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:
Type of Loan/Investment 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:
• Risk-free securities may not exceed 25% 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 million be allocated to each of the loan/investment alternatives to maximize total annual return?
Type of Loan/Investment Fund Allocation
Automobile loans $_______
Furniture loans $_
Other secured loans $__
Signature loans $_
Risk-free securities $
What is the projected total annual return?
Annual Return = $_______

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Respuesta :

anthougo anthougo · Answer 1 · 2021-05-20T05:33:57+02:00

Answer:

Employee Credit Union at State University

1. Allocation of the $2 million:

Automobile loans $____667,500_____

Furniture loans $_____332,500__

Other secured loans $___335,000_____

Signature loans $_____165,000____

Risk-free securities $____500,000____

2. The projected total annual return is:

= $188,300.

Explanation:

a) Data and Calculations:

Type of Loan/Investment Annual Rate Allocation based Annual

of Return (%) on constraints Returns

Automobile loans 8 $667,500 $53,400

Furniture loans 10 332,500 33,250

Other secured loans 11 335,000 36,850

Signature loans 12 165,000 19,800

Risk-free securities 9 500,000 45,000

Total $2,000,000 $188,300

Amount available for investment = $2 million

Restrictions:

Type of Loan/Investment Constraints Allocation based

on constraints

Automobile loans = ($332,500 + $336,000) $667,500

Furniture loans = ($667,500 - $335,000) 332,500

Other secured loans = ($500,000 - $165,000) 335,000

Signature loans = (11% * 75% * $2,000,000) 165,000

Risk-free securities = (25% * $2,000,000) 500,000

Total loans = Total funds available $2,000,000