Suppose a CEO has a compensation package which includes a bonus contingent on the firm's stock price.

Suppose a CEO has a compensation package which includes a bonus contingent on the firm's stock price. Bonus is paid only if the stock price increases above $150 by the time when his contract expires in 6 months period. If the stock price is below $150 in 6 month, the CEO does not receive a bonus. Current stock price of othe firm is $120, and it will likely remain at $120 for the next 6 months if the firm does not make an investment in one of the two risky projects. If the firm invests in project A, in 6 months the stock price can increase to $160 with 50% probability, or decline to $40 with 50%. If the firm invests in project B, then in 6 months the stock price can increase to $145 with 50% probability, or decline to $115 with 50%. The CEO can choose to invest in project A, or project B (but not both) or choose not to invest at all. Which of the following statements are true?
I. The firm's shareholders benefit if the CEO chooses project B.
II. A self-interested CEO will likely choose to take project A.
III. Project A is better than project B because it produces higher expected stock price for the firm.