Question

Suppose a firm can invest in two mutually exclusive projects that yield the following cashflows:

Project A: 150 and 50 with equal probability Project B: 350 and 20 with equal probability

The manager earns a private benefit of 1 from project A. Additionally, she is risk-avers with a utility function of U=log(x).
a. The board asks you for advice for the cheapest way to incentivize the manager to

invest in project B with equity. What do you recommend?
b. Can you think of a better way to compensate the manager to induce investment in

project B?

Answer 1

First let us analyze the cash flows of the projects A & B.

Expected cash flow from Project A : 150* 50% + 50*50% = 100

Expected cash flow from Project B : 350* 50% + 20*50% = 185

As from the above results, Project B looks more lucarative in terms of cash flows generated (185 > 100)

a) What is the cheapest way to incentivize manager to invest in project B ?

Since the manager has a private benefit of 1 from project A, the cheapest way to sway her in favor of project B, would be by offering her an amount which is > 1, so that she feels more inclined for project B

b) Can you think of a better way to compensate the manager to induce investment in project B?

A good way to compensate the manger to induce investment in project B, would be by i) Offering her ESOP (Employee Stock offer programme), ii) Profit sharing of the excess returns one earns from the profit spread of B - A (85)