Everybody is risk-neutral; the interest rate is 0 and investors (lenders) are competitive.

One Entrepreneur needs to borrow money for her project. The initial cost of the project is K. The entrepreneur has a quantity of cash of her own equal to E. Assume K > E, so if the entrepreneur wants to start the project, she will need to borrow K-E from investors. The project after one period, can either be a success depends on the entrepreneur’s behavior; is he behaves the probability of success will be equal to PH if she shirks the probability will be equal to PL (where PL). On the other hand, if the entrepreneur shirks, she will enjoy a private benefit = B that be summed to her monetary payoff. Assume the following: PH*Y > PL*Y + B, PH*Y-K>0, and 0 > PL*Y + B – K. The overall payoff Y will be shared between the entrepreneurs and the lenders. YL goes to the lenders (Face value of the bond) and YB is the amount retained by the entrepreneur. PL < PH.

What is the face value (YL) of the debt contract as a function of the probability of success, K,E, and B?

What payoff YB should the entrepreneur receive, in case of success, in order to behave? (always as a function of the probability of success, K, E and B)