Pension Valuation: PUC and TUC

A defined-benefit pension promises a future benefit based on a formula tied to salary and service. Valuing the promise today requires three things: the formula, a set of demographic and economic assumptions, and a cost method that allocates the promised benefit across the years the participant works.

Projected Unit Credit allocates a share of the projected final benefit to each year of service the participant earns. The share earned to date times the present value of the projected final benefit gives the accrued liability under PUC; that liability is the Projected Benefit Obligation (PBO) under US GAAP terminology.

Traditional Unit Credit uses the current accrued benefit (no salary projection beyond today). Its accrued liability is the Accumulated Benefit Obligation (ABO). PBO and ABO are usually different unless the plan is a flat-dollar benefit or the participant is already at the maximum salary.

The accrued benefit at valuation date t is the benefit earned to date under the plan formula, evaluated with current salary (TUC) or projected final salary (PUC).

For a typical 1.5 percent of final pay per year of service plan, a 40-year-old participant with 10 years of service and current salary 80000 has an accrued benefit (TUC) of 0.015 × 10 × 80000 = 12000 per year at retirement. Under PUC with a 3 percent salary scale and retirement at 65, projected final pay is 80000 × 1.03^25 ≈ 167479, and the PUC accrued benefit is 0.015 × 10 × 167479 = 25122 per year.

The factor that converts the annual benefit at retirement to a present value at today's age is the annuity at retirement (which depends on retirement-age mortality and the discount rate) times the actuarial present value of the survival probability and discount factor from today to retirement.

PUC values the present value of the projected final benefit and allocates it to service years on a proportional or fractional basis. The accrued liability at age x for a participant who will retire at age R is the projected annual benefit times a deferred annuity factor evaluated at age R, discounted to age x, and multiplied by the fraction of service earned to date.

Normal cost under PUC is the present value of the benefit accrued in the coming year. With the proportional allocation, this is one year's accrual times the present value of the projected final benefit per service year. The total liability is normal cost summed over years plus interest accrual on the prior liability.

PUC is the cost method required by IAS 19 and ASC 715 (FAS 87 successor), and the standard funding method under the US Pension Protection Act for most single-employer plans. The choice is not stylistic; it is the regulatory default.

TUC values only the benefit accrued to date with current salary. There is no projection of future pay. The accrued liability is the current annual accrued benefit times a deferred annuity factor at the assumed retirement age, discounted to today.

Normal cost under TUC is the present value of the increase in the accrued benefit during the coming year. Because TUC uses current salary, normal cost rises sharply as salary grows; PUC absorbs that growth in the projection and gives a smoother cost pattern.

TUC has limited US use under current accounting and funding rules but appears in some plan-termination scenarios, ABO disclosures under ASC 715, and certain Canadian solvency-valuation contexts where the legal standard is the accrued-to-date benefit without salary projection.

Demographic assumptions include mortality before and after retirement (separate tables are common, e.g. Pri-2012 with projected improvement under MP-2021), withdrawal (termination prior to retirement), disability, and retirement-age distribution.

Economic assumptions include the discount rate (typically a high-quality corporate-bond yield curve under IAS 19 and ASC 715), the salary scale (used in PUC, not TUC), the expected long-term return on assets (used for pension expense under US GAAP), and inflation (used to project indexed benefits and post-retirement increases).

Sensitivity is sharp. A 100-basis-point fall in the discount rate raises PBO by roughly the duration of the liability (commonly 10 to 20 years for active populations), which can move funded status by tens of percent.

US GAAP: ASC 715 (formerly FAS 87, FAS 88, FAS 106, FAS 132, FAS 158). Requires PUC for the service-cost calculation. The discount rate is set as a high-quality corporate-bond yield matching the cash-flow duration. Funded status (PBO minus fair value of assets) is recognized on the balance sheet under FAS 158 amendments.

International: IAS 19 (revised 2011). Also requires PUC. Defines the Defined Benefit Obligation (DBO) using projected benefits, equivalent to PBO. Eliminated corridor smoothing in 2011 in favor of immediate recognition of remeasurements in other comprehensive income.

Funding (US): the Pension Protection Act of 2006 sets the funding target as the PUC accrued liability using a segmented yield curve. Funding is therefore PUC-based, but the funding discount rate need not equal the accounting discount rate.

Participant: age 40 today, 10 years of service, current salary 80000, retires at age 65. Plan formula: 1.5 percent of final salary per year of service, life annuity from age 65. Assumptions: salary scale 3 percent, discount rate 5 percent, post-retirement annuity factor a_65 = 13.0 (combined mortality and discount).

Project final salary: S_65 = 80000 × 1.03^25 ≈ 167479. Projected total annual benefit at retirement, assuming 35 years of total service: 0.015 × 35 × 167479 = 87925.

Accrued benefit under PUC at age 40 (using fraction of service to date) = 10/35 × 87925 = 25122 per year at age 65. PV at age 40 = 25122 × 13.0 × (1 / 1.05^25) × p_{40→65}. Ignoring pre-retirement mortality and using 1.05^25 ≈ 3.386, the discount factor is 0.2953. PV ≈ 25122 × 13.0 × 0.2953 = 96433.

Normal cost at age 40 = 0.015 × 167479 × 13.0 × 0.2953 = 9643, which is the proportional one-year share of the projected benefit, discounted to today.

Under TUC, no salary projection. Accrued benefit at age 40 = 0.015 × 10 × 80000 = 12000 per year at age 65.

PV at age 40 = 12000 × 13.0 × 0.2953 = 46067. The TUC accrued liability is less than half the PUC accrued liability for this active participant, which is the typical pattern. The gap closes as the participant approaches retirement and salary growth becomes a smaller fraction of total final pay.

Normal cost at age 40 under TUC = increase in the accrued liability over the coming year, evaluated with salary moving from 80000 to 82400 (3 percent raise) and service moving from 10 to 11. The arithmetic gives roughly 6000 in this case, lower than PUC normal cost because there is no projection adjustment.

The total cost picture differs: TUC understates the cost early in a career and overstates it late, when salary growth slows but accrued benefits compound. PUC spreads cost more evenly.

Use PUC for ongoing-plan valuations under US GAAP, IFRS, and US funding rules. There is no choice in those contexts.

Use TUC (or its ABO disclosure equivalent) for plan-termination tests, solvency-valuation cash-out tests in Canada, and for situations where the legal claim is the accrued benefit with no salary projection.

Show both in client presentations when the audience is unfamiliar with pension accounting. The difference between PBO and ABO is the natural way to explain why the plan's reported deficit changes when salary assumptions move, and is the canonical exhibit on RET-201 and the equivalent CFE-101 module.

PBO is not the cash needed to settle the plan today. PBO is the present value of projected future benefits, valued at a high-quality corporate-bond rate. Settlement cost is typically higher because annuity purchase requires a market-consistent insurance premium, not an accounting discount rate.

ABO is not always lower than PBO. For a flat-dollar plan or a plan where the participant is at the salary cap, ABO equals PBO. The PUC-versus-TUC gap is driven by future salary growth.

PUC normal cost is not the cash contribution. Cash contribution is set by funding rules and the plan's actuarial cost method for funding, which may differ from PUC. Pension expense under accounting standards uses PUC; cash funding uses the funding-method liability.

The discount rate is not the expected return on assets. Under ASC 715 and IAS 19 the discount rate is a high-quality corporate-bond yield. Expected return on assets enters US-GAAP pension expense but not the liability calculation.

Pre-retirement mortality is not always negligible. For older actives, withdrawal and pre-retirement mortality assumptions can move PUC liabilities by several percent, which matters on exam problems that include them explicitly.

Pension valuation appears across ALTAM (in the long-term contingencies register), the entire RET track on the FSA pathway, and the corporate-finance and ERM courses where pension expense and risk feed enterprise-level discussions.

Dickson, Hardy, and Waters 2020: Actuarial Mathematics for Life Contingent Risks, 3rd edition, Cambridge. Chapter 11 covers pension benefits, PUC liability and normal cost, and decrement-based projection. The canonical SOA reference for ALTAM pension material.

Aitchison and Brown 1957 (historical), now superseded by ASOP 4 (Measuring Pension Obligations) and ASOP 27 (Selection of Economic Assumptions for Measuring Pension Obligations), Actuarial Standards Board. These standards govern US pension actuarial practice and are listed reading on RET-201.

Klugman, Panjer, and Willmot 2019: Loss Models: From Data to Decisions, 5th edition, Wiley. Limited direct pension coverage but provides the underlying actuarial-mathematics machinery used in pension valuation.

IAS 19 (revised 2011) and ASC 715: the accounting standards themselves are the primary reference for benefit-obligation definitions; both are publicly available from the IASB and FASB respectively.