Thanks to the latest pension accounting standards under GASB 68, analysts have a lot more information on the net pension liabilities of individual pension plans for a municipality. For cost-sharing multiple employer plans in particular, the funded ratio and the proportionate share of the net pension liability are now provided. But unlike the other two plan types, cost-sharing plans do not provide a municipality's proportionate share of the Total Pension Liability or Fiduciary Net Position. Fortunately, both the TPL and FNP can be derived with a few equations. And there is a good reason to do the calculations.

Cost-sharing plans vs other types

Providence, Rhode Island provides a good example. It contributes to two pension plans: a City Plan (single employer) and a State Plan (cost-sharing multiple employer). Here is the Net Pension Liability information on the Employee Retirement System of the City from the Required Supplementary Information of the CAFR:

And here is the Net Pension Liability information for the cost-sharing state plan:

The cost-sharing plan table is sparse but useful. It provides the city’s portion of the NPL (\$261 million) and funded ratio (57.6%). However, it does not provide the city's proportionate share of the pension plan's TPL and FNP.

A little algebra

With a pension plan’s Net Pension Liability and Funded Ratio, you have enough information to estimate its Total Pension Liability (TPL) and Fiduciary Net Position (FNP). You do this by setting up two equations with two unknowns (TPL and FNP).

The two equations are as follows:

We will skip the details on how to combine and solve these equations. Ultimately we end up with the following formula for the TPL based on the NPL and funded ratio:

And the FNP can be found by putting the TPL back into equation (2) above.

For Providence's cost-sharing plan, the city's share of the TPL is about \$615 million and its share of the plan's FNP is about \$354 million.

Why calculate the TPL and FNP for a plan?

The NPL and funded ratio provided are great for understanding the size of the liability for that specific plan. But things get complicated if you want to estimate a blended funded ratio across all pension plans. Providence’s two pension plans have funded ratios of 25% and 57%. But the blended funded ratio is not just the average of these two figures. Taking the average does not properly weight the size of the plans. Estimating the TPL and FNP for the cost-sharing plan are needed. Calculating the blended funded ratio will be covered in the next piece on pensions.

A note on accuracy

The figures generated by the equations are estimates. Their accuracy is affected by the number of significant digits provided in the NPL and funded ratio. If the funded ratio is a percent with no decimal (ie 78%), the derived FNP and TPL will be less accurate than if decimals are provided (ie 77.68%).