Actuarial camouflage II: Normal Cost Methods

As part of the new GASB rules for public sector pensions not only will the rules guiding discount rate selection change, amortization periods will shrink from 30 to 15 years. This reflects the average number of service years remaining for current employees. By way of analogy, this is similar to refinancing a 30-year loan over a 15-year period. Payments required to amortize the liability will necessarily increase.

The new rules also suggest all plans use the Entry Age Normal (EAN) actuarial method to calculate the cost of the plan.

An actuarial cost method spreads the annual cost of the pension benefit over the working life of the employee. These methods have no equivalent in economics or finance. So, to build a bridge between actuarial practice and economics M. Barton Waring in Pension Finance begins by noting a pension is simply an annuity.

A pension pays a known amount to a worker upon retirement based on a formula. The cost of the plan (the liability to the sponsor) is the total of these individual annuities due to beneficiaries. The expense to fund the benefit is spread out over time much like a mortgage payment.

Actuaries define the annual payment that grows into the full benefit amount at retirement as the “normal cost“. These annual payments can take on different “shapes.” They can be structured in different ways.

The most recognizable, and economically-sound shape is nothing more than a mortgage payment on a 30 year home loan. In actuarial lingo, call it the “level payment normal cost.”

I take this example straight from his book:

Assume an employee is guaranteed an annuity of $300,000 upon retirement 30 years from today. How much should be set aside each period to ensure that sum is available when the employee reaches retirement? Assume the discount rate is 4% and the final benefit payout is $300,000, thirty years from today. Using the Present Value (PV) formula in Excel we find the present value of is -$92,496.

Next we want to know: How much needs to be put aside each year to grow into the benefit?

Again, using Excel, this time the PMT (acronym for payment) function is used. Each year, $5,349 must be set aside to achieve a final benefit payout of $300,000, at 4% interest a year.


It’s that simple. But a bridge is needed between the economic way of thinking and actuarial science. To begin building it, Waring defines that $300,000 annuity as the economic Present Value of one individual’s Future Benefit Payments or ePVFBPi .

Why do this? Because the methods actuaries use to spread this costs over time have no economic basis, only a pragmatic one. Cost methods were devised to establish a contribution policy for the plan sponsor. As such, cost methods give rise to “subsidiary liabilities,” or  accounting identities that represent subsets of the full economic liability of the plan. One such slice of the full liability (familiar to those who read actuarial reports) is the “accrued liability” of the plan.

Economically-speaking the “accrued liability” is a steadily increasing point on the individual’s journey to $300,000. At any point until year 30, the remainder of the liability is still off-book. A road-trip analogy: on a level payment basis the “accrued liability” in year 15 is Memphis ($107,107) on a road trip between Los Angeles ($0) and New York City ($300,000).

To build up a savings account to pay for this steadily accruing liability, actuaries are really “amortizing a debt through some payment function.”

These “payment functions” include the Accumulated Benefit Obligation (ABO), the Projected Benefit Obligation (PBO) and Present Value of Benefits (PVB) cost methods. Each method divides up the present value of payments required to reach $300,000 in year 30 at different “rates of speed.” Unfortunately, this can create a practical problem for a beneficiary should the sponsor pull the plug. Here’s how.

Take the ABO method. It recognizes and calculates the normal cost to fund the benefit as it is accrued by the worker each year. It is the dashed red curve in Chart 1. as illustrated by Waring. The grey bars along the the horizontal axis represent the normal cost to fund this liability as it grows. Notice these normal costs are lower in the early years and increase the later years.

Chart 1. How the Accumulated Benefit Method spreads normal costs

Now consider the ABO against other cost methods. In Chart 2, Waring draws the solid red line to represent the ePVFBPi: the economic way of thinking about annual costs. It is curve showing “the 30 mortgage on $300,000 with level annual payments.” The other curves represent actuarial cost methods which weight annual payments differently over time.

Chart 2. Contribution Rates of Speed for different Cost Methods

The practical problem is that at any point in time different methods leave the beneficiary at a different “milepost” in terms of reaching the funding goal. All methods eventually hit the target. But if an employer ended the plan, say in year 15, depending on the cost method used by the plan to figure out the annual contributions, individual ‘i’ would have accumulated a different amount to reach the same $300,000 goal. In an “ABO world” an employee has less in their $300,000 annuity savings account at any given moment (especially before year 15), than he does if he is in a “level-payment world.” In this way, a cost method can compromise an individual’s benefit security.

Entry Age Normal calculates the annual normal cost as a constant proportion of salary. Waring points out this has advantages for negotiations between labor and management since it expresses the cost of benefits in an intuitive and meaningful way – in relation to salary.

The lesson is cost methods have benefit security consequences. That leads Waring to Proposition 7:

“The choice of normal cost method does not control costs over the long term. Long term costs are always, instead, a direct function of the present value of the benefit promise ePVFBPi, a value that the stream of normal costs (and also of contributions) must match. The normal cost method that is selected does affect benefit security however: Slower, later normal cost methods (and their attendant slower, later contributions) leave a smaller portion of the present value of the benefit promise secured at any oven time than do faster, earlier normal cost methods.”