend. Treasury bills that mature in three years yield a continuously compounded interest rate of 7.8 percent. Assume that the annual salary payments occur at the end of the year and that these cash flows should be discounted at a rate of 10 percent.

Use the Black-Scholes model to calculate the value of the stock options.
Determine the total value of the compensation package on the date the contract is signed

Answer 1

Use the Black-Scholes model to calculate the value of the stock options.

At the money call option, hence strike price K = current price = S = 62.

Snapshot from my model:

Hence value of 17,750 number of call options = C x 17,750 = $ 543,297

Determine the total value of the compensation package on the date the contract is signed

Hence, the total value of the compensation package on the date the contract is signed = PV of 3 annual salaries + Value of the options calculated above = 655,000 / r x [1 - (1 + r)^-n] + 543,297 = 655,000 / 10% x [1 - (1 + 10%)^-3] + 543,297 = $ 2,172,185