Consider a firm that needs to borrow K = 100 from a lender. It has to post a collateral to borrow. The project of the firm is risky. With probability q = 0.5 the firm does not default and pays R . With the remaining probability, the firm defaults, the lender becomes the owner of the collateral and sells it to recover its cost. The quality of the collateral is not known. With probability p = 0.2 it is high quality and its value is C. With remaining probability it is low quality and its value is 0

 

b) Suppose that there are large number of lenders and they are risk neutral. This implies that expected profit must be 0 (why?). What should be the value of collateral, C ?

c) The lender can learn the value of collateral by paying the monitoring cost = 50 before lending. If it turns out that collateral is low quality, there will be no lending, the return to lender will be . If it turns out that the

collateral is high quality, then the lender lends to the firm. Should the lender pay the monitoring cost?

d) Suppose q = 0.25 now. Does the lender has an incentive to pay the monitoring cost now? If so, why there is a difference?