Problem 9-03 (Algorithmic) The employee credit union at State University is plan
ID: 2563706 • Letter: P
Question
Problem 9-03 (Algorithmic)
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 revenueproducing investments together with annual rates of return are as follows:
The credit union will have $2.4 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 20% of the total funds available for investment.
Signature loans may not exceed 11% 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 $2.4 million be allocated to each of the loan/investment alternatives to maximize total annual return?
What is the projected total annual return?
$
Type of Loan/Investment Annual Rate of Return (%) Automobile loans 8 Furniture loans 10 Other secured loans 12 Signature loans 13 Risk-free securities 8Explanation / Answer
Investment in Risk free securities = $2.4 million * 20% = $0.48 million Investment in signature loan = 11% of funds invested in all loan = 11% * ($2.4 million - $0.48 million) = $0.2112 million Investment in other secured loan = Investment in risk free securities - Investment in signature loans = $0.48 million - $0.2112 million = $0.2688 million Investment in Furniture Loan + Investment in Automobile loan = $2.4 million - $0.48 million - $0.2112 million - $0.2688 million = $1.52 million Investment in Automobile Loan = $1.44 million - Investment in Furniture Loan Investment in Furniture Loan + Investment in other secured loan = Investment in Automobile loan Investment in Furniture Loan + $0.2688 million = $1.44 million - Investment in Furniture Loan 2*Investment in Furniture Loan = $1.1712 million Investment in Furniture Loan = $0.5856 million Investment in Automobile Loan = $1.44 million - Investment in Furniture Loan Investment in Automobile Loan = $1.44 million - $0.5856 million = $0.8544 million Allocation of $2.4 million available investment Type of loan / Investment Funds Invested (in million) Automobile loans $0.8544 Furniture Loans $0.5856 Other Secured Loans $0.2688 Signature Loans $0.2112 Risk free securities $0.4800 Total $2.4000 Calculation of projected total annual return Type of loan / Investment Funds Invested (in million) Annual rate of return Return (in million) A B A*B Automobile loans $0.8544 8% $0.068352 Furniture Loans $0.5856 10% $0.058560 Other Secured Loans $0.2688 12% $0.032256 Signature Loans $0.2112 13% $0.027456 Risk free securities $0.4800 8% $0.038400 Total $2.4000 $0.225024 Projected total annual return = $2,25,024
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