solution

An entrepreneur has two projects available, each requiring an investment outlay of 6 at t =O. The first project generates cash flow C1 {5,45} at t =1. The second project generates cash flow C2 {0,48}. The probability of getting a high cash flow is in each case equal to a, where a also denotes the level of effort of the entrepreneur. The entrepreneur has cost of effort of 40a^2 and can choose between three effort levels: a{0,1/3,1/2}. The firm has no assets in place. Everybody is risk neutral, and there is no discounting. The two projects are mutually exclusive.

1. If the entrepreneur can self-finance, what level of effort will she choose under each project? Which project is worth investing in?

2. Suppose now that the entrepreneur is cash constrained and that the project is entirely financed with debt. What face value D of debt should the entrepreneur choose under each project? Which project does she end up choosing if she can get an unconditional loan, that is, a loan that does not depend on which of the two projects she decides to invest in? Discuss.

3. Can the entrepreneur do better by issuing a fraction s of equity instead of financing the project with debt?