📖 养老金会计：PBO、计划资产

Financial Statement Analysis

I. Lesson Focus

This lesson explains the accounting for defined benefit pension plans with emphasis on the measurement of Projected Benefit Obligation (PBO), fair value of plan assets, net pension liability/asset on the balance sheet, and the components of pension expense on the income statement. Candidates must master the roll-forward calculations, the difference between service cost and interest cost, the treatment of actuarial gains/losses under the corridor approach, and the impact on financial ratios.

II. The Problem

A company promises fixed pension payments to retirees, yet the cash required may exceed or fall short of assets set aside. How should the firm report the present value of its obligation (PBO) and the resources already accumulated (plan assets) on the balance sheet? How much pension cost should be recognized in the current period’s income statement? Incorrect measurement of PBO or plan assets can materially distort liabilities, equity, and profitability. This topic appears frequently in Financial Statement Analysis vignettes on the CFA Level I exam.

III. Defined Benefit versus Defined Contribution Plans

Pension plans fall into two categories: - Defined Contribution (DC) Plans: The employer contributes a fixed amount (e.g., 10% of salary) each year. Risk rests with the employee. Accounting is simple: expense equals the contribution; no PBO is calculated. - Defined Benefit (DB) Plans: The employer promises a specified benefit (e.g., 70% of final salary). The employer bears the investment and longevity risk. The firm must measure the present value of future obligations (PBO) and the fair value of plan assets.

DB plans are the focus of this lesson. The balance sheet reports net pension liability (or asset) = PBO − fair value of plan assets.

IV. Components and Roll-Forward of Projected Benefit Obligation (PBO)

PBO is the actuarial present value of all future pension payments attributed to employee service to date, calculated using the projected unit credit method. The discount rate is the yield on high-quality corporate bonds (AA or higher).

Five main factors that change PBO: 1. Service Cost: Present value of additional benefits earned by employees during the current period; the largest operating component of pension expense. 2. Interest Cost: Beginning PBO × discount rate; reflects the passage of time. 3. Prior Service Cost: Increase in PBO from plan amendments (e.g., improved benefits) granted for past service; recognized immediately in OCI and amortized to expense over future periods. 4. Actuarial Gains and Losses: Changes in PBO due to revisions in actuarial assumptions (mortality, turnover, salary growth) or experience differences; recorded in OCI. 5. Benefits Paid: Actual cash payments to retirees, which reduce PBO.

Ending PBO formula: $$ \text{Ending PBO} = \text{Beginning PBO} + \text{Service Cost} + \text{Interest Cost} + \text{Prior Service Cost} + \text{Actuarial Loss} - \text{Actuarial Gain} - \text{Benefits Paid} $$

V. Roll-Forward of Plan Assets

Plan assets are the fair value of investments held in the pension trust.

Main factors changing plan assets: 1. Actual Return on Plan Assets: Interest, dividends, and capital gains earned during the period. 2. Company Contributions: Cash deposited by the employer. 3. Benefits Paid: Payments to retirees (same reduction as in PBO).

Ending plan assets formula: $$ \text{Ending Plan Assets} = \text{Beginning Plan Assets} + \text{Actual Return} + \text{Contributions} - \text{Benefits Paid} $$

Note: Expected return is used in pension expense; the difference between actual and expected return is an actuarial gain/loss recorded in OCI.

VI. Net Periodic Pension Cost (Pension Expense)

Pension expense reported on the income statement typically comprises: - Service Cost - Interest Cost - Expected Return on Plan Assets (reduction) - Amortization of Prior Service Cost - Amortization of Net Actuarial Gains/Losses (corridor approach under US GAAP)

Common simplified formula: $$ \text{Pension Expense} = \text{Service Cost} + \text{Interest Cost} - \text{Expected Return on Assets} + \text{Amortizations} $$

Under IFRS the presentation of service cost and net interest may differ slightly, but CFA Level I candidates should master the US GAAP corridor method (10% threshold).

VII. Balance-Sheet Presentation: Net Pension Liability/Asset

$$ \text{Net Pension Liability} = \text{PBO} - \text{Plan Assets} $$ - Positive balance → non-current liability. - Negative balance → non-current asset (subject to impairment testing).

Worked Cases

Case 1: Basic Roll-Forward

Beginning balances (in millions): PBO = 8.0, Plan assets = 6.5.
Current year: Service cost = 0.9, discount rate = 8%, expected return = 7%, actual return = 0.55, contributions = 1.2, benefits paid = 0.45. No prior service cost or actuarial gains/losses.

Calculations: - Interest cost = 8.0 × 8% = 0.64 - Expected return = 6.5 × 7% = 0.455 - Ending PBO = 8.0 + 0.9 + 0.64 − 0.45 = 9.09 - Ending plan assets = 6.5 + 0.55 + 1.2 − 0.45 = 7.80 - Net pension liability = 9.09 − 7.80 = 1.29 - Pension expense = 0.9 + 0.64 − 0.455 = 1.085

Case 2: Corridor Amortization

At the start of the next year, accumulated unrecognized net actuarial loss = 1.20. New service cost = 0.95, interest cost = 0.73, expected return = 0.55, new actuarial loss = 0.35, average remaining service life = 12 years.

Corridor calculation: - Greater of 10% of beginning PBO or plan assets = 9.09 × 10% = 0.909 - Excess = 1.20 − 0.909 = 0.291 - Amortization = 0.291 / 12 ≈ 0.0243

Pension expense = 0.95 + 0.73 − 0.55 + 0.0243 ≈ 1.1543

Case 3: Prior Service Cost

The company amends the plan, creating prior service cost of 0.60 (recorded immediately in OCI). This increases PBO by 0.60 but does not affect current service cost. The amount will be amortized from OCI to pension expense over future service years. The OCI balance (AOCI) rises initially and is gradually reclassified to retained earnings.

Traps

Key Formulas

• Net pension liability (asset) = PBO − Fair value of plan assets
• Ending PBO = Beg PBO + Service cost + Interest cost ± Actuarial (gain)/loss + Prior service cost − Benefits paid
• Ending plan assets = Beg assets + Actual return + Contributions − Benefits paid
• Pension expense = Service cost + Interest cost − Expected return + Amort. of prior service cost + Amort. of net loss (corridor)
• Actual return − Expected return = Asset gain/loss (OCI)
• Corridor = 10% of the greater of beginning PBO or beginning plan assets

Practice Questions

Q1. The most appropriate discount rate for measuring PBO is the:
A. Expected return on plan assets
B. Company’s borrowing rate
C. Yield on high-quality corporate bonds
D. Government bond yield

Q2. Which item directly increases current-period pension expense?
A. Actual return on plan assets exceeding expected return
B. An increase in service cost
C. Cash contribution to the plan
D. Actuarial gain

Q3. Beginning PBO is 500, service cost 60, interest cost 40, benefits paid 30, ending PBO 610. The actuarial loss for the period is:
A. 30
B. 40
C. 50
D. 60

Q4. Under the corridor approach:
A. All actuarial gains and losses are recognized immediately in profit or loss
B. Only the amount exceeding 10% of the greater of PBO or plan assets is amortized
C. Actuarial items stay permanently in OCI
D. They adjust plan assets directly

Q5. When fair value of plan assets exceeds PBO, the balance sheet reports:
A. Net pension liability
B. Net pension asset
C. Both a liability and an asset
D. Nothing

Q6. Prior service cost is:
A. Expensed immediately in the income statement
B. Recognized in OCI and amortized to expense over future periods
C. Deducted immediately from plan assets
D. Ignored in the PBO calculation

Q7. The employer’s cash contribution to the pension plan:
A. Directly increases pension expense
B. Has no direct effect on pension expense
C. Reduces interest cost
D. Increases service cost

Q8. Which of the following does not increase PBO?
A. Service cost
B. Interest cost
C. Actual return on plan assets
D. Increase in prior service cost

Answers

Takeaways

• Funded status equals PBO minus fair value of plan assets and is reported directly on the balance sheet.
• Service cost and interest cost drive pension expense; expected return on assets is a reduction.
• Actuarial gains/losses and prior service cost flow through OCI and are amortized into expense under the corridor approach.
• The difference between actual and expected return is recorded entirely in OCI.
• Master the roll-forward schedules for both PBO and plan assets; they are the foundation of every pension calculation.
• Distinguishing the effects on the income statement versus the balance sheet is a frequent exam differentiator.