Q. You are a bank manager. Ranga has approached your bank for a million dollar loan. The bank can charge 10% interest from Ranga for this loan. The bank will buy government bonds at 4% interest rate in case Ranga's application is rejected. You think there is 10% chance that Ranga would default on his loan based on your knowledge about Ranga. At a cost of about $1000, the bank can investigate and figure out Ranga's complete credit history.

Based on the past performance, you know that the credit reports give a favourable credit rating 80% of the time when the customer honours loan commitments; and unfavourable credit rating 20% of the time even when the customer honours loan commitments. The credit reports give a favourable credit rating 25% of the time and an unfavourable credit rating 75% of the time when the customer does not honour loan commitments.

Draw the decision Tree and Derive Optimal decision

Compute Expected Value of Perfect Information

Compute expected Value of Sample Information