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174 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

Financial Planning

Linear programming has been used for a variety of financial planning applications. The
Management Science in Action, Optimal Lease Structuring at GE Capital, describes how
linear programming is used to optimize the structure of a leveraged lease.
Hewlitt Corporation established an early retirement programme as part of its
corporate restructuring. The company has asked employees who are within a few
years of normal retirement if they would be willing to take early retirement. Staff
who do so will be given a special financial payment by the company for each year
before they reach the normal retirement age. So, for example, someone who would
normally retire at the age of 60 who decides to take early retirement at the age of 55
will get five years of financial payments from the company. The company obviously
will achieve savings by not having to pay the employee a salary plus benefits during
those five years. So, for example, the company has to find E430 000 in year 1 to pay
staff who have taken early retirement; E210 000 in year 2 and so on. At the close of
the voluntary sign-up period, 68 employees had elected early retirement. As a result
of these early retirements, the company incurs the following obligations over the
next eight years.

Year 1 2 3 4 5 6 7 8
Cash Requirement 430 210 222 231 240 195 225 255

The cash requirements (in thousands of euro) are due at the beginning of each year.
The corporate treasurer must determine how much money must be set aside
today to meet the eight yearly financial obligations as they come due. The financing
plan for the retirement programme includes investments in government bonds as
well as savings. The investments in government bonds are limited to three choices:

Bond Price, E Rate (%) Years to Maturity
1 1 150 8.875 5
2 1 000 5.500 6
3 1 350 11.750 7

The bonds have a nominal, face value of E1000. So, for example, if the company
buys Bond 1 at E1150 per bond, then it will receive an interest payment of 8.875 per
cent of E1000 from the government each year for the next five years, when Bond 1
matures. At maturity, the government buys the bond back at face value of E1000.
For the purposes of planning, the treasurer assumed that any funds not invested in
bonds will be placed in savings and earn interest at an annual rate of 4 per cent.
We define the decision variables as follows:

F ¼ total euros required to meet the retirement plan’s eight-year obligation
B 1 ¼ units of bond 1 purchased at the beginning of year 1
B 2 ¼ units of bond 2 purchased at the beginning of year 1
B 3 ¼ units of bond 3 purchased at the beginning of year 1
S i ¼ amount placed in savings at the beginning of year i for i ¼ 1; ... ; 8
So, the company has to decide how many of each of the three bonds to buy at the
start of year 1 and how much additional savings will be needed each year for the next

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