Question

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

Joan can either issue a quick decision to approve or deny the loan, or send Jim’s application to Credit Services, Inc., a firm which 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 ratings categories have been as follows:

                                   

Rating --- Default Probability

A --- 1%

B --- 10%

C --- 90%

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

1. Structure Joan’s problem as a decision tree. Draw this tree by hand or electronically and include it along with your submission.

2. Implement your tree using Precision Tree or another program. Submit your Tree implementation.

3. What is your recommended decision strategy? Make sure to state the best strategy in sentences and words.

Answer 1

Joan's decision will be based on expected amount bank will earn from the borrower. If joan 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 Joan 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.