Question

Problem 4-03 (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:

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 $1.8 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 $1.8 million be allocated to each of the loan/investment alternatives to maximize total annual return? Round your answers to the nearest dollar. Automobile Loans $ 472,500 Furniture Loans $ 127,500 Other Secured Loans $ 0 Signature Loans $ 163,636 Risk Free Loans $ 540,000 What is the projected total annual return? Round your answer to the nearest dollar. $ 170,673

Please show excel input!

Answer 1

The solution for the above problem is as follows:

Type of loans	Amount	Interest rate	Return
Automobile Loans	567000	8%	45360
Furniture Loans	153000	10%	15300
Other secured loans	414000	11%	45540
Signature Loans	126000	12%	15120
Risk free securities	540000	9%	48600
Total	1800000		169920

Maximum return is $169920

In this table we will be able to satisfy all the conditions of the problem. Lets take all the conditions one by one:

1) Total investment amount: 1,800,000 (1.8 million) completed.

2) The investment in risk-free securities should not be more than 30% of the total funds available for investment which comes to $540,000. if we take lesser proportion of funds in risk free securities the returns will go down because the total investment in signature loans and other secured loans cannot exceed the proportion of RF securities so by keeping 30% investment in RF securities we invest 30% in signature loans and other secured loans which gives us the highest returns.

3) Signature loans may not exceed 10% of the funds invested in all other loans: This also means it should be 10% of the funds available after investment in RF securities. So 1,800,000 - 540,000 = 1,260,000 and 10% of it is 126,000 the investments in signature loans.

4) Other secured loans and Signature loans should not exceed the funds invested in RF securities: Investment in RF securities is 540,000 - Investment in Signature Loans 126,000 = Investment in Other Secured Loans 414,000

5) Furniture Loans and Other secured loans may not exceed Automobile loans: We have already invested 414,000 in other secured loans. Out of the total book of loans we have invested 1,080,000 in RF securities, Signature loans and Other secured loans. Since we have invested 414,000 in other secured loans and we have to fulfill the condition mentioned we will first invest 414,000 in Automobile loans. After this step we are left out with $306,000 which we can split half in automobile loans and half in furniture loans. We may be tempted to invest the $306,000 half between other secured loans and automobile loans because other secured loans gives us higher return. If we do that we violate from the condition 4.