A customer has approached a local credit union for a $10,000 1-year loan at a 15% interest rate. If the credit union does not approve the loan application, the $10,000 will be invested in bonds that earn a 7% annual return. Without additional information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the credit union will lose the $10,000.

a) Fill in the given payoff table with Profits (Be careful) and the corresponding priors. Using Baye's Decision Rule (Expected Value approach), determine what the credit union should do, along with their expected Profit. Write your answer in a complete sentence. Do not make me interpret numbers just sitting there! (7 pts)

b) What is the most the credit union should pay for the credit report? You must show your work! (3 pts)

The bank has the option to investigate the customer's credit record by paying for a report that gives a favorable or unfavorable recommendation. Suppose that an actual (not perfectly reliable) credit report has the following characteristics based on historical data; 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 80%, while 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 25%.

c) Given this information, use the template provided to find the various posterior probabilities. I will just be looking at the values in your template table to check this part. (4 pts)

d) Using the posterior probabilities found in part c, use Payoff Tables to find the EVSI. Would the credit union be justified in purchasing the credit report for $200? Why or why not? Explain. (6 pts)