A customer has approached a local credit union for a $20,000 1-year loan at a 10%...

Transcribed Image Text:

A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not approve the loan application, the $20,000 will be invested in bonds that earn a 6% 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 $20,000. At the cost $150, the bank can thoroughly investigate the customer's credit record and supply a favorable or unfavorable recommendation. If a favorable recommendation is given, then the chance that the customer does not repay the loan drops to 1.62%. For an unfavorable recommendation, the chance that the customer defaults on the loan increases to 16.48%. The credit union believes that there is a 77.25% of the investigation yielding a favorable rating. a- Draw the decision tree of the decision problem that the credit union is facing. Be sure to clearly label the branches, include probabilities, outcomes, and results for expected profits. b- Draw the influence diagram. c- Use the decision tree to determine the course of action that should be taken to maximize expected profit. What is the maximum expected profit? What is the best course of action? d-Draw the risk profile for the best course of action. A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not approve the loan application, the $20,000 will be invested in bonds that earn a 6% 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 $20,000. At the cost $150, the bank can thoroughly investigate the customer's credit record and supply a favorable or unfavorable recommendation. If a favorable recommendation is given, then the chance that the customer does not repay the loan drops to 1.62%. For an unfavorable recommendation, the chance that the customer defaults on the loan increases to 16.48%. The credit union believes that there is a 77.25% of the investigation yielding a favorable rating. a- Draw the decision tree of the decision problem that the credit union is facing. Be sure to clearly label the branches, include probabilities, outcomes, and results for expected profits. b- Draw the influence diagram. c- Use the decision tree to determine the course of action that should be taken to maximize expected profit. What is the maximum expected profit? What is the best course of action? d-Draw the risk profile for the best course of action.