[Moral Hazard] Consider three investment projects A, B and C. Project A costs $10 and the return is $20. Project B costs $10 and the return is $40 with probability 0.4 and $-10 otherwise. Project C costs $20 and the return is $60 with probability 0.3 and $-15 otherwise.
a) Calculate the expected profit of each project. Suppose the shareholders are risk neutral and want to maximize the expected profit, which project should they invest in?
b) Suppose the shareholders delegate the investment decision to a manager. The manager’s bonus equals 1% of the company’s earning. For example, if the manager invests in Project B and the return is $40, then the manager gets a bonus of $0.4. If the return is negative then the manager quits the job and does not pay anything to shareholders. Suppose the manager wants to maximize his expected bonus, which project should he pick?
c) Is the manager’s investment decision different from the shareholders’ investment decision? Please explain.