Question

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 = $_______________

Answer 1

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