Question

Virtue Financial Group (VFG) is planning to allocate $5,000,000 funds to Unsecured Personal loans, Secured Personal loans, Payday loans, and Title loans. The annual rate of return (RoR) of each type of loan is shown in table below. The management of VFG has decided to allocate at least 30% of total funds to Title loans. In addition, the total allocation to Secured and Unsecured Personal loans cannot exceed 70% of total funds. Furthermore, the amount allocated to Payday loans should be at least 25% of amount allocated to Title loans. Type of loan Unsecured Personal loans Secured Personal loans Payday loans Title loans Rate of Return 13% 9% 8% 12%




a. Formulate a linear optimization model to determine the optimal amount of funds that should be allocated to each type of loan to maximize the total annual return for the $5 million funds. Write down the decision variables, objective function, and constraints.

b. Implement the optimization model in Excel spreadsheet and use the solver to obtain the optimal solution. How much should be allocated to each type of loan? What is the total annual return? What is the annual percentage return? Create screenshots of your excel model and solver dialog box and include them in your report.

c. Suppose that the rate of return on Unsecured Personal loans decreases to 11%. How does the amount allocated to each type of loan and total annual return change?

Answer 1

(a):

	Decision variables
Unsecured personal loans	a
Secured personal loans	b
Payday loans	c
Title loans	d

Objective function = 0.13a + 0.09b + 0.08c + 0.12d

Constraints:

1. a+b+c+d<=5,000,000 (total amount available for investment)

2. d >= 0.3*(a+b+c+d) [This is with regards to at least 30% of total funds to Title loans]

3. a+b <= 0.7*(a+b+c+d) [This is with regards to total allocation to Secured and Unsecured Personal loans cannot exceed 70% of the total funds]

4. c >= 0.25*d [This with regards to the amount allocated to Payday loans should be at least 25% of the amount allocated to Title loans.]

b: The solution is:

	Amount
Unsecured personal loans	3,125,000
Secured personal loans	-
Payday loans	375,000
Title loans	1,500,000
Total	5,000,000
Objective function	616,250

Annual % return = 616,250/5,000,000 = 12.33%

Screenshot for excel and solver dialog box:

c:

When rate of return on Unsecured Personal loans decreases to 11% then the solution will be:

Unsecured personal loans	-
Secured personal loans	-
Payday loans	1,000,000
Title loans	4,000,000
Total	5,000,000
Objective function	560,000

Rate of return = 560,000/5,000,000 = 11.20%