Quantitative Methods for Business, Business Economics

Please turn in the linear program for the following problem. No need to solve the LP.
Exercise 3 (Multi-Period Fixed Income Capital Budgeting)
As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to
make the following annual payments:

Year 1 2 3 4 5 6
Payment $190,000 $215,000 $240,000 $285,000 $315,000 $460,000

The annual payments must be made at the beginning of each year, beginning year 1. The judge will
approve an amount that, along with earnings on its investment, will over the annual payments.
Investment of the fund will be restricted to savings and government securities only. Savings pay a 4%
annual interest. It is assumed that this annual savings rate is fixed throughout the six year period. There
are only two government securities that we would like to consider. Their prices and rates are quoted from
The Wall Street Journal as follows:

Govt Security Current Price Fixed Coupon Rate Maturity
1 $1055 per unit 6.750% beginning of year 4
2 $1000 per unit 5.125% beginning of year 5

Hoxworth wants to develop a plan for making the annual payments by investing in the above two
government securities. The par value of each of these securities is $1000, that is, the government will pay
off (redeem) each unit of the security $1000 at the time of maturity. Funds not invested in these securities
will be placed in savings. After the annual payment at the beginning of year 6, there is no need to
maintain any more investment. In other words, all investment and savings accounts can be closed after
the 6th annual payment.
Assume that the interest from both savings and government securities are paid annually. Use linear
programming technique to determine the minimum total amount of cash settlement (F) at the present time
(i.e., the NPV at the beginning of year 1). The plan will be required to pay a trustee the amount required
to fund the plan.
Use the following variables in your linear program:
F = total amount of cash settlement required to meet the six years of payments
G1 = units of government security 1 to be purchased now
G2 = units of government security 2 to be purchased now
Si = investment put in savings at the beginning of year i, for i = 1, 2, 3, 4, 5
Hint: Excluding the non-negativity constraint, the linear program contains six constraints, one for each
year. There is no S6 in this problem since all assets on hand will be applied to the final and 6th
payment. The trick of this problem is to balance the cash inflow with the cash outflow.

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