18) A customer has approached a bank for a $100,000 one-year loan at a 12% interest rate. If the bank does not approve this loan application, the $100,000 will be invested in bonds (by the bank) that earn a 6% annual return. Without additional information, the bank believes that there is a 4% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the bank will lose $100,000. a) Without further information, what should the bank do to maximize EMV, and what is the maximum EMV? (4 points) b) At a cost of $1000, the bank can thoroughly investigate the customer's credit record and supply a favorable or unfavorable recommendation. Past experience indicates that in cases where the customer did not default on the approved loan, the probability of receiving a favorable recommendation on the basis of the credit investigation was 0.80. Furthermore, in cases where the customer defaulted on the approved loan, the probability of receiving a favorable recommendation on the basis of the credit investigation was 0.25. What is the probability that this customer will default on the loan if the bank receives favorable recommendation, and what is the probability that this customer will default on the loan if the bank receives an unfavorable recommendation? (Keep 3 digits for the probabilities) (4 points) Page 6 c) Develop a decision tree for the bank to decide whether to investigate the customer's credit record, and what the bank should do to maximize the annual return. (You may round the monetary values into the nearest integer.) (10 points) d) What is the EVSI? What is the efficiency of this sample information? (Keep 3 digits for the efficiency) (4 points)