Reference no: EM132402590

Consider a large multilateral development bank (MDB) that is lending to rural borrowers and wants to just break-even. All borrowers require a loan of $100 and the gross cost to the MDB of making such a loan is $160. There are two types of borrower: type 1 and type 2. A type 1 borrower can get a gross return of $200 with certainty. A type 2 borrower can obtain a gross return of $360 with probability 0.75 and 0.25 otherwise. The opportunity costs for type 1 and type 2 borrowers are, respectively, $18 and $20. However, when extending the loan, the MDB does not know the types of each borrower and only knows that 50% are of type 1 and 50% are of type 2. Assume to begin with that the MDB lends to each borrower on an individual basis.

(a) Compute the gross repayment required by the MDB from each borrow in order to just break even on average, assuming both types borrow. What is the implied interest rate on loans?

(b) Under these terms would both types of borrower actually want to borrow? What is the implied break-even interest rate given this result?

(c) Now suppose the MDB can lend to groups consisting of two borrowers each. Assume that the bank can impose a joint responsibility default clause: A borrower will have to pay for her partner when her partner fails or else both borrowers will be excluded from future financing. Assume also that the borrowers know each other's types and engage in positive assortative matching when forming their groups. If successful type 2 borrowers can always repay the debt of unsuccessful ones, what are the possible outcomes of a lending contract with a risky pair? What is the probability of each outcome? Compute the MDB's breakeven interest rate with joint responsibility default clause.

(d) Verify that the assumption made in part (c) is valid. Will both types of borrowers want to borrower under these terms? Explain.