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In B.C. (Before Computers) days, actuaries determined gain and loss only on a aggregate basis. The formula analyzed changes in the "unfunded." The actuary would calculate the "expected unfunded" and compare that with the "actual unfunded" at the end of the period in question, usually a year.For pension plans, the formula for the gain looked something like this:
(beginning of the year unfunded plus normal cost plus interest on both) minus (actual contributions) minus (the actual yearend unfunded)Actually, this formula persisted in its simplicity into years A.MS. (Anno Bill Gates) because we weren't too concerned with the elements making up the gain. Even ERISA didn't insist on very much more, merely requiring a separation of the gain between experience and amendments.
In the late 80's the IRS got concerned about the discount rates being used, suspecting that low rates were being used to increase deductions. At about the same time, the Financial Accounting Standards Board (FASB) was trying to improve pension cost reporting.
FASB, in particular, began the process of unbundling the unfunded into its components; the Projected Benefit Obligation (PBO) and the assets. FASB also promulgated an additional, previously underutilized, concept  the unprovided.
The unprovided is the accounting unfunded, adding the sponsor's Accrued Pension Cost (APC) to assets as an offset to the PBO. Unfortunately for the equation of gain from B.C. days, the APC portion of the unprovided does not have its own discount rate and must be dealt with separately. Where the discount rate equals the expected longterm rate of return on the assets, the equation of gain becomes:
(beginning of year unfunded plus the normal cost plus interest on both) minus (last year's APC) minus (NPPC) minus (the actual yearend unfunded) plus (the actual yearend APC)The Net Periodic Pension Cost (NPPC) has algebraically replaced actual contributions in the formula. When the discount rate is different from the expected longterm rate of return, the PBO must be separated from the assets. FASB added several new terms that help the explanation;
Service Cost  The Normal Cost plus interest at the discount rateInterest Cost  The interest on the PBO at the discount rate
Expected Return  The interest on the Assets at the expected longterm rate of return
The equation of gain becomes a little more complicated:
(beginning of the year PBO plus service cost plus interest cost) minus (beginning of the year assets plus expected return plus contributions) minus (last year's APC plus NPPC minus contributions) minus (the actual yearend unfunded) plus (the actual yearend APC)Notice that benefits do not have any place in the equation yet. Also notice that, if we substitute the expected yearend values for the actual yearend values, the unamortized gain changes only by the amortization component of the NPPC.
Algebraically, any number can be added to the formula to represent benefits. The B.C. years used actual benefits on both sides (liability and asset) of the equation taking advantage of the fact that gain and loss was calculated at a time when actual benefits were known.
The use of expected benefits allows us to calculate an expected PBO that is independent of actual experience. Adjusting the formula using expected benefits results in:
(beginning of the year PBO plus service cost plus interest cost minus expected benefits) minus (beginning of the year assets plus expected return plus contributions minus expected benefits) minus (last year's APC plus NPPC minus contributions) minus (the actual yearend unfunded) plus (the actual yearend APC)The first three terms are the algebraic expected values of each of PBO, assets and APC. Splitting the actual yearend unfunded into (Actual PBO minus Actual Assets), the formula has become:
(Expected PBO minus Actual PBO) minus (Expected assets minus Actual assets) minus (Expected APC minus Actual APC)Both the expected assets and the expected APC required a contribution number. Algebraically, it could have been any number at all and, if paid at the end of the year, it has no effect at all on aggregate results. The best number to use is the one that was used in developing the actual APC. Hopefully actual assets reflects the same number.
At the end of the year, actual benefits are known. Their treatment is not algebraically important, but, the difference between actual and expected benefits cannot be permitted to muddy the "actual return" on assets water!
One approach is to show a separate asset gain and loss item that carries the difference and keeps it out of investment gain. We prefer this approach.
Another, more typical approach, is to ignore expected benefits at the end of the year and use actual benefits in PBO gain and asset gain. This creates the unacceptable, in our opinion, result of getting a different "expected PBO" depending on when and how the calculation is done. We feel that the expected PBO is independent of experience and must be available before any actual results are available for the plan.
We now have three components of the gain and loss; PBO gain, asset gain and APC gain.
The PBO gain can be analyzed for decrements different from assumed, changes in the discount rate and other actuarial assumptions and salary increases different from assumed. When a sponsor is concerned about changes in the additional liability, the same analysis should be done on the Accumulated Benefit Obligation (ABO).
The asset gain can be analyzed for investment results. Changes in actuarial assumptions will not affect asset gain and loss.
The APC gain derives from the sponsor recognizing a cost other than the calculated Net Periodic Pension Cost (NPPC).
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