Question

The rate is fixed for all loans made under this program, but the bank has the discretion whether or not to approve a particular loan. Steve, a loan officer at the Bank, is reviewing an application under this program from Cat, a small business owner. If Cat repays the loan as per the terms of the loan, the Bank will earn a profit of $15,000. (All earnings are reported as present values.) However, if Cat defaults on the loan, the Bank will lose $10,000. Based on a quick examination of Cat’s application, Steve assesses Cat’s likelihood of default at 5%.

Steve can either issue a quick decision to approve or deny the loan or send Cat’s application to Credit Services Inc., a firm that conducts in-depth credit analysis and issues a rating of ”A”, ”B” or ”C” for the prospective borrower. Each application sent to Credit Services costs the Bank $2,000. Historically, the default rates for Credit Services’ three rating categories have been as follows:

Rating	Default Probability
A	1%
B	10%
C	90%

Steve believes that if she sends Cat’s case to Credit Services, there is a 40% chance that he will get an ”A” rating, a 50% chance that he will get a ”B” rating, and a 10% chance that he will get a ”C” rating.

A) Structure Steve's problem as a decision tree. Draw this tree by hand (or electronically) and include it along with your submission.

B) Implement your tree using Precision Tree. Submit your Precision Tree implementation.

C) What is your recommended decision strategy? Make sure to state the best strategy in words; otherwise, no credit will be given.

Answer 1

Steve's decision will be based on expected amount bank will earn from the borrower. If Steve does not approach the credit rating agecy, the expected return for the bank would be considering there is an equal probability of his discretion going right or wrong

0.95*15000*0.5+0.05*0*0.5= $7125

If Steve approaches Credit rating Agency, the expected return would be:

0.4*0.99*15000+0.5*15000*0.9+0.1*15000*0.1= $12840

Further the credit rating would charge $2000. Hence net expected return would be:

$12840-$2000= $10840

Clearly the bank would realize a profit in approaching credit rating agency. Hence his best strategy would be to approach them.