Exercise 4: Moral Hazard (20 pts, 5 by question)

There is no tax (corporate tax rate = 0%). Everyone is risk-neutral, and the risk-free rate is 3%.

Firm F has a project that costs $5 Mns at time 0. Cash-flows at time 1 are equal to $10 Mns in case of success, $0 in the case of failure. The probability of success is 0.7 (failure: 0.3) if the entrepreneur works. The probability of success is 0.3 (failure: 0.7) if the entrepreneur shirks. The private benefits of shirking are equal to $1.5 Mns.

Some countries use policies that limit maximum interest rates that lenders are allowed to charge to small firms. To model this, we assume in this exercise that the interest rate is necessarily equal to 5%. In this type of scenario, lenders cannot adjust interest rates to be compensated in expectation, and have instead to adjust the amount of lending. Ac- cordingly, let's call D the face value of debt.

You can check that the project is only NPV-positive if the entrepreneur works. The lender will therefore only finance the project if she believes the entrepreneur will work, and if she makes a positive profit on the loan.

1. What is the largest face value of debt D such that the entrepreneur can credibly claim that he will work?
2. What is the minimum face value of debt D such that the lender makes a profit when financing the project? Will the entrepreneur be able to finance the project?
3. At most, how much money is the lender willing to lend? How much money would the entrepreneur to finance on his own funds to have the project implemented?
4. What is the largest value for private benefits B such that the entrepreneur is able to finance the project?