Problem 8-11 The employee credit union at State University is planning the alloc
ID: 2739123 • Letter: P
Question
Problem 8-11
The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows:
The credit union will have $2.3 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments:
• Risk-free securities may not exceed 30% of the total funds available for investment.
• Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).
• Furniture loans plus other secured loans may not exceed the automobile loans.
• Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.
How should the $2.3 million be allocated to each of the loan/investment alternatives to maximize total annual return?
What is the projected total annual return?
Annual Return = $_________
Explanation / Answer
Let the fund allocation for auto, furniture, other secured, signature, risk free be "a", "b", "c", "d", "e" respectively
Return will be: 0.09a+0.11b+0.12c+0.13d+0.10e. This is the objective function and will have to be maximized.
Constraints: (i) e<=30% of $2.3 million (ii) d<=a+b+c+d (iii) b+c<=a (iv) c+d<=e
Solving in "solver" we get the following solution:
249454.2
Type of Loan/Investment Fund Allocation Rate of return Absoulte return Automobile loans 491,145.83 0.09 44,203.13 Furniture loans 428,854.17 0.11 47,173.96 Other secured loans 62,291.67 0.12 7,475.00 Signature loans 627,708.33 0.13 81,602.08 Risk-free securities 690,000.00 0.1 69,000.00 Total249454.2