Cornell University Loan Policy Linear Programming Worksheet

Question 1Goodlife Bank is formulating its loan policy for next year. The bank offers three types of
one-year bridging loans: education loans, home loans and car loans. The interest rate and
the bad-debt percentage for each loan type are as follows:
Loan type
Interest rate (per annum) Bad-debt percentage
Education
4.5%
2.1%
Home
1.6%
0.7%
Car
1.9%
0.9%
For example, if a borrower obtains an education loan of $100, he needs to repay $104.5 to
the bank after one year. The bad debt percentage is the uncollectible loan amount divided by
the total loan amount. For example, 2.1% of the education loan amount is not recoverable. In
other words, every dollar lent out has a 2.1% probability of not returning to the bank.
(a)
Identify which of these three types of loans has the highest net return.
(10 marks)
To calculate the highest net return, the ROI of the loans is calculated
(b)
The bank decides to lend up to $9 million. To support the vision of a learning
society, at least $3 million will be allocated for education loans. In order to have a
diversified customer base, home loans need to account for at least 15% of total loans;
car loans need to be at least 40% of home loans. To keep the bank running smoothly,
the overall bad-debt percentage shall not exceed 1.25%. The bank wants to determine
how much loan amount to allocate for each loan type in order to maximise the bank’s
net return.
Develop the linear programming (LP) model for the problem. Please limit the
answer to within one page.
(30 marks)