Projecting Your Own FAS 87 valuations are only required every three years. We have always recommended and still do that valuations are like medical checkups and should be done every year or more frequently when there are major changes occurring.

But, what happens when you have not had any major changes and your available resources (budget, time, etc.) will not permit a full valuation? Often, the client will return to the actuary responsible for the last report and ask him to "update" it. They often find this approach is still pretty expensive! In reality, you can do your own update. Once accomplished, you have at least two choices; ask you actuary to re

view(not redo) the work or persuade your auditor that you did it correctly.The latter is not so difficult if there is no requirement for any changes in actuarial assumptions, especially the discount rate.

The base projection is always done on a "no new gain or loss" basis; that is, all actuarial assumptions are assumed to be exactly met during the year. By base, we mean this must be done first. Our standard report includes a one-year projection for budget purposes which can be used for this first step.

The mathematics goes like this;

The net unamortized net gain and loss (including all unamortized components) for the current year equals the difference between the Projected Benefit Obligation (PBO) on the one side and the sum of the external Assets(A) and the Accrued Pension Cost (APC) on the other.UNG_{0}=PBO_{0}-(A_{0}+APC_{0})Next year's unamortized net gain and loss is similarly defined:UNG_{1}=PBO_{1}-(A_{1}+APC_{1})In this projection, we require no new net gain or loss, meaning that the only change in the UNG is the sum of any amortization payments included in the Net Periodic Pension Cost (NPPC). Now we know that the NPPC equals the sum of the Service Cost (SC), Interest Cost (IC), net Amortization Payments (AP) less the Expected Return (ER):

NPPC_{0}=(SC_{0}+IC_{0}+AP_{0})-ER_{0}We will deal with the Actual Return (AR) a little later.

As stated, UNG

_{1}= UNG_{0}-AP_{0}, since we are requiring all actuarial assumptions to be exactly realized. The new unrecognized net gain & loss equals the old minus the amortization payment.Making some substitutions, we get

UNG_{1}=PBO_{0}-(A_{0}+APC_{0})-AP_{0}=(PBO_{0}+SC_{0}+IC_{0})-(A_{0}+ER_{0}+APC_{0}+NPPC_{0})Note that neither benefits nor premiums (contributions) show up in this formula; there are a variety of manipulations available that will not disturb the balance. One, available at the end of the year, is to introduce Actual Benefits (AB) and permit AB to be divided into two pieces - that paid by the external assets (EAB) and that paid by the company directly under the terms of the plan (IAB). The formula becomes

UNG_{1}=(PBO_{0}+SC_{0}+IC_{0}-AB_{0})-([A_{0}+ER_{0}-EAB_{0}]+[APC_{0}+NPPC_{0 }-IAB_{0}])The formula only needs one more piece - actual premiums(C) - to produce reasonable estimates of PBO

_{1}, A_{1}and APC_{1}...UNG_{1}=(PBO_{0}+SC_{0}+IC_{0}-AB_{0})-([A_{0}+ER_{0}+C_{0}-EAB_{0}]+[APC_{0}+NPPC_{0}-C_{0}-IAB_{0}])In fact, APC

_{1}exactly equals APC_{0}+NPPC_{0}-C_{0}-IAB_{0}; the year-end accrued pension cost equals the beginning plus the charge less the payments. "Expected" PBO_{1}equals PBO_{0}+SC_{0}+IC_{0}-AB_{0}and "Expected" A_{1}equals A_{0}+C_{0}+ER_{0}-EAB_{0}. In the absence of additional information, these new numbers are acceptable for year-end disclosure.Usually, however, actual assets are known and Actual Return (AR) is available. The difference between ER and AR is a gain and the formula for assets adjusts to A

_{0}+C_{0}+AR_{0}-EAB_{0}with the difference being an adjustment to gain & loss. Your balance sheet will then showAPC_{1}=APC_{0}+NPPC_{0}-C_{0}-IAB_{0}and the footnotes will disclose

PBO_{1}=PBO_{0}+SC_{0}+IC_{0}-AB_{0}

A_{1}=A_{0}+AR_{0}+C_{0}-EAB_{0}UNG

_{1}will also be split into its components in the footnotes, following the amortization schedules already set out and the adjustment for actual return.These are all numbers you can calculate yourself in the absence of changes in the actuarial assumptions for the new year and any major events during the year.

Copyright 1998

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