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:
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Type of Loan/Investment
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Annual Rate of Return (%)
|
|
Automobile loans
|
8
|
|
Furniture loans
|
10
|
|
Other secured loans
|
11
|
|
Signature loans
|
12
|
|
Risk-free securities
|
9
|
The credit union will have $2 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:
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Risk-free securities may not exceed 30 percent of the total funds available for investment.
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Signature loans may not exceed 10 percent of the funds invested in all loans (automobile, furniture, other secured, and signature loans).
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Furniture loans plus other secured loans may not exceed the automobile loans.
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Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.
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Formulate a linear program that determines how the $2 million be allocated to maximize the total annual return.
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Use Excel Solver to solve this linear program. What is the optimal investment strategy? (How to allocate $2 million fund?) What is the expected total annual return?
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Use sensitivity analysis to determine how the change of constraints on Risk-free securities would result in a decreasing of 0.04% on total expected return?