Problem #2(Problem #7 in Chapter 4)

As part of the settlement for a class action lawsuit, HoxworthCorporation must provide sufficient cash to make the following annual payments (in thousands of dollars).

Year	1	2	3	4	5	6
Payment	190	215	240	285	315	460

The annual payments must be made at the beginning of each year. The judge will approve an amount that, along with earnings on its investment, will cover the annual payments. Investment of the funds will be limited to savings (at 4% annually) and government securities, at prices and rates currently quoted in The Wall Street Journal. Hoxworth wants to develop a plan for making the annual payments by investing in the following securities (par value $1000). Funds not invested in these securities will be placed in savings.

Security	Current Price	Rate (%)	Years to Maturity
1	$1055	6.750	3
2	$1000	5.125	4

Assume that interest is paid annually. The plan will be submitted to the judge and, if approved, Hoxworthwill be required to pay a trustee the amount that will be required to fund the plan.

Below is a Linear Programming model that determines the minimum cash settlement necessary to fund the annual payment.

Decision Variables:

F= total funds required to meet the six years of payments

G1= units of government security 1

G2= units of government security 2

Si= investment in savings at the beginning of year i (i=1,2,3,4,5)

Note: All decision variables are expressed in thousands of dollars

MIN F

S.T.

year 1: F -1.055G1 -1.000G2 -S1 = 190

year 2: .0675G1 + .05125G2 +1.04S1 -S2 = 215

year 3: .0675G1 + .05125G2 + 1.04S2 -S3 = 240

year 4: 1.0675G1 + .05125G2 + 1.04S3 -S4 = 285

year 5: 1.05125G2 + 1.04S4 -S5 = 315

year 6: 1.04S5 = 460

non-negativity: F, G1, G2, S1, S2, S3, S4, S5 >0

(a) Use Excel solver to determine the financial plan for the next 6 years. That is, specify the required fund (F) as well as the dollar amount that you invest in each of the government securities and how much money is invested each year in savings.

(b)Use the shadow price to determine how much more Hoxworth should be willing to pay now to reduce the payment at the beginning of year 6 to $400,000.

(c)Use the shadow price to determine how much more Hoxworth should be willing to pay to reduce the year 1 payment to $150,000.

(d)Suppose that the annual payments are to be made at the end of each year. Reformulate the model to accommodate this change. How much would Hoxworth save if this change could be negotiated?