FIFO vs Weighted Average Cost: Which Reports More Profit

Both formulas answer the same question, what the goods still on the shelf cost, and both are permitted in India. First-in-first-out (FIFO) assumes the oldest cost leaves first, so the balance sheet carries the newest prices. Weighted average blends every price into one, so neither statement carries any actual price. On identical transactions they report different profits, and which is higher depends entirely on the price path.

Here is what sits underneath that. A business buys the same thing several times a year at several different prices, and then some of what it bought is sold and some is still in the building at the year end. Nobody can say which physical reams of paper went out. Paper is paper, so it would not help if they could. So the accounts need a rule for deciding which rupees went out with the goods and which rupees stayed behind on the shelf. The rule for splitting the rupees is the whole subject. The rule is about money, not about goods, and the two formulas below are simply two different rules that a business is allowed to pick from.

Each formula is stated and worked on its own on the year two purchases of Anjani Stationers Private Limited, an invented stationery business, the two are then set against each other on identical transactions, and the price at which they agree, the effect of a change of formula and the position of last-in-first-out all follow from that comparison.

What does first-in-first-out actually assume?

First-in-first-out makes one assumption and everything else follows from it. The oldest cost in the store leaves first. Whatever is left at the year end is therefore made up of the most recent purchases, working backwards from the last one until every unit still on hand has been accounted for.

The assumption is about cost, not about goods. First-in-first-out is therefore called a cost flow assumptionA rule for deciding which recorded costs are treated as leaving with the goods sold and which are treated as staying with the goods still held. The convention is applied to the money, and it need not match how the physical items actually moved. rather than a stock rotation rule. This trips people up constantly, so hold it for a second. A godown may issue whichever bundle of paper is nearest the door. A grocer may sell the packet at the front of the shelf whatever its date. Neither fact has anything to do with the accounting. The accounting is a queue of rupees, and first-in-first-out says the rupees queue in the order they arrived and leave in that same order. Think of a household putting money into one tin through the year and taking money out of it: the notes are identical, so the household simply decides that the earliest deposits are the ones being spent, and the tin is then treated as holding the most recent ones.

Anjani Stationers Private Limited's year two numbers recur from here on, so the year is worth working in full. The business opened the year with 10,000 reams that had cost Rs 190/- each, so Rs 19,00,000. The business then bought three times: 30,000 reams at Rs 205/- for Rs 61,50,000, then 30,000 reams at Rs 220/- for Rs 66,00,000, then 15,000 reams at Rs 200/- for Rs 30,00,000. Purchases add to Rs 1,57,50,000. Add the opening stock and 85,000 reams costing Rs 1,76,50,000 were available to be used during the year. Stock count at the year end found 14,000 reams still on hand, so 71,000 reams were consumed.

Now apply the rule. The 14,000 reams still on hand are the newest 14,000, and the last purchase alone was 15,000 reams, so all 14,000 come out of that purchase and every one of them is carried at Rs 200/-. Closing inventory is 14,000 times Rs 200/-, or Rs 28,00,000. Everything else was consumed. The cost of materials consumed is Rs 1,76,50,000 less Rs 28,00,000, or Rs 1,48,50,000. Against revenue of Rs 2,70,00,000 that leaves a gross profit of Rs 1,21,50,000 and a gross margin of 45.0 per cent. First-in-first-out is the formula Anjani Stationers applies, so these are the figures it actually published for year two.

One detail in that build decides the whole direction question. Of the 15,000 reams in the last purchase, 14,000 stayed on the shelf and only 1,000 were consumed. So the newest price of Rs 200/- decides the entire balance sheet figure and touches barely one rupee in a hundred and fifty of the income statement figure. The cost charged against the year is dominated by the older prices: 10,000 reams at Rs 190/-, 30,000 at Rs 205/- and 30,000 at Rs 220/-. The three older lots average out at Rs 209.15 a ream across the 71,000 consumed. Under first-in-first-out the newest price goes almost entirely to the balance sheet and the income statement is charged with prices from earlier in the year.

What does the weighted average cost formula actually do?

Weighted average cost throws the queue away. The formula gathers every unit that was available across the period into one pool, totals the rupees, totals the units, and divides one by the other to reach a single rate. Every unit that leaves and every unit that stays is then valued at that one rate. There is no first and no last, and there is no queue to work backwards through.

Weighted average is a division. The word weighted simply means the big purchases pull the answer towards their own price harder than the small ones do. Take Anjani Stationers' year two again, on exactly the same transactions as before. A comparison is only honest on identical transactions. Rupees available: Rs 1,76,50,000. Units available: 85,000 reams. The division gives Rs 207.647 a ream, carried here as Rs 207.65/-. Where that figure sits is the thing to see. The rate is nowhere near the simple average of the four prices, Rs 203.75. The two 30,000 ream purchases at Rs 205/- and Rs 220/- carry sixty thousand of the eighty five thousand reams between them and drag the rate up towards Rs 220/-. The weighting is doing real work.

Now split the pool. The 14,000 reams still on hand are valued at 14,000 times Rs 207.647, or Rs 29,07,059. Rounded to the nearest thousand rupees in the usual way, Anjani Stationers would carry that at Rs 29,07,000. The cost of materials consumed is then Rs 1,76,50,000 less Rs 29,07,000, or Rs 1,47,43,000. Gross profit would be Rs 2,70,00,000 less Rs 1,47,43,000, or Rs 1,22,57,000, a gross margin of 45.4 per cent. Check the identity in both directions before moving on: opening stock of Rs 19,00,000 plus purchases of Rs 1,57,50,000 less closing stock of Rs 29,07,000 gives Rs 1,47,43,000, and 71,000 reams at Rs 207.647 gives the same Rs 1,47,43,000. It holds.

A timing choice hidden inside the formula changes the answer, so it has to be named. Anjani Stationers computed one rate for the whole year, dividing the whole year's pool by the whole year's units. One rate for the whole year is the periodic systemA way of running the stock records in which the value of what was used is worked out once at the end of the period, from the opening balance, the purchases and a physical count of what is left.. A business running a perpetual systemA way of running the stock records in which every issue out of store is costed at the time it happens, so the running value of stock is updated continuously rather than once at the end. instead recomputes the average after every single purchase and charges each issue at the running rate on that day. The running version is often called the moving average. Same formula, applied at a different frequency, and on a year with three price changes the two versions will not land on the same number. Anjani Stationers counts its paper once a year and works the rate once a year, so the periodic version is the one used throughout here.

The most important property of weighted average is the one nobody points at: after the first purchase, no unit is carried at a price anybody ever paid. Rs 207.65 does not appear on a single invoice from the mill. The mill charged Rs 190/-, then Rs 205/-, then Rs 220/-, then Rs 200/-. Rs 207.65 is a constructed number that exists only inside the accounts. A constructed number is exactly what smoothing requires, so the construction is no criticism. A closing inventory figure quoted to somebody as though it represented what the goods would cost to replace is a different matter.

On identical transactions, what does each one report?

Both formulas have now been built on their own, from the same opening balance and the same three purchases, so the comparison that follows changes exactly one thing and nothing else. Set the two builds against each other line by line.

Read down the two columns and notice how little separates them. The transactions are identical and neither formula touches what was bought or what it cost, so the first three rows are identical. Everything that differs flows from one cell, the rate applied to the 14,000 reams still on hand. The two formulas disagree about one number, the closing stock, and every other difference in the table is that same disagreement arriving somewhere else. Rs 29,07,000 against Rs 28,00,000 is Rs 1,07,000. Stock that does not stay on the shelf is charged to the year, so the cost of materials consumed differs by Rs 1,07,000 the other way. Gross profit differs by Rs 1,07,000. There is only ever one difference between the two formulas, and it appears three times.

Does Rs 1,07,000 matter? There is no single answer. Against revenue of Rs 2,70,00,000 it is 0.4 per cent, a figure nobody would look at twice. Against gross profit of Rs 1,21,50,000 it is 0.9 per cent, still small. Against profit before tax of Rs 38,00,000 it is 2.8 per cent, the sort of movement that changes how a year reads. And on gross margin it is four tenths of a percentage point, taking 45.0 to 45.4. The same rupees are trivial or material depending entirely on which base they are set against. A commentary or a note that calls a difference immaterial without naming the base has said nothing. Anjani Stationers' gross margin held exactly flat at 45.0 per cent across two years, and that flatness is a fact somebody is going to lean on, so the base matters more than usual here. A formula difference of four tenths of a point is not large, and it is large enough to make a flat line look like a rising one.

Which one reports the higher profit, and can that be stated as a rule?

Almost every textbook treatment of this subject ends with a rule that sounds like this: when prices are rising, the older and cheaper costs are the ones charged against sales, so first-in-first-out reports higher profit. The rule has just failed on Anjani Stationers, whose prices did rise for most of the year, and whose first-in-first-out figures report the lower profit by Rs 1,07,000. So the rule is not merely imprecise. On this case it points the wrong way.

Here is the honest version, and it is not much harder to hold. Compare the price applied to the closing units under each formula: first-in-first-out uses the latest price, weighted average uses the average price, and whichever of those two is higher leaves more on the balance sheet and therefore reports more profit. Nothing about inflation, nothing about a trend, nothing about a direction of travel across the year. Just two numbers, side by side. Anjani Stationers' latest price was Rs 200/-. Its average was Rs 207.65. Rs 200/- is lower, so first-in-first-out carries the smaller closing balance, charges the bigger cost, and reports the smaller profit. Two prices compared is the whole mechanism.

Why does the memorised rule fail here, when prices genuinely did rise? Because rising is a description of the year and the formula only ever looks at one point in it. Paper went from Rs 190/- to Rs 205/- to Rs 220/-, a rise of thirty rupees, and then eased back to Rs 200/- for the last buy. A year that opened at Rs 190/- and closed at Rs 200/- is a rising year by any ordinary description. But the average was dragged up above Rs 207/- by the two large purchases in the middle, and the last price never came back up to meet it. The rule fails because it substitutes the shape of the whole year for the position of one price, and those are different facts that only agree when prices move in one direction and never turn. A household knows this instinctively about vegetables: onions can be dearer in December than they were in April and still be cheaper this week than the average paid across the year, and which of those two statements matters depends on what is being worked out.

Work the reversed case properly rather than asserting it. Purchase three at Rs 240/- makes that purchase Rs 36,00,000 instead of Rs 30,00,000, so available cost becomes Rs 1,82,50,000 across the same 85,000 reams. The weighted average rate is Rs 1,82,50,000 over 85,000, or Rs 214.706, carried as Rs 214.71/-. First-in-first-out values the 14,000 closing reams at the latest price of Rs 240/-, giving Rs 33,60,000. Weighted average values them at Rs 214.71, giving Rs 30,05,882, presented at Rs 30,06,000. Cost of materials consumed comes out at Rs 1,48,90,000 under first-in-first-out and Rs 1,52,44,000 under weighted average, and gross profit at Rs 1,21,10,000 against Rs 1,17,56,000. First-in-first-out now reports Rs 3,54,000 more profit, not less, and the only thing that changed anywhere in the two builds was one purchase price.

A second thing in that reversed build explains why the two formulas react so differently to the same news. Under first-in-first-out only 1,000 of those reams were consumed, so raising the last price from Rs 200/- to Rs 240/- changed the cost of materials consumed by only Rs 40,000. Under weighted average the new price was blended into every one of the 71,000 reams charged against the year, so the same change moved the cost of materials consumed by Rs 5,01,000. A late price change lands almost entirely on the balance sheet under first-in-first-out and lands across the whole income statement under weighted average. The first build showed the same property from the other side.

If the direction turns on whether the latest price sits above or below the average, then somewhere between Rs 200/- and Rs 240/- there is a price at which the two formulas agree exactly. Solve for it rather than hunting for it. Call the third purchase price p. The first three lots are fixed at Rs 1,46,50,000, so available cost is Rs 1,46,50,000 plus 15,000p across 85,000 reams. First-in-first-out closing stock is 14,000p. Weighted average closing stock is 14,000 times the available cost over 85,000. Setting the two equal cancels the 14,000 from both sides and leaves p equal to the available cost over 85,000. Then 85,000p equals Rs 1,46,50,000 plus 15,000p, 70,000p equals Rs 1,46,50,000, and p is Rs 209.286, rounded to Rs 209.29/-. At a third purchase price of Rs 209.29/- both formulas carry closing stock at exactly Rs 29,30,000 and report exactly the same gross profit. The whole direction question turns on that crossover price. The check confirms it: at Rs 209.29 the available cost is Rs 1,77,89,286 and dividing by 85,000 gives Rs 209.29 back again, which is the algebra restating itself.

Readings taken off the panel, written down here so that they survive without it. At Rs 180/- a ream the gap is Rs 3,38,000 with first-in-first-out reporting less. At the published Rs 200/- it is Rs 1,07,000, still with first-in-first-out reporting less. At Rs 209.29 the gap is nil and both formulas carry Rs 29,30,000. At Rs 220/- first-in-first-out is ahead by Rs 1,24,000, and at Rs 240/- it is ahead by Rs 3,54,000. The gap moves in a straight line at roughly Rs 11,500 for every rupee the last price moves. The slope is 14,000 reams less the fourteen eighty fifths of that rupee that gets blended back into the average. Everything about direction is that one line crossing zero.

What does each formula do to the balance sheet as against the income statement?

The bigger number changes with the price path anyway and is not the interesting difference. Step back from it. The durable difference is which statement each formula keeps current and which one it lets go stale, and here the two are exact opposites.

First-in-first-out gives a balance sheet at recent prices and an income statement at old ones, and weighted average gives both statements the same smoothed rate, so each formula buys one property by giving up the other. Look at Anjani Stationers' two builds again with that in mind rather than looking at the profit. Under first-in-first-out the Rs 28,00,000 on the balance sheet is 14,000 reams at Rs 200/-, the price of a ream the last time the business bought one. If somebody asks what it would cost to replace that stock, the answer is close at hand. The income statement, meanwhile, is charged at Rs 209.15 a ream on average, and a good part of that came from paper bought in the previous year at Rs 190/-. Under weighted average both statements carry Rs 207.65, neither the current price nor the old price but a construction sitting between them.

The trade-off is the reason both formulas survive rather than one having won. A closing stock figure built from prices two years old stops meaning anything, so a business whose stock turns slowly and whose input prices move a lot cares about the balance sheet going stale. A cost line that swings with the last invoice makes one year incomparable with the next, so a business whose input prices jump about week to week cares about the income statement lurching. Neither of those preferences is more correct than the other, and neither formula produces a truer figure, so any instruction on which one to pick would be inventing a rule that the standards did not write.

Can a business switch from one formula to the other?

Yes, and the mechanism is deliberately awkward. The awkwardness is the point. The formula a business applies is an accounting policyA rule a business has settled on for how it measures and presents a particular kind of item in its accounts. Once chosen it is applied the same way every period, and one year can then be compared with the next., not a working assumption it revisits each year. Changing one is treated as a change of policy, and a change of policy comes with obligations attached.

A change of inventory formula is applied by retrospective applicationRestating the accounts as though the new rule had always been in force, rather than applying it only from the date of the change onwards.. Last year's published figures are restated as though the new formula had always been used, the comparativesThe prior period figures printed alongside the current period in a set of accounts, so the reader can see one year against the other. printed alongside this year are the restated ones, and the reason for the change and its effect are disclosed. Follow what that does to the temptation. Suppose Anjani Stationers' controller, Vaidehi Rao, worked out that switching to weighted average would add Rs 1,07,000 to gross profit and considered doing it for that reason. The prior year would be restated onto the same weighted average basis and would rise too, so the switch would not produce a jump in the accounts. The reader sees two years both on weighted average and no step at all. Then the disclosure names the change, so any reader who wants the old basis can find it. The restatement engineers away the gain from switching to flatter a year. The only reason left is the honest one: the business genuinely thinks the other formula describes its stock better.

The same discipline runs the other way, and that half is the one people forget. A business cannot use different formulas for different years, and it cannot use different formulas for stock of a similar nature and use within the same year either. A business can use different formulas for genuinely different kinds of stock, so a business holding raw paper and also holding a small number of high value machines for resale may well measure the two differently. The choice cannot float with what suits the result.

Is last-in-first-out permitted, and what follows when it turns up?

A third name turns up in older material and in some foreign accounts. Last-in-first-outA cost flow rule under which the most recently acquired costs are treated as leaving first, so the balance sheet retains the oldest costs. Last-in-first-out is not among the formulas Indian standards permit. is the mirror image of first-in-first-out: the newest costs are treated as leaving with the goods sold, so the oldest costs stay behind on the balance sheet.

Last-in-first-out is not permitted under the standards India applies, nor under the international standards those are aligned with, so a set of Indian accounts will be on one of the two formulas worked here and no other. What matters is the consequence for comparison. Certain foreign reporting regimes, most visibly the United States, do permit it. So a stock figure and a cost of sales figure taken from such a filing are not built on the same rule as the Indian figures beside them, and setting the two side by side without adjustment compares two different measurements wearing one label.

The remedy is short. The accounting policy note is where the formula is named, and it is read before any number that depends on it. If the note names a method Indian standards do not permit, the gross margin, the closing stock, the inventory days and every ratio built on them are not comparable to an Indian filing until somebody adjusts them. The filing itself will usually disclose the adjustment. The habit that protects a reader here is the one that protects a reader everywhere in accounts: the note says what the number means, so the policy note comes before the number.

Who reads the difference between the two formulas, and what do they do with it?

Three people open the same accounting policy note in the same week, and none of them is admiring the arithmetic. Each takes something different from it, so watch each of them work.

A lender reads the formula to know how quickly the stock figure it is lending against responds to a price fall, an analyst reads it to make two businesses comparable before comparing them, and Vaidehi Rao reads it to know how much of her own gross margin movement is a real cost movement. The lender's question is the most concrete. If it is lending against Rs 28,00,000 of paper, it wants to know whether that figure is close to what the paper would fetch or sell for today. Rs 200/- is what the mill charged last, so under first-in-first-out it is close. Under weighted average it sits at Rs 207.65, above the last price paid, and in a falling market that gap widens rather than closing. Neither figure is wrong, and the lender simply needs to know which one it is looking at before it decides how much of it to advance against.

The analyst's use comes earlier in the work and matters more. Two stationery businesses can hold identical paper bought on identical dates at identical prices and report gross margins four tenths of a point apart purely because one applies first-in-first-out and the other weighted average. Before any comparison of margins means anything, both policy notes have to be read and any difference has to be put onto one basis or explicitly set aside. And Vaidehi Rao's use is the one that changes a decision this week. Anjani Stationers' gross margin held at exactly 45.0 per cent across two years, and she needs to know whether that flatness is the business holding its costs or the formula smoothing something. On first-in-first-out the closing figure is a single recent price, so it is not smoothing much. Had the business been on weighted average, four tenths of a point of the same year's margin would have come from the rate construction rather than from anything that happened in the godown.

Anjani Stationers Private Limited, Chitra Binding Works Private Limited, Vaidehi Rao, the Sunrise Public School group, the unnamed paper mill and the comparator notebook maker are invented.
Educational material. Not advice on any investment, tax, budget or market position.