A customer has approached a bank for a $100,000 one-year loan at an 8% interest rate. If the bank does not approve this loan application, the $100,000 will be invested in bonds that earn a 6% annual return. Withoutadditional 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. Ata cost of $1000, the bank can thoroughly investigate the customer’s credit record and supply a favorable or unfavorable recommendation. Past experience indicates that the probability of a favorable recommendation for acustomer who will eventually not default is 0.80, and the chance of a favorable recommendation for a customer who will eventually default is 0.15.a. Use a decision tree to find the strategy the bank should follow to maximize its expected profit.b. Calculate and interpret the expected value of information (EVI) for this decision problem.c. Calculate and interpret the expected value of perfect information (EVPI) for this decision problem.d. How sensitive are the results to the accuracy of the credit record recommendations? Are there any “reasonable” values of the error probabilities that change the optimal strategy?
A customer has approached a bank for a $100,000 one-year loan at an 8% interest rate. If the bank does not approve this loan application, the $100,000 will be invested in bonds 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. 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 the probability of a favorable recommendation for a
customer who will eventually not default is 0.80, and the chance of a favorable recommendation for a customer who will eventually default is 0.15.
a. Use a decision tree to find the strategy the bank should follow to maximize its expected profit.
b. Calculate and interpret the expected value of information (EVI) for this decision problem.
c. Calculate and interpret the expected value of perfect information (EVPI) for this decision problem.
d. How sensitive are the results to the accuracy of the credit record recommendations? Are there any “reasonable” values of the error probabilities that change the optimal strategy?
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