Reference no: EM132900544

You are a banker and are confronted with a pool of loan applicants, each of whom can be either low risk or high risk. A low-risk borrower will invest the $125 loan in a project which will yield $175 with probability 0.8 and $35 with probability 0.2 one period hence. A high-risk borrower will invest the $125 loan in a project that will yield $185 with a probability of 0.7 and $20 with a probability of 0.3 one period hence. You know that 55% of the applicant pool is low risk and 45% is high risk, but you cannot tell whether a specific borrower is a high risk or a low risk. You are a monopolist banker. Everybody is risk neutral. Each borrower must be allowed to retain a profit of at least $5 in a successful state in order to be induced to apply for a bank loan. The bank wants to obtain an expected return of 4%.

Determine the rate to charge and if the bank will offer the loans. Assume no project switching.

Please show workings along with decision tree.