As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the following 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 investment, will cover the annual payments. Investment of the funds will be limited to savings (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, 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.
B. Use the dual value 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 dual value 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?