Stock Option Valuation Assignment

Questions

1. You are on the compensation committee designing compensation packages for all employees. You are trying to understand the value and incentives of what you pay people. If you ignore income taxes and assume Larry will be with the company in five years, what is the present value of the options being offered according to the Black-Scholes model?
a. Assume the stock price is $22.71 at the time Larry is making his decision.
b. Please note that we typically use risk-free rates that match the time horizon of the object being valued.
c. Larry feels 100% certain that he will exercise on the vesting date and thus for all intents and purposes, these options have an expiration date of five years rather than ten.
d. Please try several values for volatility (sensitivity analysis). The first is to reverse-engineer the volatility the market must be using to price the options expiring 1/17/15 with a strike price of $23. This is called Implied Volatility. The second is to estimate the volatility from the stock price history provided on Sakai. Practitioners often use 3 to 5 years of historical returns with no consensus on the correct estimation window. Therefore you would be wise to look at several windows of time.
e. How would all of the above values change if Larry could sell his options on the open market rather than exercising early at the five year mark?

2. As you consider the options versus the cash bonus, please discuss how the following considerations may affect the decision supported with some numerical analysis if applicable.
a. Taxes – There are three scenarios to think about: take the cash today, exercise the options in five years / sell the stock immediately, and exercise the option in five years / hold them one year / sell after that. Please note in your discussion the amount of cash Larry would have to shell out in five years if he chooses to hold on to the stock for a full year.
b. Illiquidity – When buying an option on a stock, you always have the right to sell the stock to another buyer. ESOs are not tradable. Does this have any effect on Larry’s personal perceived value of the options? (You may include this discussion with part 1e.)
c. Lack of Diversification – The stock options are based on Athena stock. Does this have any effect on Larry’s perceived value of the options?
Probability of being employed by Athena in five years

3. Suppose Larry and the CEO each own 1,000 shares of Athena stock and 20,000 options on 5/29/13. Assume they value the options based on the Black-Scholes value only (no discounts or haircuts for any other issues; use a 10-year expiration). Not that this is the correct value, but for this problem assume the volatility is 30%.
a. What percentage and dollar return do each of them make on their equity based compensation (shares and options) if Athena stock earns a 1% return (another form of Delta)? What does this say about the efficiency of options as a means of providing incentives?
b. What percentage and dollar return do each of them make on their equity based compensation (shares and options) if he can increase Athena’s standard deviation by ten percentage points (1,000 basis points) (often form of Vega)? What kind of actions is this encouraging?
c. The primary motivation for an established company to use stock options is to align incentives between the shareholders and the employee. Please discuss the effectiveness of options as incentives for a low-ranking employee like Mr. Steffen versus the CEO of the firm.
(The case, case data is attached below. Another essay from last year student’s work is also attached. You can try to paraphrase some of it, but make sure it doesn’t look the same and don’t use complicated method other than what they used. Thanks)