Pension and OPEB math every public finance professional needs

# Pension and OPEB math every public finance professional needs

A city council in Illinois approves next year's budget. Buried in footnote 47 of the audited financial statements is a single ratio: 42%. That number means the city's pension fund holds less than half of what it owes retirees, today and in the future. Nobody in the room mentions it. Eighteen months later, the city is cutting library hours to make a catch-up payment. This lesson teaches you to spot that number before the council does.

Why pensions and OPEB matter to public finance

Governments and public employers promise two big long-term benefits to workers: pensions (retirement income) and OPEB (Other Post-Employment Benefits, mainly retiree healthcare). Both are paid far in the future but often under-set-aside today. That mismatch is the single biggest hidden liability in public sector finance, bigger in many US cities and states than their entire bonded debt.

Understanding the math lets you read a pension footnote the way a credit analyst does: as an early warning system.

The core building blocks

Actuarial Accrued Liability (AAL): the present value, in today's dollars, of benefits already earned by current and retired employees. Calculated by actuaries using assumptions about salary growth, mortality, retirement age, and investment returns.

Plan assets (fiduciary net position): the market value of money actually invested in the pension or OPEB fund today.

Unfunded Actuarial Accrued Liability (UAAL), also called the Net Pension Liability under US accounting rules:

UAAL = AAL - Plan Assets

Funded ratio: the headline number everyone quotes.

Funded Ratio = Plan Assets / AAL

A funded ratio of 100% means the fund has exactly enough today to cover benefits earned to date (not future accrualsaccrualsAccrual accounting records revenue and expenses when they are earned or incurred, not when cash changes hands, giving a more accurate picture of financial performance.Voir la définition complète →). Below 100% signals a gap that must be closed by future contributions, investment returns, or benefit cuts.

Worked example: a mid-size US city pension plan

Assume a city police and fire pension fund reports (illustrative figures, not from a real city):

• AAL: $500 million
• Plan assets (market value): $310 million

Step 1: Funded ratio

310 / 500 = 0.62 → 62% funded

Step 2: UAAL

500 - 310 = $190 million unfunded liability

Step 3: Why this matters for the budget. Actuaries typically require the city to pay down the UAAL over 15 to 25 years, on top of the "normal cost" (benefits earned that year). If the amortization payment is $12 million a year and the city's total general fund budget is $150 million, that single line item is 8% of the budget, growing if returns disappoint or the workforce ages faster than assumed.

Benchmarks to know (US)

• Median funded ratio for US state pension plans: roughly 75 to 80% as of the most recent Pew Charitable Trusts state pension data (estimate, figures move each fiscal year).
• Plans below 60% are generally considered fiscally stressed; plans above 90% are considered well funded.
• Aggregate US state and local unfunded pension liabilities are commonly estimated in the $1.2 to $1.6 trillion range depending on the discount rate used (estimate; sensitive to assumptions, see below).
• OPEB is typically far less funded than pensions. Many US state and local governments fund OPEB on a pay-as-you-go basis, meaning funded ratios near 0 to 10% are common, because retiree healthcare was historically treated as a current expense, not a pre-funded benefit.

The discount rate: the assumption that changes everything

The AAL is a present value, so it is extremely sensitive to the discount rate (the assumed rate of returnrate of returnReturn on Investment: the ratio of net profit to the cost of an investment. A 300% ROI means each dollar invested returns $3.Voir la définition complète → used to convert future benefit payments into today's dollars).

US public pensions typically use the plan's expected long-term investment return as the discount rate, often around 6.5 to 7.5% (estimate, varies by plan, per governing standards from the Governmental Accounting Standards Board, GASB, specifically GASB Statement 67/68).

Lower the discount rate and the AAL rises sharply, because future dollars are worth more in present-value terms. This is a known critique: some economists argue public plans should use a lower, risk-free-like rate (closer to 3 to 4%), which would show funded ratios far worse than officially reported. There is no single "correct" answer, but as an analyst you should always ask: what discount rate produced this AAL?

Europe: a different structure, same math

Most European public pensions run on a Pay-As-You-Go (PAYGO) basis: current workers' contributions pay current retirees, with no large invested fund and therefore often no "funded ratio" in the US sense. Instead, analysts watch:

• Dependency ratio: retirees per active worker, rising across the EU as populations age (Eurostat projects it climbing significantly by 2050, see Eurostat's Ageing Europe report).
• Implicit pension debt: the present value of future PAYGO promises, estimated by some EU studies at multiples of GDP for certain member states (estimate, methodology varies widely, unlike a funded balance sheet item).
• Statutory retirement age and replacement rate (pension as a percentage of final salary), which governments adjust as levers instead of pre-funding.

For OPEB-equivalent retiree healthcare, most European countries fold this into universal health systems funded through general taxation or social insurance contributions, so it rarely appears as a discrete unfunded liability the way US OPEB does under GASB 74/75 (the accounting standards requiring US governments to report OPEB liabilities on their balance sheets since 2017).

Practical implication: you cannot directly compare a US city's 62% pension funded ratio to a French municipality's pension footnote. The US number reflects a pre-funded trust; the French system is largely a taxation-based promise. Compare structures, not just ratios.

Reading the footnote like an analyst

When you open a Comprehensive Annual Financial Report (US, often now called an Annual Comprehensive Financial Report, ACFR) or a European public entity's annual accounts, check five things:

1. Funded ratio trend: one year below 70% is a data point; five years declining is a trend.

2. Discount rate changes: a rate cut from 7.5% to 7.0% can spike the reported UAAL even with no change in benefits.

3. Amortization period: longer periods (25 to 30 years) push costs onto future taxpayers; shorter periods (15 to 20 years) are more conservative.

4. Assumed investment return versus actual 10-year return: if the plan assumes 7% but has earned 5% over the last decade, expect funded ratios to keep eroding.

5. OPEB trend rate: for retiree healthcare, actuaries assume a healthcare cost growth rate (often starting around 6 to 7% and declining over decades). Small changes here swing the liability significantly, since healthcare cost inflation compounds for decades.

A second worked example: OPEB

A US county reports an OPEB AAL of $80 million and OPEB plan assets of $4 million (it pays retiree healthcare mostly pay-as-you-go).

Funded ratio = 4 / 80 = 5%
UAAL = 80 - 4 = $76 million

This is common and not automatically a crisis, since many governments intentionally do not pre-fund OPEB. But it means the $76 million is a claim on future budgets with no cushion. If retiree healthcare costs grow faster than the county's revenue base, this becomes a structural deficit driver.

🎬 [VIDEO: "Public Pension Funding 101" - youtube.com - search for Pew Charitable Trusts or Reason Foundation explainer videos on state pension funded ratios and amortization, useful for a visual walkthrough of the same mechanics covered here]