Employee Compensation: Post-Employment and Share-Based: formula sheet

Key formulas

Funded status

Funded status = Fair value of plan assets − Present value of defined benefit obligation (PBO)

Negative = net pension liability (underfunded). Positive = net pension asset (overfunded), limited by the asset ceiling under IFRS. Applies to DB plans only.

DC plan expense

Pension expense = Employer contribution for the period

No obligation or asset beyond unpaid or prepaid contributions. Employee carries the risk.

Typical DB benefit formula

Annual pension = Years of service × Accrual rate × Final (or average) salary

Exact formula depends on the plan terms given in the vignette. Use the numbers supplied.

Funded status

Funded status = Fair value of plan assets − PBO

Negative = net pension liability. Positive = net pension asset (subject to the asset ceiling under IFRS).

PBO roll forward

Ending PBO = Beginning PBO + Current service cost + Interest cost + Past service cost + Actuarial losses (− gains) − Benefits paid

Interest cost = Beginning PBO × discount rate. Include past service cost only if the plan was amended in the period.

Plan assets roll forward

Ending plan assets = Beginning plan assets + Actual return + Employer contributions − Benefits paid

Actual return is the return actually earned on the plan assets (in the exhibit, or expected return plus the difference between actual and expected return). Employee contributions, if any, are also added.

Net interest under IFRS

Net interest = Discount rate × (Beginning PBO − Beginning plan assets)

IFRS applies the discount rate to the net pension liability (asset); the P&L includes this net interest, and the difference between actual return and the amount of interest on assets goes to OCI as a remeasurement.

Balance sheet amount

Net pension liability (asset) = PBO − Plan assets

Same number as funded status, with the sign reversed. Check the sign before answering.

ABO vs PBO

ABO ≤ PBO when future pay increases are expected

US GAAP only. ABO uses current pay. PBO uses projected pay.

US GAAP total periodic pension cost

Cost = Current service cost + Interest cost − Expected return on plan assets + Amortization of prior service cost + Amortization of actuarial losses (or − gains)

Interest cost = discount rate × beginning PBO. Amortization terms are the smoothing items analysts often remove.

IFRS net interest

Net interest expense (income) = Discount rate × Net defined benefit liability (asset)

Recognized in profit or loss with service cost. Remeasurements go to OCI and are not reclassified to profit.

Analyst adjusted pension cost (US GAAP)

Adjusted total cost = Service cost + Interest cost − Actual return on plan assets

Replaces expected return with actual return and drops amortization. The adjusted total includes interest and actual return, but only service cost is classed as operating. Interest cost and actual return are shown as non-operating items. Use only when the question asks for actual-return treatment.

Adjusted pre-tax income

Adjusted income = Reported income + Reported pension cost − Adjusted pension cost

If adjusted cost is lower than reported, income rises. Check the sign each time.

Adjusted operating cash flow

Adjusted CFO = Reported CFO + (Employer contribution − Service cost) × (1 − tax rate)

The after-tax excess of contributions over service cost is reclassified from CFO to CFF, so adjusted CFF falls by the same amount. Applies when contributions exceed service cost; total cash flow is unchanged.

Direction of assumption effects

Higher discount rate → lower PBO and service cost; higher compensation growth → higher PBO and service cost; higher expected return (US GAAP) → lower expense

Interest cost is the awkward item: a higher rate applies to a smaller PBO, so the net effect is not clear-cut. State it only if the vignette gives numbers.

Total expense (equity-settled)

Total expense = Grant-date fair value per award × Number of awards expected to vest

Fair value is fixed at grant. If forfeiture estimates change, revise the number expected to vest and apply the change as a cumulative catch-up.

Annual expense, straight-line

Annual expense = Total expense ÷ Vesting period (years)

Applies to cliff vesting. Expense is recognized over the service period. For graded vesting, IFRS treats each tranche as a separate award, each expensed over its own vesting period. Revised forfeiture estimates are applied as a cumulative catch-up in the period of change.

Restricted stock fair value

Fair value per share = Market price at grant date

Only for shares with service conditions. No option model needed.

Option intrinsic value

Intrinsic value = max(Share price − Exercise price, 0)

Fair value of an option is at least this, plus time value.

Cash-settled award liability

Liability at date t = Fair value at t × Awards expected to vest × (Service rendered ÷ Total vesting period)

This formula applies to cliff-vesting awards. Remeasured each period. Expense = change in liability plus any cash paid.

Effect of assumptions on option value

Higher volatility, longer term, lower dividend yield → higher option value

Higher value means higher expense.

Annual compensation expense (straight-line)

Expense per year = Fair value per option × Options expected to vest ÷ Vesting period (years)

Options expected to vest = options granted × (1 − expected forfeiture rate). Fair value is fixed at grant for equity-settled awards.

Cumulative catch-up on forfeiture revision

Period expense = Revised cumulative expense to date − Expense already recognized

Revised cumulative expense = fair value × revised options expected to vest × (years elapsed ÷ vesting period).

Treasury stock method (options)

Incremental shares = Options × (1 − Exercise price ÷ Average market price)

Applies only when options are in the money (average price above exercise price). Otherwise they are antidilutive and ignored.

Direction of inputs on call option fair value

↑ Volatility, ↑ Expected term, ↑ Risk-free rate, ↑ Share price → ↑ value; ↑ Dividend yield, ↑ Exercise price → ↓ value

Use this to judge whether an assumption change raises or lowers reported expense.

Diluted EPS with options

Diluted EPS = Net income ÷ (Basic shares + Incremental shares from options)

No preferred dividends or convertible adjustments in simple cases.

Quick revision

• Defined contribution: employer cost equals the contribution; the employee bears investment risk.
• Defined benefit: employer bears investment and longevity risk; obligation is estimated.
• Funded status = fair value of plan assets − present value of defined benefit obligation.
• A net pension liability appears when the plan is underfunded; a net asset when overfunded, subject to rules on asset limits.
• Under IFRS, service cost and net interest go to profit or loss; remeasurements go to other comprehensive income and are not later recycled to profit or loss.
• Under US GAAP, periodic pension cost in profit or loss comprises service cost, interest cost on the obligation, expected return on plan assets (which reduces cost), amortisation of prior service cost from accumulated other comprehensive income, and amortisation of any net actuarial gain or loss in accumulated other comprehensive income that exceeds the corridor. The corridor is 10% of the greater of the projected benefit obligation and the fair value of plan assets. The expected return is used in the cost, not the actual return.
• A lower discount rate raises the present value of the obligation and raises current service cost. Interest cost = opening obligation × discount rate. The opening obligation is fixed at the start of the period, so a lower rate reduces that period's interest cost. The higher obligation then raises the base for later periods, so the net effect on interest cost over time can vary.
• Higher assumed compensation growth raises the obligation.
• Higher expected return on plan assets under US GAAP lowers reported pension cost but does not change the cash paid.
• Share-based pay is expensed at grant-date fair value over the vesting period.
• Higher volatility, longer term and higher stock price raise call option value; a higher exercise price lowers it.
• Options are a real cost to shareholders even though no cash leaves the company at grant.

Common mistakes

• Saying the employer bears investment risk in a DC plan. Fix: Ask who gets the shortfall. In DC the employee's account balance falls; the employer owes nothing more.
• Recording a pension liability for a DC plan. Fix: For DC, recognise only the contribution as expense. A liability appears only for an unpaid contribution.
• Using the ABO instead of the PBO to compute funded status. Fix: For the balance sheet, use the PBO (IFRS: the defined benefit obligation). Use the ABO only when the question asks for it.
• Using the expected return on plan assets rather than the actual return in the asset roll forward. Fix: The asset balance reflects what really happened. Use the actual return, which is the return actually earned on the plan assets (in the exhibit, or expected return plus the difference between actual and expected return). The expected return is a P&L assumption under US GAAP.
• Saying a higher expected return on assets improves funded status or cash flow. Fix: Expected return is an estimate used only in the expense calculation under US GAAP. Funded status uses actual plan asset fair value.
• Applying the expected-return effect to an IFRS company. Fix: Under IFRS the asset return in profit is the discount rate × plan assets (inside net interest). Check the framework before reasoning.
• Using the current share price to update option expense each year for equity-settled options. Fix: Equity-settled fair value is fixed at grant. Only cash-settled awards are remeasured.
• Expensing the full value in the grant year. Fix: Spread the cost over the vesting period, since it pays for service during that period.
• Remeasuring equity-settled options at each reporting date. Fix: For equity-settled awards, fair value is locked at grant date. Only the forfeiture estimate changes expense later.
• Saying higher volatility lowers the expense. Fix: An option holder gains from upside and is protected on the downside, so volatility raises value and expense.

Exam tips

• Identify what is fixed before reading the options. It settles most classification questions quickly.
• In DB numeric questions, extract plan assets and PBO from the exhibit, ignoring other figures such as contributions or benefits paid unless asked.
• Questions often disguise a DC plan as employer-friendly. Look for phrases like 'employee selects investments' or 'account balance'.
• When an assumption changes, reason about direction first: lower discount rate raises PBO, higher salary growth raises PBO.
• Remember IFRS and US GAAP differ in DB cost recognition, so check which framework the vignette uses before answering cost questions.
• Read the exhibit labels carefully. Items such as service cost, interest cost and actuarial loss are often given separately, and the question may add distractors such as ABO or expected return.
• The vignette may give only the discount rate. Compute interest cost yourself as beginning PBO × discount rate.
• When asked for the change in funded status, you can skip benefits paid since it hits both sides equally.