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: Type of Loan/Investment Annual Rate of Return (%) Automobile loans 8 Furniture loans 11 Other secured loans 13 Signature loans 14 Risk-free securities 8 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 13% 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? Automobile Loans $ 630,000 Furniture Loans $ 332500 Other Secured Loans $ 335000 Signature Loans $ 165000 Risk Free Loans $ 44160 What is the projected total annual return?

Answer 1

Let	Investments in	Rs.	Rate of Return	Return
	Automobile loans	a	8%	.08a
	Furniture loans	b	11%	.11b
	Other secured loans	c	13%	.13c
	Signature loans	d	14%	.14d
	Risk-free securities	e	8%	.08e
	Total Return	+.08a+.11b+.13c+.14d+.08e
	Total Investment Available			$ 20,00,000.00
Given Constraints
	Investment in
	Risk Free Securities ( e )	≤ 500000	=0.25*2000000
	Signature Loan (d)	d ≤ 13% (a+b+c+d)
	b+c≤a
	c+d≤e
	a+b+c+d+e=$20,00,000
	Converted all inequalities in to Equalities
	e = $500000
	then c+d = $500000
	a+b+c+d= $ 15,00,000 ($20,00,000-$5,00,000)
	a+b= $ 10,00,000 ($20,00,000-$5,00,000-$5,00,000)
	d=13% ($1500000)
	d = $ 1,95,000
	c = $ 3,05,000 ($ 5,00,000- $ 1,95,000)
	b+$305000=a
	a-b = $ 3,05,000
	a+b = $ 10,00,000
	2a = $ 13,05,000
	a = $6,52,500 ($ 1305000/2)
	b = $ 3,47,500 ($1000000-$652500)
	Allocation
	a = $ 6,52,500
	b = $ 3,47,500
	c = $ 3,05,000
	d = $ 1,95,000
	e = $ 5,00,000
	Expected Return
	Investments in	Amount (Rs.)	Return	Return Amount (Rs.)
	Automobile loans	$ 6,30,000.00	8%	$       50,400.00
	Furniture loans	$ 3,32,500.00	11%	$       36,575.00
	Other secured loans	$ 3,35,000.00	13%	$       43,550.00
	Signature loans	$ 1,65,000.00	14%	$       23,100.00
	Risk-free securities	$     44,160.00	8%	$          3,532.80
	Return			$    1,57,157.80