A customer has approached a bank for a $50K one year loan at 12% annual interest. If the bank does not approve the loan, the $50k will be invested in bonds that earn a %6 annual return. Without further info, the bank feels that there is a %4 chance that the customer will totally default on the loan. If the customer totally defaults, the bank loses $50k. At a cost of $500, the bank can hire a credit agency to thoroughly investigate the customer’s credit record and supply a favorable or unfavorable recommendation. Past experience working with this agency indicates:
P(favorable recommendation | customer does not default) = 77/96
P(favorable recommendation | customer default) = .25
(a) Use a decision tree to determine what the bank should do to maximize expected profits.
(b) Provide a risk profile for the optimal decision.
(c) What is the maximum amount of money the bank should pay to hire the agency.
(d) What is the maximum amount of money the bank is willing to pay to find out for sure if the customer will default or not?