Valuing Defined‑Benefit Pension Plan Losses in Present‑Value Calculations

Introduction

Defined-benefit (DB) pension plans promise retirees specified monthly benefits based on salary history and years of service. Unlike defined-contribution plans (401(k)s), DB pensions shift investment and longevity risk from employees to employers. When employment terminates prematurely due to wrongful discharge, disability, or death, valuing lost pension benefits involves actuarial calculations. The present value depends on benefit formulas, vesting schedules, early retirement provisions, cost-of-living adjustments (COLAs), mortality probabilities, and appropriate discount rates. This article provides a comprehensive framework for valuing DB pension losses in forensic economic contexts, incorporating Pension Benefit Guaranty Corporation (PBGC) data, ERISA regulations, and actuarial practices.

1. Understanding Defined-Benefit Pension Plans

1.1 Basic Structure and Formulas

Most DB plans use a formula combining three elements:

Where:

• $B$ = Annual benefit at normal retirement age
• $k$ = Benefit multiplier (typically 1.0% to 2.5%)
• $YOS$ = Years of service
• $FAS$ = Final average salary (often highest 3-5 years)

1.2 Key Plan Provisions

1. Normal Retirement Age (NRA): Typically 65, sometimes 62
2. Early Retirement: Often available at 55 with actuarial reduction
3. Vesting: ERISA requires 100% vesting within 5-7 years
4. COLAs: Some plans provide inflation adjustments
5. Survivor Benefits: Joint & survivor options reduce benefits
6. Integration with Social Security: Some plans offset SS benefits

2. Actuarial Present Value Methodology

2.1 Basic Present Value Formula

The actuarial present value (APV) of future pension benefits:

Where:

• $B_t$ = Benefit payment at age $t$
• ${}_tp_x$ = Probability of surviving from current age $x$ to age $t$
• $v^t$ = Discount factor $(1+i)^{-t}$
• $r$ = Retirement age
• $\omega$ = Maximum age (typically 120)

2.2 Incorporating Multiple Decrements

Comprehensive valuation considers multiple exit probabilities:

Where decrements include:

• $q_t^{(d)}$ = Probability of death at age $t$
• $q_t^{(w)}$ = Probability of withdrawal/termination
• $q_t^{(i)}$ = Probability of disability
• ${}_tp_x^{(\tau)}$ = Probability of surviving all decrements

3. Data Sources for Pension Valuation

3.1 Pension Benefit Guaranty Corporation (PBGC)

PBGC provides valuation guidance:

• Interest rates: Monthly updates for immediate and deferred annuities
• Mortality tables: Prescribed tables for plan terminations
• Maximum guaranteed benefits: 2025 limit is $6,750/month at age 65

PBGC Rate Type	July 2025 Rate	Application
Immediate annuities	2.72%	Benefits starting within 7 years
Deferred annuities (7-15 years)	3.39%	Mid-term benefit commencement
Deferred annuities (15+ years)	3.98%	Long-term benefit commencement

3.2 IRS/Treasury Regulations

• 417(e) rates: Minimum lump-sum calculations
• 430 funding rates: 3-segment yield curve
• Mortality tables: Current standard is Pri-2012 with MP-2021 projection

3.3 Actuarial Standards

• Society of Actuaries: RP-2014/Pri-2012 mortality studies
• Actuarial Standards Board: ASOP No. 27 (economic assumptions)
• American Academy of Actuaries: Practice notes on pension valuation

4. Step-by-Step Valuation Process

4.1 Step 1: Determine Accrued Benefit

Calculate benefit earned through termination date:

1. Identify benefit formula from plan document
2. Determine years of service (actual vs. projected)
3. Calculate final average salary
4. Apply formula to get annual benefit

4.2 Step 2: Apply Early Retirement Factors

If claiming before NRA, reduce benefits actuarially:

Where:

• $ERF$ = Early retirement factor
• $p$ = Penalty per year (often 5-7%)
• $NRA$ = Normal retirement age
• $ERA$ = Early retirement age

4.3 Step 3: Select Mortality Assumptions

Mortality Table	Application	Key Features
Pri-2012 with MP-2021	Private sector pensions	Latest IRS prescribed, generational projection
PubG-2010	Public sector pensions	Separate tables by job category
Social Security 2025	General population	Period life table, conservative
Annuity 2000	Individual annuities	Selection effects, lowest mortality

4.4 Step 4: Choose Discount Rate

Three primary approaches:

1. PBGC rates: Regulatory standard for plan terminations
2. Corporate bond rates: High-quality (AA) corporate yields
3. Treasury rates: Risk-free rate for guaranteed benefits

4.5 Step 5: Calculate Present Value

Apply the comprehensive formula:

Where:

• $B$ = Annual benefit at NRA
• $ERF$ = Early retirement factor (if applicable)
• $\ddot{a}_{x:n}$ = Life annuity factor at retirement age
• $v^{r-x}$ = Discount from current age to retirement

5. Case Study: Wrongful Termination at Age 50

5.1 Facts

• Current age: 50
• Years of service at termination: 20
• Final average salary: $90,000
• Benefit formula: 1.75% × YOS × FAS
• Normal retirement age: 65
• Early retirement: Available at 55 with 6% annual reduction
• COLA: None

5.2 Calculations

1. Accrued benefit at NRA:
   $$B_{65} = 0.0175 \times 20 \times 90,000 = \$31,500$$
2. Early retirement benefit at 55:
   $$B_{55} = 31,500 \times [1 - 0.06 \times (65-55)] = 31,500 \times 0.40 = \$12,600$$
3. But-for benefit (30 years service):
   $$B_{65}^{BF} = 0.0175 \times 30 \times 100,000 = \$52,500$$
4. Lost benefit:
   $$\Delta B = 52,500 - 31,500 = \$21,000 \text{ annually}$$
5. Present value of loss:
   • Life annuity factor at 65 (Pri-2012): 13.45
   • Discount factor (15 years @ 3.98%): 0.5580
   • PV = $21,000 × 13.45 × 0.5580 = $157,500

6. Special Considerations

6.1 Cash Balance Plans

Hybrid plans with different valuation approach:

• Account balances grow with pay and interest credits
• Convert to annuity at retirement using plan factors
• Often provide lump-sum options

6.2 COLAs and Post-Retirement Increases

Plans with COLAs require adjusted annuity factors:

Where $g$ = COLA rate (often capped at 2-3%)

6.3 Coordination with Other Benefits

1. Social Security integration: Some plans reduce benefits by SS offset
2. Disability benefits: May receive unreduced benefits if disabled
3. Survivor options: J&S elections reduce participant benefits
4. Return of contributions: Some plans refund employee contributions

6.4 Tax Considerations

• Pension benefits typically taxable as ordinary income
• Apply marginal tax rates to get after-tax value
• Consider state tax treatment (some states exempt pensions)

7. Common Valuation Challenges

7.1 Missing Plan Information

• Request Summary Plan Description (SPD)
• Obtain benefit statements from plan administrator
• Check Form 5500 filings for plan details
• Use PBGC premium filings for participant counts

7.2 Plan Amendments and Freezes

Many DB plans have been frozen:

• Hard freeze: No new accruals for any participant
• Soft freeze: Closed to new entrants only
• Partial freeze: Benefits capped at certain date/amount

7.3 Multiemployer Plans

Union-sponsored plans with unique features:

• Benefits based on contribution rates and hours
• Portability between employers
• Different PBGC guarantee limits
• Potential benefit reductions if underfunded

8. Best Practices for Expert Reports

8.1 Documentation Standards

1. Cite specific plan provisions and page numbers
2. Show all calculation steps with formulas
3. Identify mortality table and projection scale
4. Justify discount rate selection
5. Provide sensitivity analysis for key assumptions

8.2 Sensitivity Analysis

Variable	Base Case	Low	High	Impact on PV
Discount rate	3.98%	3.48%	4.48%	±12%
Mortality	Pri-2012	+10% rates	-10% rates	±5%
Retirement age	65	62	67	±8%

8.3 Alternative Scenarios

Consider multiple loss scenarios:

1. Total loss: No mitigation, full career loss
2. Partial mitigation: Replacement job with lesser pension
3. Delayed entry: Re-employment after gap period
4. Alternative retirement dates: Early vs. normal retirement

Conclusion

Valuing defined-benefit pension losses involves integrating actuarial science, regulatory requirements, and economic principles. The value of pension benefits can be substantial—often exceeding $500,000 in present value terms. Following PBGC guidelines for interest rates and mortality assumptions, documenting plan provisions, and conducting sensitivity analyses, forensic economists can provide courts with valuations based on established methodologies. As DB plans continue their decline in the private sector, expertise in valuing these benefits remains important in employment litigation.

References

• Actuarial Standards Board. (2013). Actuarial Standard of Practice No. 27: Selection of economic assumptions for measuring pension obligations. Retrieved from http://www.actuarialstandardsboard.org/asops/selection-of-economic-assumptions-for-measuring-pension-obligations/
• Anderson, A. W. (2006). Pension mathematics for actuaries (3rd ed.). ACTEX Publications.
• Employee Retirement Income Security Act of 1974 (ERISA), 29 U.S.C. § 1001 et seq. (1974).
• Internal Revenue Service. (2025). Section 430 pension funding rules—Segment rates for July 2025. Retrieved July 25, 2025, from https://www.irs.gov/retirement-plans/minimum-present-value-segment-rates
• McGill, D. M., Brown, K. N., Haley, J. J., Schieber, S. J., & Warshawsky, M. J. (2010). Fundamentals of private pensions (9th ed.). Oxford University Press.
• Pension Benefit Guaranty Corporation. (2025). Interest rates and factors for July 2025. Retrieved July 25, 2025, from https://www.pbgc.gov/prac/interest/vls
• Pension Benefit Guaranty Corporation. (2025). Maximum monthly guarantee tables. Retrieved July 25, 2025, from https://www.pbgc.gov/wr/benefits/guaranteed-benefits/maximum-guarantee
• Society of Actuaries. (2019). Pri-2012 private retirement plans mortality tables report. Retrieved from https://www.soa.org/resources/experience-studies/2019/pri-2012-private-retirement-plans-mortality-tables/
• Turner, J. A., & Witte, H. D. (2009). Pension policy: An international perspective. W.E. Upjohn Institute for Employment Research.
• Winklevoss, H. E. (1993). Pension mathematics with numerical illustrations (2nd ed.). University of Pennsylvania Press.