Problem 7 Employee stock options are call options issued to employees by their company to motivate them to act in the best interests of the company's shareholders. They are usually at the money at the time of issue. There is a vesting period during which the options cannot be exercised. After that period, employees are free to exercise them. If the company does well so that the company's stock price goes beyond the strike price, employees obtain gains by exercising the options and then selling the underlying stock. (a) Generally, employees are not allowed to sell the option. Hence if employees want to realize a gain from the option, they have to exercise it and sell the underlying stock. Due to this constraint, employee stock options tend to be exercised earlier than similar call options. The expected life of the employee stock option is the average time for which employees hold the option before it is exercised or expires. We can approximately price the employee stock option by using the Black-Scholes option pricing formula with maturity set equal to this expected life. Now suppose a company has granted the employee stock option to its employees today. Its stock price is $100 today and the strike price of the option is the same. The expected life of this option is estimated to be 4.5 years. Assume that the risk-free interest rate is 3% per annum (continuously compounded) and the volatility of the stock price is 35% per annum. Also here we ignore the dividend payment. Under this setting, compute the present value of this employee stock option. (b) In order to make capital markets work effectively, it is important that the interests of a company's shareholders and employees are well aligned. At first sight employee stock options seem to be a good idea for realizing this alignment. However, some people argue that whether 5 employee stock options help align the interests of shareholders and employees is not so obvious. Can you come up with any concern about the possibility of the misalignment of interests? Is there any idea to alleviate such a problematic situation? Taking that issue into consideration, do you support the employee stock option as a company's incentive scheme? Describe your idea along with the reason. Problem 7 Employee stock options are call options issued to employees by their company to motivate them to act in the best interests of the company's shareholders. They are usually at the money at the time of issue. There is a vesting period during which the options cannot be exercised. After that period, employees are free to exercise them. If the company does well so that the company's stock price goes beyond the strike price, employees obtain gains by exercising the options and then selling the underlying stock. (a) Generally, employees are not allowed to sell the option. Hence if employees want to realize a gain from the option, they have to exercise it and sell the underlying stock. Due to this constraint, employee stock options tend to be exercised earlier than similar call options. The expected life of the employee stock option is the average time for which employees hold the option before it is exercised or expires. We can approximately price the employee stock option by using the Black-Scholes option pricing formula with maturity set equal to this expected life. Now suppose a company has granted the employee stock option to its employees today. Its stock price is $100 today and the strike price of the option is the same. The expected life of this option is estimated to be 4.5 years. Assume that the risk-free interest rate is 3% per annum (continuously compounded) and the volatility of the stock price is 35% per annum. Also here we ignore the dividend payment. Under this setting, compute the present value of this employee stock option. (b) In order to make capital markets work effectively, it is important that the interests of a company's shareholders and employees are well aligned. At first sight employee stock options seem to be a good idea for realizing this alignment. However, some people argue that whether 5 employee stock options help align the interests of shareholders and employees is not so obvious. Can you come up with any concern about the possibility of the misalignment of interests? Is there any idea to alleviate such a problematic situation? Taking that issue into consideration, do you support the employee stock option as a company's incentive scheme? Describe your idea along with the reason
