Please answer only question c-e. Thanks

Assumptions: 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 A. 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 be either a success and pay off Y, or a

failure and pay off 0. The probability for the project to be a success depends

on the entrepreneurs behavior: if she behaves the probability of success will be

equal to P1, if she shirks the probability will be equal to P1 < P2. On the other

hand, if the entrepreneur shirks, she will enjoy a private benefit (non-transferable

to others) equal to B > 0 that can be summed to her monetary payoff. Assume

the following: p1*Y > p2*Y + B, p1*Y K > O and 0 > P2*Y + B K.

Before the project is undertaken and before the entrepreneur makes the

choice between behaving and shirking, the entrepreneur and the investors can

enter a debt contract. The entrepreneur cannot commit to behave and she

enjoys limited liability.

The sequence of actions is the following:

1. Loan agreement is signed (one period zero coupon bond)

2. The investment is made

3. The entrepreneur decides whether to shirk or behave

4. Payoff is realized

a) Assume for a moment that E > K. If the entrepreneur had E > K and used

her own financial resources to fund the project, would she shirk?

Back to the case E < K. The overall payoff Y will be shared between the

entrepreneurs and the lenders. Y_l is the part of Y going to the lenders (face

value of the bond), and Y_B is the amount retained by the entrepreneur.

b) What is the face value (Y_l) of the debt contract as a function of the

probability of success, K, E and B?

c) What payoff Y_B 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)?

d) What is the largest Y_l that can be paid out to lenders in case of success,

that will keep the entrepreneur from shirking?

e) What is the minimum amount of cash E that the entrepreneur needs to

have (and invest in the project) in order to credibly behave in case of debt

financing? (Hint: ask yourself when the lenders would be willing to lend money

to the entrepreneur, given that they have to provide her with enough incentives

to behave.)