Fair warning: This post is going to get way off in the weeds of the complex math that defined benefit pension plans entail.  So if you are a mathphobe you may want to skip to the next item in your inbox.  Unfortunately, because defined benefit pension plans are such complicated financial arrangements, there is no way to fully understand their impact without getting into the weeds, so here goes.

The amount an employer needs to set aside to fully fund a defined benefit pension each year consists of two parts.  The first is the estimated cost of the benefits earned by employees that year.  This is referred to as the “normal cost” or “service cost.”

Of course that estimate is an educated guess at best.  It is fundamentally unknowable how much money needs to be set aside today for an indeterminate benefit to be paid 30 years from now.  We know from experience, however, that employers almost always underestimate this cost, which results in the plans becoming underfunded over time.  This is equivalent to the employer borrowing money from the pension plan.  It is debt, plain and simple.

That brings us to the second part of what the employer should be contributing to its pension plan.  In addition to the current cost, the employer should be contributing something toward paying off its debt to the plan.  But how much should that be?

To be considered “actuarially sound” the employer should be contributing enough to pay off the unfunded liability in 30 years or less.  Most people would assume that if an employer were going to pay off the debt in 30 years, the employer would run an amortization schedule to see how much it would need to contribute to the plan each year to pay off the debt, exactly the same way your bank calculates your mortgage payment.

But that is not how amortizations are done in the bizarre world of pension accounting.  Rather, pension plans normally calculate the amortization schedule to pay off the debt using something called the “level percentage of payroll method.”  It is a complete scam.

This amortization method estimates the total payroll for the employer over the next 30 years and calculates what percentage of that total payroll the employer will have to contribute to pay off the pension debt.  When you work through the math, this amortization schedule results in a negative amortization for about the first ten years (i.e. the debt increases for the first ten years) because the payments are dramatically back-end loaded.

I have learned that this is the amortization method the City intends to use in its proposed pension plan.  So let’s see what that looks like.

For the purposes of this example, I am assuming that the concessions the pension plans have agreed to really reduce the pension debt by $2.5 billion, something that has yet to be demonstrated.  I am also ignoring the debt service on the $1.6 billion of pension bonds that taxpayers will be saddled with if this plan goes through.

Making those assumptions, the City’s remaining pension debt would be $4.1 billion.  Assuming the City’s payroll increases by 3% each year and assuming the pension plans earn 7% during the entire 30-year amortization period, the City will need to make an annual contribution of about 19% of payroll.  This is what the amortization schedule would be.

As you can see, the overall pension debt remains above 2017 levels until 2031.  More significantly, the payments begin low and then dramatically ramp up over the 30-year period, more than doubling.  So if you are only going to be mayor, say until 2020 or even 2024, you don’t have worry too much about how to pay off the pension debt.

Here is what the numbers look like graphically:

Now let me add this caveat.  This is a very simplified model of how this amortization method works.  Very small changes in the assumptions make enormous differences in the outcome.  For example, if the City’s payroll goes up by 5% annually, the payments are even more back-end loaded and the debt balloons to over $5 billion before it starts down.  Also, other factors, like the inflation rate, can dramatically affect the future contributions and scheduled pay-down of the pension debt.

Of course, even the presumption that we can project what the City’s payroll will be over the next 30 years is absurd on its face in the first place.

But make no mistake.  The only reason to use this squirrelly method to amortize the pension debt is to kick this can down the road to the next City administration.