A recent MBA graduate is considering an offer of employment at a biotech company

Question

A recent MBA graduate is considering an offer of employment at a biotech company, where she has been offered stock options as part of her compensation package. The options give her the right, but not the obligation, to buy 2500 shares of stock either one year from now or two years from now at a price of $50, which is the current market price of the stock. If the price of the stock has risen above $50 at either time, she can buy 2500 shares at $50 and then immediately sell at the current price, thereby making a risk-free profit. On the other hand, if the price of the stock has dropped below $50, she will not exercise the option because it is “out of the money” and she would loose money. Based on historical market information, she estimates that the stock price in the first year will either go up by 25% from its current price, with probability of 0.55, or it will go down by 15%, with probability of 0.45. In either case, she can exercise the options or wait to see what will happen in the second year. If she decides to wait, the in the second year, the stock price will again go up or down by the same amounts and with the same probabilities, starting from either the “up” or “down” price at the end of the first year.

(A) What is the optimal decision making policy regarding the options in all possible scenarios over the next two years?

(B) What is the expected value of the stock options? Ignore the time value of money (assume no discounting of future payoffs)

(C) If her estimates of the increases/decreases or probabilities are inaccurate, could the options have a negative EMV?

Please show steps in calculations! Thank you.

Explanation / Answer

Solution:

(A) The tree above shows that whether the price goes up or down in the first year, she should wait and not exercise the options. If the stock price has gone up in the first year, then in the second year, she should exercise whether the price goes up or down. However, if the price has gone down, she will only want to exercise the options if the price goes back up during the second year. If the price goes down in both years, she will let the option expire.

(B) The expected value of the option on one share, as shown in the above decision tree, is $10.05. Therefore the option on 2500 shares is worth $25,125 in additional compensation.

(C) No, the ability to make the decision not to exercise the option at every point in time protects the option-holder from any possible loss. In the worst case, she will let the options expire and their value will be $0.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.