for daniel johnson

Leung/MS3053/Spring2016 4

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.