Reference no: EM133239384

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 $155 loan in a project which will yield $195 with a probability of 0.8 and $85 with a probability of 0.2 in one period hence. A high-risk borrower will invest the $155 loan in a project that will yield $245 with a probability of 0.7 and $45 with a probability of 0.3 in one period hence. You know that 60% of the applicant pool is low risk and 40% is a 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 $2.50 in a successful state to be induced to apply for a bank loan. The bank wants to obtain an expected return of 3.5%.

Determine the rate to charge and if the bank will offer the loans. (Hint, consider switching and non-switching scenarios.)