Question

A financial planner wants to design a portfolio of investments for a client. The client has $300,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 25% of the money in any one investment, at least one third should be invested in long-term bonds which mature in seven or more years, and no more than 25% of the total money should be invested in C or D since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio.

		Years to
Investment	Return	Maturity	Rating
A	6.45%	9	1-Excellent
B	7.10%	8	2-Very Good
C	8.20%	5	4-Fair
D	9.00%	8	3-Good

Let	X1 = Dollars invested in A
	X2 = Dollars invested in B
	X3 = Dollars invested in C
	X4 = Dollars invested in D
MAX:	.0645 X1 + .071 X2 + .082 X3 + .09 X4
Subject to:	X1 + X2 + X3 + X4 ≤ 300000
	X1 ≤ 75000
	X2 ≤ 75000
	X3 ≤ 75000
	X4 ≤ 75000
	X1 + X2 + X4 ≥ 100000
	X3 + X4 ≤ 75000
	X1, X2, X3, X4 ≥ 0

	A	B	C	D	E	F	G	H
1		Amount	Maximum		Years to	7+ Years?		Good or worse?
2	Bond	Invested	25.00%	Return	Maturity	(1 - yes, 0 - no)	Rating	(1 - yes, 0 - no)
3	A	$0	$75,000	6.45%	9	1	1 - Excellent	0
4	B	$0	$75,000	7.10%	8	1	2 - Very Good	0
5	C	$0	$75,000	8.20%	5	0	4 - Fair	1
6	D	$0	$75,000	9.00%	8	1	3 - Good	1
7	Total Invested:	$0	Total:	$0	Total:	$0	Total:	$0
8	Total Available:	$300,000			Required:	$100,000	Allowed:	$75,000

a) What formula should be entered in cell D7 in the accompanying Excel spreadsheet to compute the total return?  (Click to select)  =B7*SUM(D3:D6)  =SUM(B3:B6)  =SUMPRODUCT(B3:B6,D3:D6)  =SUMPRODUCT(B3:E3,B6:E6)

b) Which cells are changing cells in the accompanying Excel spreadsheet?  (Click to select)  C7  B3:B6  B7:I7  E7

c) What formula should be entered in cell B7 in the accompanying Excel spreadsheet to compute total dollars invested?  (Click to select)  =TALLY(B3:B6)  =ADD(B3:B6)  =SUM(B3:B6)  =TOTAL(B3:B6)

Answer 1

By entering the fig.3 in to excel and adding the Constraints of Fig.2 in the solver of Excel sheet, we can find the values of X1,X2,X3 &X4. I herewith attach 2 images, one showing how inputs are made into the solver and the values of X1,X2,X3,X4 i.e B3:B6 and the other showing the formulae used in each cell

a) Ans is Option 3

D7 represents the value of the total return on the portfolio. By running solver, we already got the values of investment into each bond i.e B3:B6. For calulating return on each bond, we have simply multiply the investment amount in that bond with the rate of return of that bond i.e B3*D3, B4*D4, B5*D5, B6*D6. The total return is just the sum of indivisual returns.

Therefore; D7 = (B3*D3)+(B4*D4)+(B5*D5)+(B6*D6).

-> D7 = SUMPRODUCT(B3:BE,D3:D6)

b) Ans is Option 2

We solve for the Values of X1,X2,X3,X4 such that the total return i.e D7 is maximum. Therefore, the changing cells are B3:B6

c) Ans is Option 3

B7 is the total amount invested such that all the given constraints get satisfied. This is equal to X1+X2+X3+X4 = SUM(B3:B6)