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**Question: **What If the Pension Payments Decrease or Stop?

**Answer:** This note explains how to value a pension whose payments decrease, or decline, or stop after a set number of years.

You can do this in the software, by creating entries for two pensions.

Enter the two pensions as follows:

1. Pension A: This pension pays the benefit at the initial amount and begins when the actual pension begins.

2. Pension B: This pension pays the negative amount of the net reduction and begins when the payments reduce.

The value of the actual pension is the value of Pension A + Pension B. (The value of Pension B will be a negative number.)

Note that you may have to enter the coverture fraction manually on Pension B. Override the coverture fraction on that pension with the coverture fraction from Pension A.

To see why this works, imagine a pension whose annual payments go like this:

100 100 100 100 60 60 60 60 ...

That is, a pension pays $100 for each of the first four years, and $60 for each year thereafter.

(They could be payments of $100,000 for each of the first four years, and $60,000 for each year thereafter. The principle is the same.)

Now imagine two pensions, each of which has level payments, as follows:

Pension A:

100 100 100 100 100 100 100 100 ...

Pension B:

0 0 0 0 -40 -40 -40 -40 ...

You can see that if you add each year's payments of these two payment streams together, you get the payment stream you want:

100 100 100 100 60 60 60 60

In each of the first four years, the combination of Pension A + Pension B pays $100, and each year after that the combination pays $60 -- same as the declining pension.

Thus, if you take the value of Pension A + Pension B + Pension C, you get the value of the original pension.

For a pension that is for a fixed time period, Pension B would just be the negative amount of Pension A.

In our example, above, Pension B would be:

0 0 0 0 -100 -100 -100 -100...

...and the resulting combination of Pension A and Pension B would be:

100 100 100 100 0 0 0 0...

...which is exactly what we want.