As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the following annual payments (in thousands of dollars) Year 1 2 3 4 5 6 Payment 170 210 250 310 340 500 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 3 25 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 of Maturity 1 1075 6 55 3 2 1000 5 125 4 Assume that interest is paid annually The plan will be submitted to the judge and, if approved, Hoxworth will be required to pay a trustee the amount that will be required to fund the plan (a) Use linear programming to find the minimum cash settlement necessary to fund the annual payments Let F total funds required to meet the six years of payments G 1 units of government security 1 G 2 units of government security 2 S i investment in savings at the beginning of year i Note All decision variables are expressed in thousands of dollars If required, round your answers to five decimal places For subtractive or negative numbers use a minus sign even if there is a sign before the blank (Example 300) 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 Hoxworth shoud be willing to pay anything less than $ d) Suppose that the annual payments are to be made at the end of each year Reformulate the model to accommodate this change Note All decision variables are expressed in thousands of dollars If required, round your answers to five decimal places For subtractive or negative numbers use a minus sign even if there is a sign before the blank

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Aug 29, 2024

As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the following annual payments (in thousands of

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

Year	1	2	3	4	5	6
Payment	170	210	250	310	340	500

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 3.25% 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 of Maturity
1	1075	6.55	3
2	1000	5.125	4

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

(a)

Use linear programming to find the minimum cash settlement necessary to fund the annual payments.

Let	F = total funds required to meet the six years of payments
	G₁ = units of government security 1
	G₂ = units of government security 2
	S_i = investment in savings at the beginning of year i

Note: All decision variables are expressed in thousands of dollars.

If required, round your answers to five decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

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 Hoxworth shoud be willing to pay anything less than $____

d) Suppose that the annual payments are to be made at the end of each year. Reformulate the model to accommodate this change.

Note: All decision variables are expressed in thousands of dollars.

If required, round your answers to five decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank