Employee Benefits: Defined-Benefit Obligations and Share-Based Payment in Depth

Phase 1 · Accounting: The Language of Business · Week 15 · ~16 focused hours · Mastery gate ≥ 85%

Nandan Forgings owes its workers ₹47,80,00,000. Nobody has invoiced it, no employee has asked for it, and the amount appears in no contract. It is the discounted present value of a promise, and it moves by ₹4,12,51,400 if one number in the actuary's report moves by one percentage point.

Nothing has gone wrong in the accounting here. It was built to work this way.

Two Indian companies with the same workforce, the same wage bill and the same gratuity formula can report obligations 8.63% apart because their actuaries picked points a percentage point apart on the government bond curve. An American manufacturer reports $5,513,166.67 of pension expense where a filer under the international rulebook, holding the same plan and the same assets through the same year, reports $5,106,000. Both are correct. The balance sheets are identical to the cent, and the total charged against comprehensive income is identical too, at $5,890,000 in each. Only the income statement disagrees, and it disagrees by $407,166.67 for reasons that have nothing to do with what either company did for its employees.

Pinnacle Diagnostics granted two batches of performance shares on the same morning to the same executives. Both batches missed their targets and neither vested. One cost the shareholders nothing at all, and the other cost them $11,520,000 that missing the target couldn't take back.

Employee benefits produce more of these gaps than any other area of accounting, and they produce them in the two places an analyst looks first: operating profit and net debt. A pension deficit is a claim that ranks ahead of equity, funded by the same cash that pays dividends, and it's kept below the borrowings line, where nobody adds it up. Share-based compensation is a real transfer of ownership that leaves the cash flow statement untouched and reappears in the tax line as a benefit whose size depends on the share price.

The mechanics aren't hard. A pension promise is a bond the employer wrote, and you already know how to roll a bond forward. An option grant is a cost measured once and spread, and you already know how to spread a cost. What makes this area expensive is that four separate things get called "pension expense", and three of them are wrong. The number a filing prints also suits the framework it files under, and that's often a different number from the one that describes the year.

By the end you can rebuild both roll-forwards from a published note, produce the expense under either rulebook, compute the economic cost that neither rulebook prints, and say in figures how much of a company's reported operating profit is an artefact of how it accounts for the people who work there.

Learning objectives

By the end you can:

1. Explain why a defined-benefit promise is economically a bond issued to employees, and identify the discount rate as the single assumption that decides most of its reported size.
2. Build a defined-benefit obligation roll-forward from opening balance, service cost, interest cost, benefits paid, past service cost and actuarial remeasurement, and derive whichever component the disclosure leaves out.
3. Build a plan-asset roll-forward, separate the actual return into the part that reaches profit and the part that does not, and apply the asset ceiling to a plan in surplus.
4. Compute the defined-benefit expense under IFRS and Ind AS 19, split it correctly between operating profit and finance cost, and route remeasurements to other comprehensive income where they stay.
5. Compute net periodic pension cost under ASC 715 including the expected return, prior-service-cost amortisation and corridor amortisation, place each component correctly, and quantify the reported-earnings gap against the international answer by two independent routes.
6. Compute total periodic pension cost by two independent routes and rank it against reported expense and employer contributions.
7. Make the four analyst adjustments a benefit note calls for, and read the note that supports them: the assumption table, the sensitivity disclosure, the asset allocation and the expected contributions.
8. Account for the Indian statutory benefits that make every Indian annual report carry a defined-benefit note: gratuity, the guaranteed exempt provident-fund trust and leave encashment.
9. Distinguish service, non-market performance and market conditions in a share-based award, predict which of them can reverse a recognised expense, and compute a graded-vesting award under both attributions with the forfeiture true-up.
10. Trace a share-based award through the dilution arithmetic, the cash flow statement and the tax line, and dismantle an adjusted-earnings measure that removes share-based compensation while keeping the share count fixed.

Prerequisites & connections

Builds on. M1.02 gave you other comprehensive income and the split between profit and total comprehensive income, which is the whole architecture of pension reporting under both rulebooks. M1.03 gave you the equity block, including the reserve where remeasurements come to rest and never leave. M1.08 gave you the effective-interest method, which is what an obligation roll-forward is, and the deferred-tax machinery that the share-based-payment tax work below assumes. M1.09 gave you equity-settled share-based payment at grant-date fair value, the treasury-stock method and the argument against reading share-based compensation as a non-cash item. Everything here starts where that stops. M1.11 gave you cash-settled awards, remeasured liabilities and the identity that a cash-settled award's lifetime charge equals the cash eventually paid.

Feeds forward. M1.10 is the capstone filing read, where the benefit note has to be found in a real document and priced. M2.01 and M2.02 supply the ratio panel that a pension deficit and a share-based charge both distort, and M2.03's return on invested capital needs the deficit inside the capital base. M2.06 to M2.08 hunt the abuses, including the expected-return assumption that flatters an American income statement and the adjusted-earnings measure that removes share-based compensation without touching the share count. M3.02 and M3.04 need the deficit in enterprise value before any multiple means anything. M1.13 takes the multinational and financial-institution completions, and a foreign subsidiary's pension plan is translated like everything else it owns. AA1.05 looks at the same plan from the other side, as an institutional investor with an asset allocation and a liability to match.

Four neighbouring modules own material that isn't rebuilt here. M1.03 owns the equity components and the reserve architecture. M1.08 owns effective interest, discounting and deferred tax, all of which are used below without re-derivation. M1.09 owns the equity-settled basics: what an option and a restricted stock unit are, how grant-date fair value is measured, the triple entry across the three statements, and the treasury-stock method itself. The work below extends that into condition types, attribution, forfeiture true-ups and tax. M1.11 owns cash-settled share-based payment in full, including the stock appreciation right remeasured against its equity-settled twin and the settlement identity that closes it. Where those modules own a concept, cite and move on.

Core teaching content

4.5 The expense under IFRS and Ind AS 19

Three components, and the split between them is the entire point of the 2011 revision to the standard.

Service cost is current service cost plus any past service cost plus any gain or loss on settlement. It goes to profit, and it belongs in operating profit because it's compensation. Nandan Forgings charges ₹4,35,00,000.

Net interest is the discount rate applied to the net defined-benefit liability at the start of the year: 7.20% of ₹10,50,00,000, or ₹75,60,000. It goes to profit as a financing item. The construction is neat, because that same ₹75,60,000 is also the interest cost of ₹3,02,40,000 less the interest income of ₹2,26,80,000. Deficit funding costs the company the discount rate on the shortfall, and the standard says so in one line.

Remeasurements go to other comprehensive income and are never recycled to profit. For Nandan Forgings that's the ₹1,22,60,000 actuarial loss on the obligation less the ₹44,20,000 asset gain, a net charge of ₹78,40,000. A company may transfer accumulated remeasurements within equity, from one reserve to retained earnings, but no future income statement will ever see them.

The total charge to profit is ₹5,10,60,000, of which the net interest is 14.8061%. The reconciliation that proves the whole thing:

opening net liability      10,50,00,000
+ profit-and-loss charge    5,10,60,000
+ remeasurement to OCI         78,40,000
- employer contributions    5,00,00,000
= closing net liability    11,39,00,000

Run that reconciliation on any published note. If it doesn't close, you have missed a component, and the component people miss is past service cost, because some filers disclose a plan amendment in prose and leave it out of the movement table.

One practical warning about presentation. Ind AS 19 requires the split between service cost and net interest, but it doesn't tell a company which line of the income statement to use, and Schedule III doesn't settle it either. Plenty of Indian filers put the whole ₹5,10,60,000 into employee benefits expense, which pushes ₹75,60,000 of financing cost above the operating line and understates operating profit and EBITDA by that amount. Read the benefit note, find the net interest, and move it yourself.

4.8 Total periodic pension cost, the economic number

Neither income statement prints the year's economic cost, so compute it.

Total periodic pension cost is what the plan actually cost the sponsor in the period, and there are two routes to it. The first works off the balance sheet: employer contributions plus the increase in the deficit. Allegheny contributed $5,000,000 and its deficit grew from $10,500,000 to $11,390,000, so the cost was $5,890,000. The second works off the components: current service cost plus interest cost less the actual return on plan assets plus actuarial losses, which is $4,350,000 plus $3,024,000 less $2,710,000 plus $1,226,000, and gives $5,890,000 again.

Two routes to the same figure, and the agreement is the check.

Rank the four candidate numbers and the pattern is stark:

Every published figure understates what the year cost, and the ranking isn't stable. A year with strong asset returns will invert it, and a year with a discount-rate rise will invert it further, because a rise cuts the obligation and produces an actuarial gain that never touches profit. Compute total periodic pension cost for at least three years before drawing any conclusion from one.

4.9 Contributions, cash flow and the reclassification

Employer contributions are an operating outflow under both rulebooks. That treatment is defensible for the part of the contribution that funds the year's service, and indefensible for the rest.

Split the contribution in two. The portion equal to current service cost is compensation for work done this year and belongs in operating cash flow beside wages. The excess is a repayment of a debt-like obligation built up in earlier years, and it belongs where debt repayments belong, in financing.

Allegheny contributed $5,000,000 against a service cost of $4,350,000, so $650,000 is deficit reduction. Reclassifying it lifts operating cash flow to $59,050,000 and free cash flow from $37,400,000 to $38,050,000, an uplift of 1.7380%. On this plan the adjustment is small. On a company whose deficit is a meaningful fraction of its market capitalisation, it's anything but. Companies in that position have been known to advertise depressed operating cash flow as evidence of conservatism. In fact it's evidence of a legacy liability being paid down.

The mirror case is more dangerous. A company that contributes less than its service cost is letting the deficit grow while reporting operating cash flow that looks better than the business generated. At Allegheny's rate of $650,000 of net funding a year, the $11,390,000 deficit takes 17.5231 years to clear. That number's worth computing, because it turns an abstract deficit into a claim on future cash with a horizon attached.

Read the expected-contributions disclosure alongside. Both rulebooks require the sponsor to state what it expects to contribute next year, and a jump in that figure is often the first public sign that a discount-rate fall or an asset shortfall has changed the funding arithmetic.

4.10 The four analyst adjustments

Four moves, in the order they change a conclusion.

The first is to treat the deficit as debt. It ranks ahead of shareholders, it must be funded in cash, and it isn't in the borrowings line. Add it to net debt and to enterprise value. Whether to add it gross or net of tax depends on whether contributions attract a deduction, which in both India and the United States they generally do, so the after-tax figure is the better default. State which you used. Nandan Forgings' ₹11,39,00,000 deficit is 9.2602% of its ₹1,23,00,00,000 of net debt, and becomes ₹8,52,33,648 after tax at 25.168%. That Indian rate is the concessional corporate rate with surcharge and cess, and the American examples below use 21%. Both statutory rates move with each year's finance legislation. Verify the rate in force for the company and the year you are reading, and prefer the filer's own disclosed effective rate where its deferred tax position makes that the better proxy; checked September 2026.

The second is to move the financing components out of operating profit. Where a filer has buried net interest in employee benefits expense, take it out. For Nandan Forgings that lifts EBITDA from ₹68,00,00,000 to ₹68,75,60,000. Combine both adjustments and net debt to EBITDA goes from 1.808824 times to 1.912900 times, which is 0.104077 turns, or 5.7538%. A covenant set at two turns has just moved appreciably closer without the business changing at all.

The third is the excess-contribution reclassification covered above, where the direction matters more than the size. It moves cash out of operating and into financing when the company is repairing a deficit, and it flatters nobody.

The fourth is to stress the assumptions. The disclosure gives you the obligation's sensitivity to the discount rate and to salary growth. Use it in both directions, because the sensitivity isn't symmetric. A 100 basis point fall raises Nandan Forgings' obligation 8.63% and a 100 basis point rise cuts it 7.61%, which is a duration of 8.12 years and a convexity of 102.0 on the same definitions the fixed-income work uses.

An obligation is a bond, so it has a bond's convexity. Reading the two disclosed percentages as if they were one number in opposite directions throws that away.

A fifth move, less often needed, is to check whether the discount rate is defensible at all. Both rulebooks require an observable market rate, so a filer whose rate is well outside the government or high-grade corporate curve for its country and duration is making a choice, and the choice is disclosed. Compare the rate against a peer with a similar plan duration in the same jurisdiction and the same year.

4.16 Adjusted earnings before share-based compensation

A company that adds back share-based compensation to reach an adjusted profit measure is asserting that paying people in shares is free. Don't argue with it. Test it with arithmetic.

Granite Peak charged $7,300,000 of expense, reported net income of $159,588,000 and offers an adjusted net income of $166,888,000, giving adjusted earnings per share of $1.668880 on 100,000,000 shares. Build a corrected figure alongside. Keep the expense, because it's compensation. Normalise the tax rate to 21%, which removes the $17,388,000 windfall and gives net income of $142,200,000. Use the diluted share count of 100,925,000. The result is $1.408967 a share, and the adjusted figure is 18.4471% above it. That's a big gap for a number the company chose to put in front of you.

Two of the three adjustments matter more than the third. Removing the tax windfall is worth 12.2278% of net income before it. Adding the expense back is worth 3.8975% of pre-tax profit before it. The share count contributes least here, and would contribute far more at a company whose overhang runs at eight or ten percent of shares outstanding instead of two.

There are two internally consistent treatments and neither of them is the company's. Either treat the compensation as a cash cost, subtract it from free cash flow, and value on the current diluted share count. Or leave free cash flow alone and grow the share count for expected future issuance while valuing the existing awards separately. Adding the expense back while holding the share count fixed values the company as though the employees work for nothing, and the arithmetic above says what that's worth in cents a share.

The operating cash flow line deserves the same treatment. Granite Peak reported $214,000,000, which includes the $7,300,000 expense add-back and the $17,388,000 tax windfall. Strip both and the figure is $189,312,000, which is 11.5364% lower. Neither item is a lie and neither is cash the business generated by selling anything.

4.17 Where a tool helps here, and where it must not

The work splits along a clean line. Rebuilding a roll-forward from a note is transcription and arithmetic, and a machine does it faster and, with the right checks, more accurately than a tired human at eleven at night. Deciding whether an 8.50% expected return is defensible against a portfolio that's three-quarters investment-grade debt is judgement, and no model has an opinion worth having about it.

The failure mode in this area is specific. Benefit notes are dense tables spread across several pages, and a document model reading them transposes rows, mixes the gratuity table with the leave-encashment table, and returns a beautifully formatted roll-forward that reconciles to nothing. The reconciliation is the whole defence, because an obligation roll-forward that closes is almost certainly right and one that doesn't close is certainly wrong.

Four checks, and they take five minutes.

1. Does the obligation roll-forward close to the disclosed closing obligation, and does the plan-asset roll-forward close to the disclosed closing assets?
2. Does opening net liability plus profit-and-loss charge plus other comprehensive income charge less contributions equal closing net liability?
3. Does the interest cost equal the disclosed discount rate times the opening obligation, to within the partial-period convention you named?
4. Do the components you extracted come from the same plan, the same table and the same reporting date, where the disclosure covers three or four separate plans?

{
  "skill": "Rebuilding both benefit roll-forwards from a published note and computing total periodic pension cost",
  "use": "Have an assistant extract the obligation and plan-asset movement tables from a filing's employee-benefit note into structured rows, then write the code that recomputes interest cost, net interest, the expense split and total periodic pension cost by two independent routes, with assertions that fire when a roll-forward does not close.",
  "tools": ["Chat assistants with code execution - Claude, ChatGPT, Gemini", "Python: pandas for the tables, plain arithmetic for the roll-forwards", "A PDF or document reader grounded on the filing you already hold", "A spreadsheet for the side-by-side reconciliation"],
  "prompt": "From this employee-benefit note, extract into two tables: (1) the defined benefit obligation movement - opening, current service cost, past service cost, interest cost, benefits paid, actuarial remeasurement split by source, closing; (2) the plan asset movement - opening, return on assets, employer contributions, benefits paid, closing. Then write Python that recomputes interest cost as the disclosed discount rate times the opening obligation, derives the remeasurement as a residual, computes the expense split between operating and finance under IAS 19, computes total periodic pension cost by both the balance-sheet route and the component route, and asserts that (a) each roll-forward closes to the disclosed closing balance to within one currency unit and (b) the two routes to total periodic pension cost agree to within 1e-6. State every assumption you made about the timing of contributions and benefits within the year. List every figure in the note that you could NOT reconcile.",
  "verify": "Do not accept the extracted tables. Trace every row back to the note by page and line yourself, because document models transpose rows in dense financial tables and a swapped contributions and benefits-paid pair is invisible downstream and reverses the sign of the asset remeasurement. Check that all rows come from the SAME plan: an Indian note commonly carries gratuity, leave encashment and a provident-fund interest guarantee in adjacent tables with identical headings. Recompute interest cost by hand from the disclosed discount rate and opening obligation. Match the reporting dates, the currency unit (crore, lakh, million) and the funded-versus-unfunded status on both sides before comparing anything. Confirm the reconciliation assertion actually fires by feeding it a deliberately wrong closing balance. Cite the filing, the note number and the page for every input. A roll-forward that does not close is not a rounding problem; it means a component is missing, and the component usually missing is past service cost.",
  "diy": "You must be able to build both roll-forwards, split the expense and compute total periodic pension cost by both routes on paper for a five-line plan; the worked examples are the drill and the gate tests exactly that. A tool cannot tell you that an 8.50% expected return sits above what the disclosed asset allocation can plausibly earn, that a salary assumption was cut in the same year as the discount rate, or that a leave-encashment remeasurement belongs in profit while the identical gratuity remeasurement does not. Those readings are yours.",
  "market": "IN"
}

A machine helps most with the sensitivity work. Recomputing an obligation across a grid of discount rates and salary assumptions, and reading the duration and convexity out of the result, is arithmetic no one should do by hand more than once. Do it by hand once, on the two-point sensitivity the note already gives you, so you know what the grid means.

Common mistakes & how experts think differently

1. Reading "pension expense" as one number. Four different quantities travel under that name: the income-statement charge under the international rulebook, net periodic pension cost under the American one, the employer's cash contribution, and total periodic pension cost. On Allegheny Tool Works' single year they are $5,106,000, $5,513,166.67, $5,000,000 and $5,890,000. An expert asks which of the four a source means before using it, and computes the fourth one because no filing prints it.

1. Accreting interest on the closing obligation. The obligation is a bond and the interest accrues on what was owed at the start of the year. Using the closing figure overstates interest cost by the discount rate applied to a year of service and remeasurement, which at Nandan Forgings would be ₹41,76,000 too much on a ₹3,02,40,000 charge. The check is one multiplication against the disclosed rate, and it's the first thing an expert runs on any rebuilt roll-forward.

1. Believing the expected return on plan assets. It's management's assumption, it isn't constrained by any market rate, and every percentage point of it is a percentage point of plan assets added to pre-tax profit with no cash consequence. Allegheny's 8.50% against a 7.20% discount rate is worth $409,500 a year, which is 7.4277% of its whole pension charge. An expert reads the assumption against the disclosed asset allocation and treats a high return on a bond-heavy portfolio as a finding, and doesn't wave it through as a detail.

1. Adding the disclosed sensitivities together. They are computed one assumption at a time. Stressing Nandan Forgings' discount rate down 100 basis points and its salary growth up 100 basis points together gives ₹56,04,79,961.16, where adding the two disclosed percentages gives ₹55,72,04,600. The ₹32,75,361.16 difference is compounding, and it grows with the size of the stress. An expert multiplies the factors instead of adding the percentages, and says which they did.

1. Treating a plan surplus as an asset. Under the international rulebook a surplus is capped at the economic benefit actually available, and the excess is written off through other comprehensive income. A ₹5,00,00,000 surplus with a ₹1,80,00,000 contribution holiday available carries ₹1,80,00,000 on the balance sheet, and 64.00% of it never appears. An expert looks for the asset-ceiling line in the reconciliation before adding a surplus to anything.

1. Leaving the deficit out of enterprise value because it isn't in the borrowings note. It ranks ahead of equity and it's funded with the same cash. Nandan Forgings' deficit is 9.2602% of its net debt and adds 0.104077 turns to net debt over EBITDA once the presentation is also corrected. An expert adds it after tax, states the rate used, and checks whether a covenant is measured on the reported or the adjusted figure. The expert then converts it into a horizon, because Allegheny's net funding rate of $650,000 a year against an $11,390,000 deficit implies 17.5231 years to clear it, and a horizon is something a forecast can carry where an abstract liability isn't.

1. Reading a leave-encashment remeasurement as though it were a gratuity remeasurement. Compensated absences are other long-term employee benefits, so their remeasurements go to profit and not to other comprehensive income. The two liabilities appear in adjacent tables in the same note, valued by the same actuary on the same day, and only one of them can move reported earnings. An expert checks which table a movement came from before deciding where it lands.

1. Assuming a missed target means a reversed expense. It depends entirely on the condition type. A missed earnings target reverses everything. A missed total-shareholder-return hurdle reverses nothing, because the possibility of missing was priced into the grant-date fair value. Pinnacle Diagnostics' two awards both delivered zero shares and cost $0 and $11,520,000. An expert reads the condition type in the note before forecasting a single year of the expense line.

1. Comparing share-based expense across rulebooks without checking the attribution. Identical graded awards produce ₹3,40,50,000 under the Indian rulebook and ₹1,76,25,000 under the American election in year one, and the ordering reverses by year four. The gap is 0.8831 percentage points of Vellore Analytics' revenue in the first year. An expert asks whether an apparent margin difference between two employers is a grant difference or an attribution difference, and answers it from the vesting schedule.

1. Taking a share-based-payment company's reported earnings at face value. Two things flatter them at once. Granite Peak's effective tax rate is 11.3400% against a 21.00% statutory rate, and every point of the difference is a share-price-driven windfall that reverses when the price falls. The same facts under the international rulebook produce no rate effect at all, because the excess goes to equity. Then the company adds the expense back, reaching an adjusted $1.668880 a share against a corrected $1.408967, a gap of 18.4471%. An expert normalises the rate before forecasting, and either treats the compensation as a cash cost with the current diluted count or leaves cash flow alone and grows the count, never both and never neither.

Worked examples

Every figure below was produced by a Python computation run before it was written down. All entities are synthetic, and all rates, assumptions and fair values are illustrative but internally consistent. Contributions and benefits are assumed to fall at the year end unless stated otherwise, which keeps interest arithmetic clean and understates interest slightly against an actuary's mid-year convention. Each example is verified by a route independent of the one that produced it.

Worked example 1: An Indian gratuity plan, both roll-forwards (India, ₹)

Nandan Forgings Ltd (synthetic) forges automotive components in Pune and funds its statutory gratuity plan through an insurer-managed trust. At the start of the financial year the defined-benefit obligation is ₹42,00,00,000 and the fair value of plan assets is ₹31,50,00,000. The actuary's discount rate is 7.20%, current service cost for the year is ₹4,35,00,000, benefits of ₹2,80,00,000 are paid, the company contributes ₹5,00,00,000, the trust's actual return is ₹2,71,00,000, and the actuary's closing obligation is ₹47,80,00,000. Build both roll-forwards, split the Ind AS 19 expense, and adjust the leverage panel. Reported EBITDA is ₹68,00,00,000, borrowings are ₹1,45,00,00,000 and cash is ₹22,00,00,000.

Solution. Step 1, the obligation. Interest cost is 7.20% of the opening obligation, or 42,00,00,000 × 0.0720 = ₹3,02,40,000.

Step 2, the plan assets. Interest income is credited at the same 7.20%, giving 31,50,00,000 × 0.0720 = ₹2,26,80,000. The actual return of ₹2,71,00,000 exceeds that by ₹44,20,000, which is a remeasurement gain and never enters profit.

Step 3, funded status. The deficit moves from ₹10,50,00,000 to 47,80,00,000 − 36,41,00,000 = ₹11,39,00,000. That single figure is what the balance sheet carries, and it would be identical under either rulebook.

Step 4, the Ind AS 19 expense. Service cost of ₹4,35,00,000 to operating profit. Net interest of 7.20% × 10,50,00,000 = ₹75,60,000 to finance cost, which is 14.8061% of the total charge of ₹5,10,60,000. Remeasurement of 1,22,60,000 − 44,20,000 = ₹78,40,000 of net loss to other comprehensive income, where it stays.

Step 5, verify by a second route. Net interest computed the other way is interest cost less interest income, 3,02,40,000 − 2,26,80,000 = ₹75,60,000, which agrees. The full reconciliation closes to the rupee: 10,50,00,000 + 5,10,60,000 + 78,40,000 − 5,00,00,000 = ₹11,39,00,000.

Step 6, the leverage adjustment. Net debt is 1,45,00,00,000 − 22,00,00,000 = ₹1,23,00,00,000, so reported net debt over EBITDA is 1,23,00,00,000 ÷ 68,00,00,000 = 1.808824 times. Nandan Forgings presents the whole ₹5,10,60,000 inside employee benefits expense, so restoring the ₹75,60,000 of net interest to finance cost lifts EBITDA to ₹68,75,60,000. Adding the deficit after tax at 25.168%, which is 11,39,00,000 × 0.74832 = ₹8,52,33,648, gives adjusted net debt of ₹1,31,52,33,648 and a ratio of 1.912900 times. Taken gross the ratio would be 1.976324 times.

Read it. The adjustment adds 0.104077 turns, which is 5.7538%, and it comes from a liability that appears nowhere in the borrowings note. The deficit is 9.2602% of net debt, so for a company this size the effect is real but survivable. The same arithmetic on an old-economy employer whose deficit runs to half its net debt moves a credit rating instead of a decimal place. None of this tells you whether ₹47,80,00,000 is the right obligation. That depends on a discount rate, and the next example prices what the rate is worth.

Worked example 2: What the discount rate is worth (India, ₹)

Nandan Forgings' benefit note discloses the standard sensitivities: a 100 basis point fall in the discount rate raises the obligation by 8.63%, a 100 basis point rise cuts it by 7.61%, and a 100 basis point rise in salary escalation raises it by 7.94%. Price each stress, extract the duration and convexity, and work out what happens to next year's expense.

Solution. Step 1, the obligation at each rate. Starting from ₹47,80,00,000:

Step 2, the deficit moves further than the obligation. A 100 basis point fall raises the obligation 8.63% and raises the deficit by ₹4,12,51,400, which is 36.2172% of it. Plan assets don't move with the discount rate, so the whole obligation change falls on the net figure. A plan that's 76% funded turns an 8.63% liability move into a 36.22% equity-relevant move, and a plan that's 95% funded would turn it into something much larger still.

Step 3, duration and convexity. Treat the obligation as a bond and use the effective definitions:

effective duration  = (V- - V+) / (2 x V0 x dy)
                    = (51,92,51,400 - 44,16,24,200) / (2 x 47,80,00,000 x 0.01)
                    = 7,76,27,200 / 95,60,000 = 8.120000 years

effective convexity = (V+ + V- - 2 x V0) / (V0 x dy^2)
                    = 48,75,600 / 47,800 = 102.0000

Step 4, verify the duration against the disclosure. A first-order estimate of the 100 basis point fall is 47,80,00,000 × 0.01 × 8.12 = ₹3,88,13,600. Adding the convexity term, 0.5 × 102.0 × 47,80,00,000 × 0.0001 = ₹24,37,800, gives ₹4,12,51,400, which reproduces the disclosed move to the rupee. The asymmetry between 8.63% and 7.61% isn't sloppiness in the actuary's report. It's convexity, and it's the reason the two percentages differ.

Step 5, next year's expense, which moves the other way. Interest cost is the discount rate times the opening obligation, so a lower rate applied to a larger obligation can cut it:

Gross interest cost falls ₹22,22,413.20 when the rate drops, because the rate fell proportionally more than the obligation rose. Net interest goes the other way and rises ₹14,18,586.80, because the deficit it's applied to grew 36.2172%. Two figures from the same shock moving in opposite directions, and a reader who tracks only one of them draws the wrong conclusion.

Step 6, the two stresses together. Salary escalation up 100 basis points gives 47,80,00,000 × 1.0794 = ₹51,59,53,200. Applying both stresses multiplicatively gives 47,80,00,000 × 1.0863 × 1.0794 = ₹56,04,79,961.16, a deficit of ₹19,63,79,961.16 and 17.2552% above the base obligation. Adding the two disclosed percentages instead gives ₹55,72,04,600, which understates the joint effect by ₹32,75,361.16.

Read it. An 8.12-year duration means this plan behaves like a medium-dated bond, and the analyst who reads a benefit note without computing it is carrying unmeasured rate exposure inside an equity position. It tells you nothing about the plan's assets, though. If the trust holds long bonds, the assets move with the obligation and the deficit is stable. If it holds equities, the two legs move independently and the deficit is the volatile residual. The asset-allocation disclosure settles that, and the duration alone doesn't.

Worked example 3: The same plan under ASC 715 (US, $)

Allegheny Tool Works Inc. (synthetic) runs the same plan in an American filing, each of Nandan Forgings' rupee figures read across as a dollar figure and not converted at any rate: opening obligation $42,000,000, plan assets $31,500,000, service cost $4,350,000, discount rate 7.20%, benefits paid $2,800,000, contributions $5,000,000, actual return $2,710,000, closing obligation $47,800,000. Add the American ingredients: an expected long-term return of 8.50%, unrecognised prior service cost of $4,800,000, an accumulated net actuarial loss in other comprehensive income of $9,200,000, and an average remaining service period of 12 years. Compute net periodic pension cost, place each component, and quantify the earnings gap against the international answer.

Solution. Step 1, the corridor. Ten percent of the greater of the obligation and the plan assets is 10% × $42,000,000 = $4,200,000. The accumulated net loss of $9,200,000 exceeds it by $5,000,000, and that excess amortises over twelve years at $416,666.67 a year.

Step 2, the five components.

Of that total, $4,350,000 is in operating profit and $1,163,166.67 is below it.

Step 3, the balance sheet, which doesn't differ. Plan assets close at 31,500,000 + 2,710,000 + 5,000,000 − 2,800,000 = $36,410,000, and the funded status is 47,800,000 − 36,410,000 = $11,390,000 of net liability. That's the Ind AS figure to the cent.

Step 4, the earnings gap. The international expense is service cost plus net interest, or 4,350,000 + (10,500,000 × 0.0720) = 4,350,000 + 756,000 = $5,106,000. The American figure is $5,513,166.67, so the gap is $407,166.67, which is 7.9743% higher.

Step 5, prove the gap a second way. Two components create it and they pull opposite ways. The expected-return assumption relieves the American income statement of (0.0850 − 0.0720) × 31,500,000 = $409,500. The two amortisations add 400,000 + 416,666.67 = $816,666.67. The net is 816,666.67 − 409,500 = $407,166.67, which agrees with step 4 to seven decimal places. At a 21% rate the after-tax gap is $321,661.67.

Step 6, the other comprehensive income leg, and the identity that closes it. The actuarial loss on the obligation is $1,226,000 under both frameworks. The asset remeasurement differs, because the American version measures against the expected return and the international version against interest income at the discount rate:

Read it. Both rulebooks charge shareholders $5,890,000 and disagree only about which statement carries it and when. The American filer reports $407,166.67 less comprehensive income above the line and $407,166.67 more below it, and an analyst comparing reported operating results across the two is comparing presentation. That identity doesn't make the two equivalent for valuation, though. Earnings-based multiples read profit and ignore other comprehensive income, so the framework choice changes the price a market puts on identical economics. That's why the adjustment is worth making.

Allegheny carries $9,976,833.33 of net loss and $4,400,000 of prior service cost forward in accumulated other comprehensive income, both of which will drip into future profit. The international filer carries its remeasurements in a reserve that will never touch profit again.

Worked example 4: The number neither statement prints (US, $)

Using Allegheny Tool Works' year from Worked Example 3, compute total periodic pension cost by two routes, rank it against the published measures, and adjust the cash flow statement. Reported operating cash flow is $58,400,000 and capital expenditure is $21,000,000.

Solution. Step 1, the balance-sheet route. Total periodic pension cost is what the sponsor gave up: employer contributions plus the increase in the deficit. That's 5,000,000 + (11,390,000 − 10,500,000) = $5,890,000.

Step 2, the component route. Current service cost plus interest cost less the actual return on plan assets plus the actuarial loss: 4,350,000 + 3,024,000 − 2,710,000 + 1,226,000 = $5,890,000. The two routes agree to the dollar, and that's your check that the extraction is right.

Step 3, rank the four measures.

Contributions cover 84.8896% of the year's economic cost, so the deficit grew even though the company paid in more than either income statement charged.

Step 4, the cash flow reclassification. Contributions of $5,000,000 against a service cost of $4,350,000 leaves $650,000 of deficit reduction, which belongs in financing activity instead of operating. Operating cash flow becomes $59,050,000 and free cash flow rises from 58,400,000 − 21,000,000 = $37,400,000 to $38,050,000, an uplift of 1.7380%.

Step 5, convert the deficit into a horizon. At $650,000 a year of net funding, the $11,390,000 deficit takes 17.5231 years to clear, assuming nothing else moves. Nothing else will, but the number is what makes the liability forecastable, and it's the figure to put beside the company's own expected-contribution disclosure.

Read it. The economic cost exceeds every published measure in this year, and the ranking isn't a law. A year of strong asset returns cuts total periodic pension cost through the actual-return term while leaving the American expense untouched, because that expense uses the expected return. A discount-rate rise cuts it through an actuarial gain that no income statement sees. Compute the series over three or five years before treating any single year's ranking as a characteristic of the company.

Worked example 5: A plan amendment, both rulebooks (India, ₹)

Six months into the following year, on 1 October, Nandan Forgings improves its gratuity formula from fifteen days to twenty days of last-drawn salary per completed year. The actuary values the increase in the obligation at ₹6,20,00,000, of which ₹4,10,00,000 relates to employees who have already completed five years and ₹2,10,00,000 to employees who will vest over an average of five further years. The average remaining service period of all active employees expected to receive the benefit is 11 years. Earnings before interest and tax before the amendment are ₹52,00,00,000 on revenue of ₹4,15,00,00,000. Report the year under both rulebooks.

Solution. Step 1, the balance sheet, which is identical. Both frameworks recognise the full ₹6,20,00,000 increase in the obligation on 1 October. Nothing about the vested and unvested split changes that.

Step 2, Ind AS 19. Past service cost goes to profit immediately and in full, vested or not, at the earlier of the date the amendment occurs and the date any related restructuring cost is recognised. The charge is ₹6,20,00,000, in service cost, in operating profit, in this year.

Step 3, ASC 715. Prior service cost goes to other comprehensive income at the amendment date and is amortised into profit over the eleven-year average remaining service period, giving 6,20,00,000 ÷ 11 = ₹56,36,363.64 a year. The amendment is effective from 1 October, so this year carries six months, or ₹28,18,181.82.

Step 4, the cumulative gap.

The Indian charge is 22.0000 times the American one in year one, and the two converge only in year twelve, half a year after the amortisation begins its twelfth instalment.

Step 5, what it does to the margin. Operating profit falls to ₹45,80,00,000 under Ind AS 19 and to ₹51,71,81,818.18 under ASC 715, so the operating margin is 11.0361% against 12.4622%. The gap of 1.4261 percentage points is 11.3811% of the pre-amendment operating profit, and it exists because two accountants disagreed about when a decision taken on 1 October becomes an expense.

Step 6, verify. Both cumulative columns reach ₹6,20,00,000 and the difference between them is zero at the end. The balance sheets agreed from day one. Only the split between profit and other comprehensive income, and its timing, ever differed.

Read it. A plan amendment is the cleanest demonstration in accounting that the balance sheet and the income statement answer different questions. Under one rulebook the whole cost of a decision hits the year of the decision, which is arguably the right signal. Under the other it's spread over the working lives of the people who benefit, which has a fair claim to be the right matching. Nobody can settle that from the numbers. Your job is to notice that a company reporting a sudden ₹6,20,00,000 hit to operating profit and a company reporting ₹28,18,181.82 may have done the identical thing.

One further point of mechanics under the international rulebook. When a plan is amended part-way through a period, the sponsor remeasures the net liability with updated assumptions and recomputes service cost and net interest for the remainder of the period on that basis, so the amendment changes more than the past-service-cost line alone.

Worked example 6: Graded vesting under both attributions (India, ₹)

Vellore Analytics Ltd (synthetic) grants 4,00,000 employee stock options on 1 April, vesting 25% at the end of each of years 1 to 4, with a service condition only. Because expected life differs by tranche, the grant-date fair values differ: ₹142.00, ₹168.00, ₹189.00 and ₹206.00 per option for tranches 1 to 4. Revenue is ₹1,86,00,00,000. At the end of year 2, two teams leave, forfeiting 12,000 units of tranche 3 and 15,000 of tranche 4. Compute the expense under the Ind AS 102 accelerated attribution and under an ASC 718 straight-line election, apply the vested-portion floor, and true up.

Solution. Step 1, the grant. Each tranche is 1,00,000 options.

Step 2, the base attributions, before any forfeiture. Under Ind AS 102 each tranche is expensed over its own period, so year 1 carries 1,42,00,000 ÷ 1 + 1,68,00,000 ÷ 2 + 1,89,00,000 ÷ 3 + 2,06,00,000 ÷ 4 = ₹3,40,50,000. Straight-line gives 7,05,00,000 ÷ 4 = ₹1,76,25,000 a year. Year 1 differs by ₹1,64,25,000, or 93.1915%.

Step 3, the floor test, which you have to run every time. Cumulative straight-line expense must never fall below the grant-date value of the vested portion.

Step 4, the forfeiture true-up. Tranche 3 falls to 88,000 units, worth ₹1,66,32,000, and tranche 4 to 85,000 units, worth ₹1,75,10,000. The revised grant total is ₹6,51,42,000, which is ₹53,58,000 or 7.6000% below the original. Both rulebooks true up by recomputing the cumulative expense the award should carry and taking the difference.

Step 5, verify. Both columns sum to ₹6,51,42,000, the fair value of what actually vests, and no other figure in the two schedules has to agree. The year-2 Indian charge of ₹1,67,93,000 is ₹30,57,000 below the no-forfeiture path of ₹1,98,50,000, and that ₹30,57,000 credit never appears as a line anywhere. It's embedded in a smaller charge.

Step 6, the comparison that matters. In year 1 share-based expense is 1.8306% of Vellore's revenue against 0.9476% for an identical American grant, a margin gap of 0.8831 percentage points. By year 4 the American filer charges ₹1,62,85,500 against the Indian filer's ₹43,77,500, a ratio of 3.7203 times the other way.

Read it. Two companies granting the same options to the same people on the same terms report expense profiles that cross over. An analyst comparing employee-cost ratios in year 1 concludes the Indian firm is more generous, and in year 4 concludes the opposite, and both conclusions are artefacts. The arithmetic can't tell you which attribution better describes the economics, because the employees earned the awards over four years either way. Read the vesting schedule and the attribution policy in the note before treating a share-based-expense line as a fact about compensation.

Worked example 7: Three conditions, one grant date (US, $)

Pinnacle Diagnostics Inc. (synthetic) grants three awards on the same day to the same executive group, each of 300,000 units with a three-year vesting period.

• Award A, restricted stock units with a service condition only, grant-date fair value $52.00.
• Award B, performance units whose payout scales with cumulative earnings per share over three years against a $12.00 target, grant-date fair value $52.00. Management's best estimate of the payout is 100% of target at the end of year 1 and 60% at the end of year 2; the threshold is missed altogether, so the final payout is nil.
• Award C, performance units conditional on total shareholder return exceeding an index over three years, valued by Monte Carlo at $38.40. The hurdle is missed.

Pre-tax profit before share-based compensation in year 3 is $96,000,000. Compute the expense in each year and read the income statement.

Solution. Step 1, Award A. Service conditions don't enter the fair value, and no forfeitures occur, so the total is 300,000 × $52.00 = $15,600,000 spread straight-line at $5,200,000 a year.

Step 2, Award B. A non-market performance condition stays out of the fair value and drives the number expected to vest, which is re-estimated every period. Cumulative expense at each date is units × fair value × expected payout × elapsed fraction:

The lifetime charge is $0.00, because the target was missed and everything reverses.

Step 3, Award C. A market condition is priced into the grant-date fair value. That's why $38.40 is lower than the $52.00 of the otherwise identical Award B. The charge is 300,000 × $38.40 ÷ 3 = $3,840,000 a year for three years. Missing the hurdle changes nothing, because the possibility of missing was paid for in the measurement.

Step 4, the income statement.

Step 5, verify against what was delivered. Only Award A vests, delivering 300,000 shares. Cumulative expense across all three awards is $27,120,000, or $90.40 per share actually delivered, against a $52.00 share price at grant. The multiple is 1.7385 times.

Step 6, what year 3 looks like on the page. The three awards net to a charge of $2,800,000, against $10,080,000 the year before, so the line collapses by 72.2222% and swings $7,280,000 in twelve months. Pre-tax profit falls from $96,000,000 to $93,200,000, which is 2.9167%. A reader who takes the smaller charge as restraint has it backwards. The compression is a reversal of an award that failed, and Award B's reversal of $6,240,000 came within $2,800,000 of turning the whole line negative. A slightly larger performance grant would have done it, and a negative share-based-compensation line in a year of missed targets is a real thing that appears in real filings.

Read it. Award B cost nothing and Award C cost $11,520,000, both delivered zero shares, and nothing on the face of the income statement distinguishes them. It all comes down to one word in the note, whether the condition is a market condition. That doesn't mean Award C was worthless to grant. The executives held something with a $38.40 expected value on the day it was given, and they lost it fairly. The accounting is measuring the grant, and the reader who reads it as a measure of what was delivered will be wrong in both directions across the cycle.

Worked example 8: The tax line, the cash and the count (US, $)

Granite Peak Software Inc. (synthetic) grants 2,000,000 options with a $40.00 strike and a four-year cliff, at a grant-date fair value of $14.60. At the end of year 4 the options vest and are exercised immediately, with the share price at $96.00. The average market price during year 2 was $88.00. Shares outstanding are 100,000,000, the corporate tax rate is 21%, pre-tax profit in year 4 after the share-based charge is $180,000,000, and reported operating cash flow is $214,000,000. Work through the tax, the cash and the share count, and test the company's adjusted earnings measure.

Solution. Step 1, the expense and the deferred tax asset. Total grant-date value is 2,000,000 × $14.60 = $29,200,000, charged at $7,300,000 a year. Under ASC 718 a deferred tax asset is built on the cumulative book expense, so $7,300,000 × 21% = $1,533,000 a year, reaching $6,132,000 by vesting.

Step 2, the actual deduction. The employer's deduction is the intrinsic value at exercise, 2,000,000 × ($96.00 − $40.00) = $112,000,000, worth 112,000,000 × 21% = $23,520,000 of tax.

Step 3, the windfall. The excess of the actual benefit over the deferred tax asset is 23,520,000 − 6,132,000 = $17,388,000. Under ASC 718 that goes into the income statement's tax line as a discrete item in the period of exercise, and it's classified as an operating cash flow.

Reported net income is 12.2278% above the normalised figure, and the windfall is 10.8956% of it.

Step 4, the same facts internationally. Under IFRS 2 with IAS 12 the deferred tax asset is measured on the estimated future deduction instead of the book expense, and the excess over cumulative book expense is taken directly to equity. The profit-and-loss credit is the $6,132,000 that corresponds to the book charge, spread at $1,533,000 a year, and the $17,388,000 never reaches the tax line. An international filer on identical facts reports an effective rate close to 21% and an American filer reports 11.3400%.

Step 5, dilution before exercise. At the end of year 2 the options are unexercised and enter diluted earnings per share through the treasury-stock method. Assumed proceeds are the exercise price plus unrecognised compensation cost: 2,000,000 × $40.00 + $14,600,000 = $94,600,000. At the $88.00 average price that repurchases 1,075,000 shares, leaving 925,000 incremental shares. Ignoring the unrecognised cost would give 2,000,000 × (1 − 40 ÷ 88) = 1,090,909 shares and overstate the dilution by 165,909.

Basic earnings per share on year 4's figures are $159,588,000 ÷ 100,000,000 = $1.595880; diluted on 100,925,000 shares are $1.581253, a dilution of 0.9165%.

Step 6, the cash. Three flows, and only one of them is in operating.

Step 7, verify. The net financing outflow of $112,000,000 equals the intrinsic value transferred to employees, to the dollar. Neutralising the dilution costs the company what the employees gained, in cash, in a section nobody includes in free cash flow.

Step 8, test the adjusted measure. Granite Peak adds the $7,300,000 expense back to reach an adjusted net income of $166,888,000, or $1.668880 a share on the basic count. Build the corrected figure. Keep the expense, normalise tax to 21% for net income of $142,200,000, and use the diluted count of 100,925,000, giving $1.408967. The adjusted figure is 18.4471% higher. Operating cash flow gets the same treatment: strip the $7,300,000 add-back and the $17,388,000 windfall from the reported $214,000,000 and $189,312,000 remains, which is 11.5364% lower.

Read it. Three separate things flatter this company's reported year and all three are permitted. The expense is added back in operating cash flow, the tax benefit is recognised in one go in the tax line, and the adjusted measure removes the expense without touching the share count. None of them is aggressive on its own. Together they turn $1.408967 a share into $1.668880 a share and $189,312,000 of cash into $214,000,000. The arithmetic doesn't tell you what happens next year. The tax windfall won't repeat unless the share price rises again, and that's the part of this pattern that catches forecasters.

Verify block

Every headline figure, at the precision the computation produced.

• Nandan Forgings, base year. Interest cost 3,02,40,000; obligation before remeasurement 46,57,40,000; actuarial loss 1,22,60,000. Interest income 2,26,80,000; asset remeasurement gain 44,20,000; closing plan assets 36,41,00,000. Funded status 10,50,00,000 to 11,39,00,000. Service cost 4,35,00,000, net interest 75,60,000 (14.8061% of the charge), profit-and-loss expense 5,10,60,000, other comprehensive income charge 78,40,000. Reconciliation closes at 11,39,00,000 exactly. Net debt 1,23,00,00,000; after-tax deficit at 25.168% 8,52,33,648; EBITDA 68,00,00,000 and 68,75,60,000; ratios 1.808824x, 1.976324x, 1.912900x; 0.104077 turns added, 5.7538%; deficit as a share of net debt 9.2602%.
• Nandan Forgings, stress. Obligation 51,92,51,400 at 6.20%, 44,16,24,200 at 8.20%, 51,59,53,200 on the salary stress, 56,04,79,961.16 on both. Deficits 15,51,51,400, 7,75,24,200, 15,18,53,200, 19,63,79,961.16. Deficit rise on a 100 bp fall 4,12,51,400, or 36.2172%. Effective duration 8.120000 years, effective convexity 102.0000; first-order estimate 3,88,13,600 plus convexity term 24,37,800 equals 4,12,51,400. Year-2 interest cost 3,21,93,586.80 / 3,44,16,000 / 3,62,13,184.40; net interest 96,19,386.80 / 82,00,800 / 63,56,984.40. Naive sum of stresses 55,72,04,600, understating by 32,75,361.16. Joint stress 17.2552% above base.
• Nandan Forgings, amendment. Increase 6,20,00,000 (vested 4,10,00,000, unvested 2,10,00,000). American amortisation 56,36,363.64 a year, 28,18,181.82 in the first six months. Year-1 gap 5,91,81,818.18, a multiple of 22.0000. Operating profit 45,80,00,000 and 51,71,81,818.18 on revenue 4,15,00,00,000; margins 11.0361% and 12.4622%, gap 1.4261 percentage points, being 11.3811% of pre-amendment operating profit.
• Asset ceiling illustration. Surplus 5,00,00,000, economic benefit 1,80,00,000, written off 3,20,00,000, being 64.0000%.
• Allegheny Tool Works. Corridor 4,200,000.00, excess 5,000,000.00, amortisation 416,666.67; prior-service amortisation 400,000.00. Interest cost 3,024,000.00, expected return 2,677,500.00, net periodic pension cost 5,513,166.67, of which 1,163,166.67 below operating. International expense 5,106,000.00 on net interest of 756,000.00. Gap 407,166.67, or 7.9743%, proved as 816,666.67 less 409,500.00; after tax at 21% 321,661.67. Funded status 11,390,000.00 on both. Asset remeasurement 32,500.00 American and 442,000.00 international; other comprehensive income charge 376,833.33 and 784,000.00; total charged against equity 5,890,000.00 on both. Accumulated other comprehensive income carried forward: net loss 9,976,833.33, prior service cost 4,400,000.00.
• Allegheny, economic cost. Total periodic pension cost 5,890,000.00 by both routes. Shortfalls: American expense 376,833.33 (6.3978%), international expense 784,000.00 (13.3107%), contributions 890,000.00 (15.1104%); contributions cover 84.8896%. Excess contribution 650,000.00; free cash flow 37,400,000.00 to 38,050,000.00, up 1.7380%; 17.5231 years to clear the deficit.
• Vellore Analytics. Tranche totals 1,42,00,000 / 1,68,00,000 / 1,89,00,000 / 2,06,00,000, grand total 7,05,00,000. Base accelerated 3,40,50,000 / 1,98,50,000 / 1,14,50,000 / 51,50,000; straight-line 1,76,25,000 a year; year-1 gap 1,64,25,000, or 93.1915%. Floor tests 1,76,25,000 against 1,42,00,000, 3,52,50,000 against 3,10,00,000, 5,28,75,000 against 4,99,00,000, 7,05,00,000 against 7,05,00,000; none binds. Revised total 6,51,42,000, down 53,58,000 or 7.6000%. Post-forfeiture accelerated 3,40,50,000 / 1,67,93,000 / 99,21,500 / 43,77,500; straight-line 1,76,25,000 / 1,49,46,000 / 1,62,85,500 / 1,62,85,500; both total 6,51,42,000. Year-2 credit embedded 30,57,000. Year-4 ratio 3.7203x. Share-based expense over revenue 1.8306% and 0.9476%, gap 0.8831 percentage points.
• Pinnacle Diagnostics. Award A 5,200,000.00 a year, 15,600,000.00 total. Award B 5,200,000.00 / 1,040,000.00 / (6,240,000.00), total 0.00. Award C 3,840,000.00 a year, 11,520,000.00 total. Annual totals 14,240,000.00 / 10,080,000.00 / 2,800,000.00; cumulative 27,120,000.00; 90.4000 a share delivered, a multiple of 1.7385. Year-3 profit 96,000,000.00 to 93,200,000.00, down 2.9167%; year-2 to year-3 swing 7,280,000.00, a fall of 72.2222% in the line.
• Granite Peak Software. Annual expense 7,300,000.00, total 29,200,000.00; deferred tax asset 1,533,000.00 a year to 6,132,000.00. Intrinsic value 112,000,000.00, benefit 23,520,000.00, windfall 17,388,000.00. Tax 37,800,000.00 to 20,412,000.00, effective rate 11.3400%; net income 159,588,000.00 against 142,200,000.00, up 12.2278%; windfall 10.8956% of net income and 9.6600% of pre-tax profit. Treasury-stock proceeds 94,600,000.00, repurchase 1,075,000, incremental 925,000, naive figure 1,090,909. Earnings per share 1.595880 basic and 1.581253 diluted. Financing: 80,000,000.00 in, 192,000,000.00 out, net 112,000,000.00, equal to intrinsic value. Adjusted net income 166,888,000.00 and 1.668880 a share against an honest 1.408967, a gap of 18.4471%. Operating cash flow 214,000,000.00 to 189,312,000.00, down 11.5364%; the year's expense is 3.8975% of pre-tax profit before it.

Practice set

Work each problem fully before reading its solution. A calculator is assumed and no software is needed. Unless a problem says otherwise, answers within 0.5% of the stated figure count as correct; where a problem asks for a routing, a classification or a direction, the answer is exact. All entities are synthetic and all rates are illustrative. Contributions and benefits fall at the year end throughout.

P1 (guided). Derive the actuarial remeasurement (India, ₹). Bhilai Castings Ltd opens the year with a gratuity obligation of ₹88,00,00,000, a discount rate of 7.05%, current service cost of ₹7,20,00,000 and benefits paid of ₹5,40,00,000. The actuary's closing obligation is ₹97,60,00,000. Compute the interest cost, the obligation before remeasurement, and the actuarial gain or loss.

Solution. Interest cost is 88,00,00,000 × 0.0705 = ₹6,20,40,000, accrued on the opening balance and not the closing one. The obligation before remeasurement is 88,00,00,000 + 7,20,00,000 + 6,20,40,000 − 5,40,00,000 = ₹96,00,40,000. The residual is 97,60,00,000 − 96,00,40,000 = ₹1,59,60,000, and it's a loss, because the obligation came out higher than the four known movements predicted. It goes to other comprehensive income and never returns to profit.

P2 (guided). Complete the picture and reconcile (India, ₹). Bhilai Castings' plan assets open at ₹64,00,00,000, earn an actual return of ₹5,92,00,000, receive contributions of ₹8,00,00,000 and pay the same ₹5,40,00,000 of benefits. Using P1's figures, compute the asset remeasurement, the closing plan assets, the funded status at both dates, the Ind AS 19 expense split, and the reconciliation.

Solution. Interest income is 64,00,00,000 × 0.0705 = ₹4,51,20,000, so the asset remeasurement is 5,92,00,000 − 4,51,20,000 = ₹1,40,80,000 of gain. Closing plan assets are 64,00,00,000 + 5,92,00,000 + 8,00,00,000 − 5,40,00,000 = ₹72,52,00,000. The deficit moves from 88,00,00,000 − 64,00,00,000 = ₹24,00,00,000 to 97,60,00,000 − 72,52,00,000 = ₹25,08,00,000. Service cost of ₹7,20,00,000 goes to operating profit; net interest of 24,00,00,000 × 0.0705 = ₹1,69,20,000 goes to finance cost, which also equals 6,20,40,000 − 4,51,20,000; the profit charge is ₹8,89,20,000. Remeasurement is 1,59,60,000 − 1,40,80,000 = ₹18,80,000 of net loss to other comprehensive income. Reconciliation: 24,00,00,000 + 8,89,20,000 + 18,80,000 − 8,00,00,000 = ₹25,08,00,000, which closes.

P3 (guided). The same plan under ASC 715 (US, $). Take Bhilai Castings' figures in dollars: obligation $88,000,000, plan assets $64,000,000, service cost $7,200,000, discount rate 7.05%. Add the American ingredients: expected return 8.00%, unrecognised prior service cost $3,600,000 over an average remaining service period of 9 years, accumulated net actuarial loss $12,400,000. Compute net periodic pension cost, then the gap against the international expense, and prove the gap twice.

Solution. Interest cost is 88,000,000 × 0.0705 = $6,204,000. Expected return is 64,000,000 × 0.0800 = $5,120,000. Prior service cost amortises at 3,600,000 ÷ 9 = $400,000. The corridor is 10% of the greater of $88,000,000 and $64,000,000, which is $8,800,000; the accumulated loss exceeds it by 12,400,000 − 8,800,000 = $3,600,000, amortising at 3,600,000 ÷ 9 = $400,000. Net periodic pension cost is 7,200,000 + 6,204,000 − 5,120,000 + 400,000 + 400,000 = $9,084,000. The international expense is 7,200,000 + (24,000,000 × 0.0705) = $8,892,000, so the gap is $192,000. Proved a second way: the expected-return relief is (0.0800 − 0.0705) × 64,000,000 = $608,000 and the two amortisations add $800,000, giving 800,000 − 608,000 = $192,000.

P4 (guided). Total periodic pension cost (US, $). The P3 sponsor contributes $8,000,000 in the year, and a heavier actuarial loss than the Indian illustration carried moves its deficit from $24,000,000 to $29,400,000. Compute total periodic pension cost and state what net periodic pension cost from P3 understates it by.

Solution. Total periodic pension cost is contributions plus the increase in the deficit: 8,000,000 + (29,400,000 − 24,000,000) = $13,400,000. Net periodic pension cost of $9,084,000 understates it by $4,316,000, which is 32.2090% of the economic cost. The gap is large because a year with a big actuarial loss produces an economic cost the income statement postpones through the corridor and the expected-return assumption.

P5. Stress the discount rate (India, ₹). Bhilai Castings' actuary discloses a duration of 9.4 years on the closing obligation of ₹97,60,00,000. A first-order estimate is all that's asked. Compute the obligation and the deficit after a 75 basis point fall in the discount rate, using the closing plan assets from P2.

Solution. A first-order move is duration × the rate change × the obligation: 9.4 × 0.0075 = 7.0500%, so the obligation rises by 97,60,00,000 × 0.0705 = ₹6,88,08,000 to ₹1,04,48,08,000. The deficit rises from ₹25,08,00,000 to 1,04,48,08,000 − 72,52,00,000 = ₹31,96,08,000. The deficit grows 27.44% on a 7.05% obligation move, because the assets don't move with the rate. A second-order estimate would add a convexity term and land slightly higher, and the disclosure would give the exact figure.

P6. Put the deficit into enterprise value (India, ₹). Bhilai Castings has a market capitalisation of ₹9,60,00,00,000, borrowings of ₹3,40,00,00,000, cash of ₹88,00,00,000 and EBITDA of ₹1,54,00,00,000. Using the closing deficit from P2 and a tax rate of 25.168%, compute enterprise value over EBITDA before and after treating the deficit as debt.

Solution. Enterprise value before the adjustment is 9,60,00,00,000 + 3,40,00,00,000 − 88,00,00,000 = ₹12,12,00,00,000, giving 7.8701 times EBITDA. The after-tax deficit is 25,08,00,000 × 0.74832 = ₹18,76,78,656, so adjusted enterprise value is ₹12,30,76,78,656 and the multiple is 7.9920 times. The adjustment adds 0.1219 turns, which looks modest until you notice it's a claim that consumes cash before any dividend and appears in no debt schedule.

P7. A plan amendment, both rulebooks (India, ₹). An Indian employer improves its gratuity formula, and the actuary values the increase in the obligation at ₹9,90,00,000. The average remaining service period of employees expected to receive the benefit is 9 years. The amendment takes effect on the first day of the financial year. State the first-year charge under Ind AS 19 and under ASC 715, and the difference.

Solution. Under Ind AS 19 the whole ₹9,90,00,000 goes to profit immediately, in service cost, whether the employees are vested or not. Under ASC 715 the amount goes to other comprehensive income at the amendment date and amortises at 9,90,00,000 ÷ 9 = ₹1,10,00,000 a year, so the first-year charge is ₹1,10,00,000. The difference is ₹8,80,00,000 in year one, and the two cumulative charges converge only at the end of year nine. Both balance sheets carry the same larger obligation from day one.

P8. Graded vesting, two attributions (India, ₹). A company grants 1,80,000 options in three equal tranches vesting at the end of years 1, 2 and 3, with a service condition only. Per-unit grant-date fair values are ₹96.00, ₹112.00 and ₹127.00. Compute the expense under the Ind AS 102 accelerated attribution and under a US straight-line election, and run the floor test.

Solution. Tranche totals are 60,000 × 96 = ₹57,60,000, 60,000 × 112 = ₹67,20,000 and 60,000 × 127 = ₹76,20,000, a grand total of ₹2,01,00,000. Accelerated attribution gives year 1 = 57,60,000 ÷ 1 + 67,20,000 ÷ 2 + 76,20,000 ÷ 3 = ₹1,16,60,000, year 2 = 33,60,000 + 25,40,000 = ₹59,00,000, year 3 = ₹25,40,000, summing to ₹2,01,00,000. Straight-line gives 2,01,00,000 ÷ 3 = ₹67,00,000 a year, and year 1 differs by ₹49,60,000, or 74.0299%. The floor test compares cumulative straight-line with the vested portion: ₹67,00,000 against ₹57,60,000, ₹1,34,00,000 against ₹1,24,80,000, and ₹2,01,00,000 against ₹2,01,00,000. It doesn't bind in any year, but it must be shown, because a grant whose first tranche carried a higher fair value than its later ones would breach it.

P9. Condition types (US, $). A company grants 180,000 performance units whose payout scales with an earnings target, at a grant-date fair value of $44.00, and 180,000 performance units with a relative total-shareholder-return condition at a Monte Carlo value of $31.50, both over three years. The expected payout on the earnings award is assessed at 100% of target, then 75%, and the threshold is then missed altogether. The total-shareholder-return hurdle is also missed. Compute each year's expense for both awards and the combined year-3 figure.

Solution. The non-market award's cumulative expense is units × fair value × expected payout × elapsed fraction, giving $2,640,000, then $3,960,000, then nil, so the annual charges are $2,640,000, $1,320,000 and ($3,960,000), and the lifetime charge is $0.00. The market-condition award is priced at grant and never reversed, charging 180,000 × 31.50 ÷ 3 = $1,890,000 a year and $5,670,000 in total. Year 3 combines to ($2,070,000), a net credit in a year when both plans failed. The two awards delivered zero shares between them and cost $5,670,000.

P10. The tax windfall and the effective rate (US, $). A company recognised 750,000 options at a grant-date fair value of $9.20 each. They are exercised when the share price is $61.00 against a $28.00 strike. The tax rate is 21% and pre-tax profit is $64,000,000. Compute the deferred tax asset, the actual tax benefit, the windfall, the reported tax expense and the effective rate.

Solution. Cumulative book expense is 750,000 × 9.20 = $6,900,000, so the deferred tax asset is 6,900,000 × 0.21 = $1,449,000. Intrinsic value at exercise is 750,000 × (61.00 − 28.00) = $24,750,000, worth 24,750,000 × 0.21 = $5,197,500. The windfall is 5,197,500 − 1,449,000 = $3,748,500. Tax at 21% would be $13,440,000, so reported tax is $9,691,500 and the effective rate is 15.1430% against a statutory 21.00%. Under IFRS 2 the $3,748,500 would go to equity and the rate would stay at 21.00%.

P11. Treasury-stock method with unrecognised cost (US, $). 1,400,000 options with a $52.00 strike and a grant-date fair value of $17.00 are one year into a three-year vest. The average market price for the period is $74.00. Compute the incremental diluted shares, and compute what the naive method that ignores unrecognised compensation cost would have given.

Solution. Unrecognised compensation cost is 1,400,000 × 17.00 × 2 ÷ 3 = $15,866,666.67. Assumed proceeds are 1,400,000 × 52.00 + 15,866,666.67 = $88,666,666.67, buying back 88,666,666.67 ÷ 74.00 = 1,198,198.20 shares, so the incremental count is 1,400,000 − 1,198,198.20 = 201,801.80. The naive calculation gives 1,400,000 × (1 − 52 ÷ 74) = 416,216.22, overstating dilution by 214,414.41 shares. The unrecognised cost is treated as proceeds because the employee still owes service the company has not paid for, and ignoring it double-counts the dilution.

P12. Leave encashment, and where the movement lands (India, ₹). An Indian employer's compensated-absence obligation opens at ₹6,40,00,000, with a discount rate of 7.05%, current service cost of ₹1,15,00,000 and payments of ₹95,00,000. The actuary's closing obligation is ₹7,40,00,000. Compute the interest cost, the remeasurement, the total charge for the year, and state where each component lands.

Solution. Interest cost is 6,40,00,000 × 0.0705 = ₹45,12,000. The obligation before remeasurement is 6,40,00,000 + 1,15,00,000 + 45,12,000 − 95,00,000 = ₹7,05,12,000, so the remeasurement is 7,40,00,000 − 7,05,12,000 = ₹34,88,000 of loss. Compensated absences that aren't expected to be settled wholly within twelve months are other long-term employee benefits, so all three components go to profit or loss and none goes to other comprehensive income. The total charge is 1,15,00,000 + 45,12,000 + 34,88,000 = ₹1,95,00,000. The identical ₹34,88,000 arising on the gratuity plan in the same note would bypass profit entirely, which is the difference to carry.

Applied mini-project

You'll rebuild two benefit notes and reach one verdict on whose operating profit is more distorted.

Take one Indian annual report and one US Form 10-K from companies large enough to run a funded defined-benefit plan and to grant equity to employees. Both filings must cover a completed financial year and every figure must be traced to the primary source, meaning the company's own filing on its website, on BSE or NSE, or on EDGAR, with the year and the note number recorded. Five artefacts, each carrying a numbered test it must pass before it counts.

The first artefact is the rebuilt roll-forwards. For each filing, reconstruct the defined-benefit obligation movement and the plan-asset movement from the note, and state the partial-period convention you assumed for contributions and benefits. Where the filer runs several plans, pick one and say which. Test 1: each roll-forward must close to the disclosed closing balance to within one currency unit, or the gap must be named and attributed to a specific disclosed item such as a transfer, an acquisition or a foreign-currency movement. Test 2: interest cost must reproduce the disclosed discount rate applied to the opening obligation, within the convention you named.

The second is the expense reconciliation. Split the charge into service cost, net interest or the five American components, and remeasurement. Then run the balance-sheet reconciliation: opening net liability, plus the profit charge, plus the other comprehensive income charge, less contributions, equals closing net liability. Test 3: the reconciliation must close exactly, and if it doesn't, the missing component must be identified by name. Past service cost is the usual culprit.

Third, total periodic pension cost by two routes. Compute it from contributions plus the change in funded status, and again from service cost plus interest cost less the actual return plus actuarial losses. Test 4: the two routes must agree to within one currency unit. Then rank total periodic pension cost against the reported expense and against contributions for each filer, and state which of the three a reader of the income statement alone would have taken as the year's cost.

Fourth, the adjustment panel. For each filing compute, on both a reported and an adjusted basis: net debt over EBITDA with the after-tax deficit as debt and financing components removed from operating profit; enterprise value over EBITDA on the same basis; and operating profit with any misplaced net interest restored. Then apply the disclosed sensitivities to produce the obligation and the deficit under a 100 basis point discount-rate fall and a 100 basis point salary-growth rise, separately and together. A US filer will often disclose no sensitivity at all, so estimate a duration from the plan's profile, say how you estimated it, and mark the result as constructed so nobody mistakes it for a disclosed figure. Test 5: the joint stress must be computed multiplicatively and reported alongside the naive additive figure, with the difference stated.

Fifth, the share-based payment panel. For each filing extract the year's expense, the condition types of the outstanding awards, the vesting pattern and attribution policy, the diluted share count and the tax effect in the rate reconciliation. Compute the expense as a percentage of revenue and of pre-tax profit before it, and the option and unit overhang as a percentage of shares outstanding. Test 6: where the filer publishes an adjusted earnings measure that excludes share-based compensation, rebuild the corrected figure by keeping the expense, normalising the tax rate to statutory and using the diluted count, and report the gap in percentage terms and in cents or paise a share.

Deliverable. One page of numbers and one page of argument. The numbers page carries both rebuilt roll-forwards, both expense reconciliations, the total periodic pension cost comparison, the adjustment panel and the share-based panel, with the six test residuals shown in full and never just asserted. The argument page answers one question in figures: which of the two companies' reported operating profit is more distorted by benefit accounting, and by how much. Close with the single assumption whose movement would change your answer, and quantify what it would take.

Rubric. The rubric carries 21 points, and you pass at 17 with no zero on any row.

Any artefact whose test fails scores zero for that row, however well the note reads. A roll-forward that doesn't close isn't a presentation problem. It means a movement is missing, and the whole argument built on it is standing on a number nobody has verified.

Reading & resources

• IAS 19 and Ind AS 19, read side by side. The two texts are almost identical, and the discount-rate paragraph is where they part: the Indian version mandates government bonds where the international version prefers high-quality corporate bonds. Twenty minutes with both open settles a difference that moves every Indian obligation. [Free] [Intermediate]
• ASC 715-30, the pension subtopic, and ASU 2017-07 on income statement presentation. The subtopic carries the five components and the corridor; the update is what forced the four non-service components below operating profit. [Free] [Intermediate]
• IFRIC 14 on the asset ceiling, available funding refunds and minimum funding requirements. Short, and the only place the surplus question is settled properly. [Free] [Advanced]
• The Payment of Gratuity Act, 1972 as amended, and the Employees' Provident Funds and Miscellaneous Provisions Act, 1952. Read the sections on the benefit formula, vesting and the ceiling in the first, and the exemption provisions in the second. These are the statutes behind every Indian benefit note. [Free] [Beginner to Intermediate]
• The Code on Social Security, 2020 and the rules notified under it. The consolidating legislation for gratuity and provident fund, brought into force in stages. Check the commencement position and the notified rules directly rather than from any summary. [Free] [Intermediate]
• The Institute of Actuaries of India's actuarial practice standards on employee benefits, particularly the one governing the actuary's report to the employer. It tells you what the actuary was required to disclose and therefore what you can ask for. [Free] [Advanced]
• IFRS 2 and Ind AS 102, and ASC 718. The condition-type architecture, the graded-vesting attribution and the forfeiture rules are all short readings. The implementation guidance to IFRS 2 on graded vesting is the paragraph that produces the front-loading. [Free] [Intermediate]
• ASU 2016-09 on improvements to employee share-based payment accounting. This is the update that moved excess tax benefits into the income statement, allowed the forfeiture policy election, and settled the net-share-settlement question. Reading the basis for conclusions is the fastest way to understand why the American tax treatment differs from the international one. [Free] [Intermediate to Advanced]
• IAS 12 paragraphs 68A to 68C. Three paragraphs that decide whether a share-based tax benefit reaches the income statement or goes to equity. [Free] [Advanced]
• Any large legacy manufacturer's or public-sector undertaking's benefit note, in either country. Companies with plans closed to new members and long durations show every feature at a scale where it matters, including asset ceilings, settlements and curtailments that a young company's note never carries. [Free] [Intermediate]
• The SEC's comment letters on EDGAR, searched for pension and share-based-payment correspondence. Reading a regulator argue with a filer about an expected-return assumption or a forfeiture policy shows you exactly which parts of the note are contested. [Free] [Intermediate to Advanced]
• Kieso, Weygandt and Warfield, Intermediate Accounting, for the American mechanics, and Anthony, Hawkins and Merchant, Accounting: Text and Cases, for the reasoning. The first works the corridor and the amortisations exhaustively; the second explains why smoothing was invented and what it was meant to solve. [Paid] [Intermediate]
• Aswath Damodaran's writing on treating pension deficits and share-based compensation in valuation. He takes a stronger position than most on both, and reading someone who has committed to a treatment is more useful than reading a survey of options. [Free] [Intermediate]

One exercise is worth more than rereading any of these. Open a benefit note in either country and try to rebuild both roll-forwards from it, without looking at the closing balances until you have finished. Whatever fails to close is the thing the note buries, and half an hour of that teaches more about disclosure quality than any chapter can.

Teach it back & journal

Feynman prompt. Sit with someone who can read an income statement and has never opened a benefit note. Put two figures in front of them: an Indian company reporting ₹5,10,60,000 of pension expense and an American company reporting $5,513,166.67 on an identical plan. Ask them which company had the more expensive year. Let them commit to an answer before you tell them the plans are the same and the real cost was $5,890,000 in both. Then walk them to the funded status, which is identical, and to total comprehensive income, which is identical, and make them say in their own words what the income statements were disagreeing about.

Then the harder half. Show them Pinnacle Diagnostics' two failed performance awards and ask which cost more. Almost everyone says they cost the same, because nothing vested. Make them find the word in the note that decides it, and then make them explain, out loud, why paying for the probability of failure at grant means you cannot get the money back when failure arrives. If they afterwards ask, unprompted, whether a company's share-based expense line contains a market-condition award, the mechanism has installed.

Finish with the arithmetic that catches everyone. Give them Granite Peak's 11.3400% effective tax rate and ask what the company did to earn it. Accept nothing except that the share price rose, and then ask what happens to that rate next year if it falls.

Journal prompt. For two weeks, every time you read a company's results, find the employee-benefit note before you look at any ratio, and write down four things: the discount rate, the expected return if the filer is American, the funded status, and the expected contribution for the coming year. Do it for at least six companies, split between the two jurisdictions and including one old-economy employer with a legacy plan.

Then answer in writing. Say how many of the six you could reconcile from the note alone, and name what was missing in the ones you could not. Identify the company with the largest deficit as a share of net debt, and record whether any published commentary on it mentioned the plan at all. For the American filers, judge whether the expected return was defensible against the disclosed asset allocation, and set down how you decided. For the Indian filers, say whether you could separate gratuity from leave encashment, and whether the two carried the same assumptions.

Close with a paragraph on the habit this area asks for. Benefit accounting is the clearest case you'll meet of a real economic obligation that reporting rules are allowed to smooth, delay and relocate, and every one of those moves is disclosed somewhere in the note. Which of the four verification checks are you most likely to skip when you are tired? Write down what specifically goes wrong when you skip it, and what you will change this month to make skipping harder than doing.

This module's flashcards and mastery quiz are wired into the app: see the node's Quiz and Reviews.