50.1K

Verified Solution

Link Copied!

Provident Financial Services Corporation (also known as PFS) manages a well-regarded pension fund that is used by a number of companies to provide pensions for their employees. Management takes pride in the rigorous professional standards used in operating the fund since the near collapse of the financial markets during the protracted recession that began in late 2007 , PFS has redoubled its efforts to provide prudent management of the fund. It is now 2023. By its estimate, the total pension payments that will need to be made by the fund over the next 10 years are shown in the table below. PFS would like to make a number of investments whose payouts would match the pension payments over the next 10 years. It is considering investing in a money market fund and in four bonds. The money market fund pays an annual interest rate of 2 percent. The characteristics of each unit of the four bonds under consideration are shown in the next table. All of these bonds will be available for purchase on January 1 , 2024 , in as many units as desired. The coupon rate is the percentage of the face value that will be paid in interest on January 1 of each year, starting one year after purchase and continuing until (and including) the maturity date. Thus, these interest payments on January 1 of each year are in time to be used toward the pension payments for that year. Any excess interest payments will be deposited into the money market fund. To be conservative in its financial planning, PFS assumes that all the pension payments for the year occur at the beginning of the year immediately after these interest payments (including a year's interest from the money market fund) are received. The entire face value of a bond also will be received on its maturity date and deposited into the money market fund. Since the current price of each bond is less than its face value, the actual yield of the bond exceeds its coupon rate. Bond 3 is a zero-coupon bond, so it pays no interest but instead pays a face value on the maturity date that greatly exceeds the purchase price. PFS would like to make the smallest possible investment (including any deposit into the money market fund) on January 1 , 2024 , to cover all its required pension payments through 2033. PFS top management has given you the assignment of modeling and analyzing this problem. c. Formulate the above problem mathematically as a linear programming model. Define your decision variables clearly; define the notation you use. Using your decision variables, formulate the objective function and constraints

Answer & Explanation Solved by verified expert

See Answer