The First National Bank has been losing money on automobile consumer loans and is considering the implementation of a new loan procedure that requires a credit check on loan applicants. Experience indicates that 82% of the loans were paid off, whereas the remainder defaulted. However, if the credit check is run, the probabilities can be revised as follows:
An estimated 80% of the loan applicants receive a favorable credit check.
Assume that the bank earns 18% on successful loans, loses 100% on defaulted loans, suffers an opportunity cost of 18% when the loan is not granted but would have been successful, and an opportunity cost of 0% when the loan is not granted and would have defaulted.
If the cost of a credit check is 5% of the value of the loan and the bank is risk neutral, should the bank go ahead with the new policy?