The whole promise, sliced into yearly bites
By now you know what a defined-benefit pension is: the employer promises a worker a stream of income for life, often something like 1.5% of final salary for every year served. You have also met the two backbone numbers — the accrued liability and the normal cost. The accrued liability is the present value of the pension *already earned* up to today; the normal cost is the slice of new pension *being earned this year*. This guide answers the question those numbers leave hanging: who decides exactly *how* the total cost gets spread across a career — and what happens when the assumptions behind it shift?
Picture a 30-year-old who will work 35 years and then draw a pension for perhaps 25 years after that. The total cost of her pension is one enormous lump, payable far in the future. We cannot wait until she retires and then scramble for the cash — the whole point of *funding* is to set money aside, year by year, while she works, so the fund grows to meet the promise. An actuarial cost method is simply an agreed recipe for cutting that one giant lump into a sensible yearly slice. Different recipes cut it differently. They do not change the *total* cost of the pension — only its *timing*: how much you book early versus late.
Two recipes: projected unit credit and entry age normal
The two recipes you must know are projected unit credit and entry age normal — the workhorses of pension valuation. Projected unit credit (PUC) is the more literal of the pair. It says: each year of service earns one *unit* of pension, so let each year carry the cost of the unit *earned that year*. The twist hidden in the word "projected" is crucial: the benefit is tied to *final* salary, so when you cost this year's unit you project salary forward to retirement and value the unit on that future, higher salary. The normal cost under PUC is the present value of just *one more year's* slice of the eventual pension.
Because pension units valued on a projected final salary grow more expensive as a worker ages — each later unit sits closer to retirement and rides on a bigger salary — PUC produces a normal cost that *rises* over a career. It starts low for the young worker and climbs steeply near retirement. That is exactly the pattern accountants like, which is why most modern accounting standards mandate PUC for the figures in company reports. It is honest about one thing: it never books a cost for service not yet rendered.
Entry age normal (EAN) takes the opposite philosophy: stability over literalism. Stand at the worker's *entry age*, look at her entire projected pension, and find the single *level* contribution — a flat percentage of salary, say — that, paid every year from entry to retirement, would exactly fund the whole thing. That level percentage *is* the normal cost. Where PUC's cost ramps up year after year, EAN's stays smooth and predictable across the career, which is why funding rules (especially for public-sector plans) often favour it: a stable contribution is easier for a budget to live with than one that lurches upward as the workforce ages.
The assumptions: a string of guesses about the future
A cost method is just the slicing rule. To put real numbers on it you need to know what the future will actually do, and that is where the valuation assumptions come in. To value one worker's pension you must answer a chain of "what will happen?" questions reaching decades ahead, and each answer is an explicit, reasoned estimate. There are two families. Economic assumptions are about money: how fast salaries grow (the salary scale) and what return the fund will earn — which becomes the all-important discount rate. Demographic assumptions are about people: when they retire, how many quit before vesting (the withdrawal rate), and how long they live once retired.
Each assumption pulls the liability in a direction you can reason out. A faster salary scale means a bigger final salary, so each accrued pension unit is worth more — the liability rises. A higher retirement rate at younger ages means benefits start sooner and run longer — the liability rises. A higher withdrawal rate means more workers quit before their pension vests, forfeiting some of the promise — the liability *falls*. And a longer assumed lifespan — the heart of longevity risk — means more years of payments, so the liability rises. None of these is known; each is a judgement the actuary must defend.
Two honest cautions. First, a set of assumptions is not a forecast of any one person — nobody retires "40% at age 62." It is a *portfolio* statement: across hundreds of members, the rates are meant to come out roughly right in aggregate, the same pooling logic you met in the earliest rungs. Second, assumptions are not chosen one at a time in a vacuum; they must be coherent *together*. A salary scale far above the inflation baked into the discount rate, for instance, would quietly contradict itself. A valuation is only ever as trustworthy as the weakest assumption holding it up.
The discount rate: one number that swings everything
Of all the assumptions, one dominates: the discount rate, the rate used to bring those far-future pension payments back to a value today. You already know the mechanics from the interest-theory rungs — discounting a future cash flow divides it by (1 + i) once for each year of waiting, the same compounding you saw with the force of interest. What makes the discount rate so explosive in pensions is *leverage from time*. A retiree's pension is paid out across decades, and a payment 30 years away is divided by (1 + i) thirty times over. Change i even slightly and you are changing the divisor of a very tall power — the effect compounds with frightening speed.
Watch a single payment make the point. Suppose a worker is owed 100,000 in 30 years. At a 6% discount rate its present value is 100,000 ÷ 1.06^30 ≈ 17,411. Now drop the rate to 5% — a change of just one percentage point. The present value jumps to 100,000 ÷ 1.05^30 ≈ 23,138. That single step *up* in value, about 33%, came from one point *down* in the rate. Spread that same sensitivity across a fund holding billions in liabilities and a one-point move in the discount rate can swing the headline number by hundreds of millions — enough to flip a plan from "comfortably funded" to "in deficit" overnight, with not one promise having changed.
One payment of 100,000 due in 30 years, valued at two discount rates: at 6% : PV = 100,000 / 1.06^30 = 100,000 / 5.7435 ~= 17,411 at 5% : PV = 100,000 / 1.05^30 = 100,000 / 4.3219 ~= 23,138 one point lower rate -> ~33% higher liability Rule of thumb: liability moves by roughly (duration) x (rate change). A pension liability with ~15-year duration moves ~15% per 1% rate change.
This is why the *choice* of discount rate is one of the most contested decisions in the whole field, and why honest people disagree. One school says: discount by the *expected return on the fund's assets* — if you hold equities expecting 7%, use something near 7%, because that is the money you really expect to earn. The other says: discount by a *risk-free or bond yield*, because the pension promise itself is close to a guarantee, and a guaranteed liability should be valued like a guaranteed bond, not like a hopeful stock portfolio. The first makes the liability look smaller and contributions cheaper today; the second is more conservative and books trouble sooner. Neither is a lie — but they answer different questions, and a reader who does not ask "discounted at what rate?" has not really read the number at all.
Putting it together — and watching reality push back
Here is how a real valuation runs, end to end, for one member — and it draws on every rung you have climbed.
- Project the salary forward to retirement using the salary scale, then apply the benefit formula to get the annual pension she would receive.
- Turn that lifelong pension into a present value at retirement using a life annuity factor — the mortality-weighted present value of 1 per year for life, exactly the annuity tool from the life-contingencies rung.
- Discount that retirement-date value back to today with the discount rate, and weight it by the probability she survives in service to retirement — netting out the withdrawal and pre-retirement mortality rates.
- Apply the cost method (PUC or EAN) to split that present value into the accrued liability already earned and this year's normal cost.
- Sum across all members, compare the total accrued liability with the fund's assets, and read off the funding ratio — the plan's headline health check.
That final ratio — assets divided by accrued liability — is the funding ratio, and the gap below 100% is the unfunded liability. But here is the crucial twist that ties the whole guide together: the funding ratio is *not* a fact you measure, like a temperature. It is a *consequence of your assumptions*. Pick the optimistic high discount rate and the same plan looks 105% funded; pick the conservative bond yield and that very same plan, with the very same assets and the very same promises, looks 80% funded and in trouble. The pension has not changed at all. Only the ruler has.
Then reality pushes back. Each year, the actual world differs from the assumed one — salaries grew faster, the fund earned less, people lived longer than the table said. The difference between assumed and actual surfaces as an experience gain or loss, and the cost method also tells you how to spread that surprise across future contributions. This is the heartbeat of the actuarial control cycle you met at the very start: assume, observe, compare, adjust, repeat. A funding method is never a one-time calculation. It is a living loop that keeps a decades-long promise honest, one annual valuation at a time.