Question

Question 8 options:

Investment and Loan Planning. The employee credit union at State University is planning the usage of funds for the coming year. The credit union makes four types of loans to its members. In addition, it invests in “risk-free” securities in order 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 (%)
Secured Loans
Automobile	5
Furniture	6
Other Secured Loans	8
Signature Loans	9
“Risk Free Securities	4

State laws and credit union policies impose the following restrictions on the composition of the credit union’s loans and investments:

1. “Risk-Free” securities may not exceed 30% of the total funds.
2. Signature loans may not exceed 30% of total loans
3. Furniture loans plus “other secured loans” may not exceed 50% of the total of the three types of secured loans
4. Signature loans plus “other secured loans” may not exceed the amount invested in “Risk-Free” securities.

If the firm projects $1,500,000 available for loans and investments during the coming year, how should the funds be allocated to each of the investment alternatives in order to maximize total annual return?


Please, Do not use Commas in your answers.


Total Annual Return = $

Hint: Total Return is Between $88875 and $89675
Amount invested in Automobile loans = $

Amount invested in Furniture Loans = $

Amount invested in Other Secured Loans = $

Amount invested in Signature Loans = $

Amount invested in “Risk Free” Securities = $

Answer 1

Let the amount invested in Automobile loans be Xa, Furniture Loans be Xf, Other Secured Loans be Xo, Signature loans be Xs, Risk-free loans be Xr

Based on the Annual returns rate given, total annual returns = 5%*Xa + 6%*Xf + 8%*Xo + 9%*Xs + 4%*Xr

We have to maximize this return, hence, we get Objective function as

Maximize Total returns R = 5%*Xa + 6%*Xf + 8%*Xo + 9%*Xs + 4%*Xr

Various constraints given can be written as follows:

Xa + Xf + Xo + Xs + Xr = 1,500,000.........Constraint for the amount available for investment

Xr <= 30%*1,500,000...............................Constraint for the maximum risk-free investment

Xs <= 30%*(Xa + Xf + Xo + Xs)................Constraint for the maximum amount in signature loans

Xf + Xo <= 50%*(Xa + Xs + Xr).................Constraint for Furniture and other secured loans

Xs + Xo <= Xr............................................Constraint for other secured loans and signature loans

We solve the above problem in excel solver as shown below:

Above solution in the form of formulas and Solver Extract is shown below for better understanding and reference:

Automobile Loans	$ 367,500
Furniture Loans	$ 232,500
Other Secured Loans	$ 135,000
Signature Loans	$ 315,000
Risk-Free Loans	$ 450,000

The projected total annual return = $ 89,475

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