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Worked-example setupScope and assumptions
- Cedar Trail, the plan, the actuarial measures, the trustee records, and all dates and amounts are fictional and supplied for instruction.
- The plan is a single-employer defined benefit pension plan; the employer and the benefit trust remain distinct reporting entities.
- The signed actuarial report supports opening PBO, service cost, interest cost, prior-service cost, actuarial loss, benefits, and ending PBO.
- Trustee evidence supports opening and ending fair value, the employer contribution, benefits, and the stated actual return; there are no participant contributions, fees, acquisitions, or settlement transfers.
- The calculation recomputes supplied measurements and does not value participant benefits, select assumptions, assess legal funding, or determine plan or sponsor solvency.
- Period
- Year ended December 31, 20X6
- Units
- US dollars and one annual measurement period
- Rounding
- Retain full precision; display dollars with commas and no decimals
Problem
Cedar Trail's draft says pension expense is $1.20 million because that is the cash contribution. It reports the $20 million PBO as the employer liability, places $16.15 million of trust assets among corporate investments, and records the $1.10 million paid to retirees as current compensation. Rebuild the close without letting four different ledgers collapse into one number.
Establish the route before calculating
The plan is a single-employer defined benefit pension plan. The employer accounts for its obligation, plan assets, periodic cost, OCI/AOCI, cash contribution, and funded status under the supplied Topic 715 facts. The benefit trust is a distinct reporting entity; its assets are restricted for benefits, not available as Cedar Trail operating cash.
VBO, ABO, and PBO answer different measurement questions. This example uses PBO because the funded-status measure is built from the actuarial present value of pension benefits attributed to service to date with projected compensation where the formula requires it. No arithmetic in this file converts one obligation measure into another.
Roll the PBO forward
| PBO movement | Effect | Running PBO |
|---|---|---|
| Opening supported PBO | — | $18,000,000 |
| Current service cost | +$1,200,000 | 19,200,000 |
| Interest cost | +900,000 | 20,100,000 |
| July amendment: prior-service cost | +600,000 | 20,700,000 |
| Actuarial loss | +400,000 | 21,100,000 |
| Benefits paid by the plan | −1,100,000 | $20,000,000 |
Service and interest are movements in the obligation, not cash contributions. Benefits reduce the obligation because the plan has discharged those benefits. The amendment and actuarial loss enter the PBO here even though their income statement recognition follows a different rail.
Roll plan assets forward independently
| Plan-asset movement | Effect | Running fair value |
|---|---|---|
| Opening fair value | — | $15,000,000 |
| Actual return | +$1,050,000 | 16,050,000 |
| Employer contribution | +1,200,000 | 17,250,000 |
| Benefits paid by the plan | −1,100,000 | $16,150,000 |
The trustee's reported increase of $1.15 million is not actual return. Solve for return only after controlling cash flows:
$16,150,000 ending assets
− 15,000,000 opening assets
− 1,200,000 employer contribution
+ 1,100,000 benefits paid
= $1,050,000 actual return
Expected return is $900,000. It belongs in periodic cost. The $150,000 excess of actual over expected return belongs in the gain-and-loss/OCI bridge. A market-related value used under the supplied accounting policy would not replace ending fair value in funded status.
Join only at funded status
Ending fair value of plan assets $16,150,000
Less: ending PBO (20,000,000)
Ending underfunded status $(3,850,000)
Opening funded status was $15 million minus $18 million, or $(3.00) million. The underfunded position therefore deepened by $850,000, producing an $850,000 increase in the recognized net pension liability under the supplied facts. The $3.85 million liability is neither the gross PBO nor PBO plus AOCI.
Reconcile the seven-ledger join
Net periodic pension cost is $1.40 million, current pretax OCI is a $650,000 loss, and the cash contribution is $1.20 million. Together they explain the liability change without a plug:
Pension cost recognized $1,400,000
+ current OCI loss 650,000
− employer cash contribution 1,200,000
= increase in pension liability $850,000
Benefits do not appear in that employer entry because the same $1.10 million reduces both PBO and plan assets. Their net funded-status effect is zero.
Interpret without overclaiming
A lower discount-rate scenario produces a supplied $21.20 million obligation; a higher-rate scenario produces $19.00 million. Relative to the $20.00 million base, those are conditional changes of +$1.20 million and −$1.00 million. They are not probability bounds, forecasts, or independently calculated actuarial values. Likewise, underfunded accounting status does not by itself establish legal funding noncompliance, illiquidity, benefit insecurity, or sponsor insolvency.
Quantitative companions
Choose from 2 ways to work with this calculation.
Verified calculation · pension accounting analysis
The curriculum loader recomputed this example before it entered the site build. Expand any structured input to inspect the stated facts.
- actual return
- 1,050,000
- assets acquired
- 0
- benefit type
- pension
- benefits paid
- 1,100,000
- corridor amortization period
- 10
- corridor greater opening base
- 18,000,000
- corridor opening net loss
- 2,600,000
- corridor rate
- 0.1
- employer contributions
- 1,200,000
- expected return
- 900,000
- interest cost
- 900,000
- net loss amortization
- 80,000
- obligation actuarial gain
- 0
- obligation actuarial loss
- 400,000
- obligation sensitivity
- 2 fields
Inspect data
{
"higher_discount_rate": 19000000,
"lower_discount_rate": 21200000
}- obligations assumed
- 0
- obligations settled
- 0
- opening aoci loss
- 2,000,000
- opening obligation
- 18,000,000
- opening plan assets
- 15,000,000
- participant contributions
- 0
- plan expenses paid
- 0
- prior service amortization
- 120,000
- prior service cost
- 600,000
- reported current oci loss
- 650,000
- reported ending aoci loss
- 2,650,000
- reported ending funded status
- -3,850,000
- reported ending obligation
- 20,000,000
- reported ending plan assets
- 16,150,000
- reported net periodic benefit cost
- 1,400,000
- service cost
- 1,200,000
- settlement assets transferred
- 0
- special event cost
- 0
- transition amortization
- 0
Recomputed result
| Measure | Value |
|---|---|
| actual minus expected return | 150,000 |
| corridor amortization | 80,000 |
| corridor excess | 800,000 |
| corridor threshold | 1,800,000 |
| current oci loss | 650,000 |
| ending aoci loss | 2,650,000 |
| ending funded status | -3,850,000 |
| ending obligation | 20,000,000 |
| ending plan assets | 16,150,000 |
| entry balance difference | 0 |
| funded status change | -850,000 |
| net periodic benefit cost | 1,400,000 |
| opening funded status | -3,000,000 |
| other net periodic benefit cost components | 200,000 |
| recognized liability increase | 850,000 |
| sensitivity higher discount rate change | -1,000,000 |
| sensitivity higher discount rate obligation | 19,000,000 |
| sensitivity lower discount rate change | 1,200,000 |
| sensitivity lower discount rate obligation | 21,200,000 |
| service cost presentation component | 1,200,000 |