Operating Leverage: How Fixed Costs Amplify a Revenue Movement

Operating leverage measures how hard a revenue movement lands on operating profit, and every bit of it comes from fixed costs. Contribution divided by earnings before interest and tax (EBIT) gives the multiple. Anjani Stationers, an invented stationery business, moved from 1.94 to 2.78 in one year, so a 10 per cent revenue movement that once shifted EBIT by 19.4 per cent now shifts it by 27.8 per cent, in whichever direction revenue went.

The opening boxes hold Anjani Stationers Private Limited's published year two. Revenue of Rs 2,70,00,000 gives up Rs 1,54,50,000 of cost that travels with volume, leaving contribution of Rs 1,15,50,000. Contribution is 42.78 per cent of every rupee that came in. The standing bill of Rs 74,00,000 comes off that and EBIT is Rs 41,50,000, the same figure reached by taking profit before tax of Rs 38,00,000 and adding back the finance cost of Rs 3,50,000. Contribution over EBIT is 2.78. Break-even revenue is Rs 1,72,98,701 and the room above it is 35.93 per cent, and those last two are one fact stated the two ways up.

The machinery underneath is short. The split of Anjani Stationers' costs into the ones that move with volume and the ones that do not is already in hand, and EBIT is already on the statement of profit and loss. Operating leverageA measure of how far a percentage movement in revenue is magnified by the time it reaches operating profit. The magnification comes entirely from costs that do not move when revenue moves. is the result of setting those two facts side by side. Fixed costs sit still while revenue moves, so the whole of a revenue movement, less only the variable cost that travels with it, arrives at the profit line untouched. Profit is a small number sitting at the end of a large one, and a rupee that lands on a small number moves it a long way in percentage terms.

What is operating leverage, and what actually causes it?

Take a household first. The shape is the same one and the figures stay small enough to hold in mind. Two neighbours each take home Rs 50,000 a month. The first pays Rs 10,000 of rent and loan instalments and spends the rest as the month goes. The second pays Rs 40,000 of rent and loan instalments and spends Rs 10,000. Both are level at the end of an ordinary month. Now cut both incomes by a fifth, to Rs 40,000. The first neighbour trims spending and still has Rs 30,000 of room. The second neighbour has Rs 40,000 of commitments against Rs 40,000 of income and no room at all. Identical incomes, identical shortfalls, and the one with the larger standing bill felt it several times harder.

The entire cause of operating leverage is the size of the fixed cost baseThe total of the costs a business carries in a period whether it sells a great deal or very little: rent, salaries, insurance, audit fees and depreciation are the usual members. relative to the profit sitting above it, and no decision, strategy or intention is involved at any point. A business with almost no fixed cost passes a revenue movement through to profit nearly one for one. A business carrying a large standing bill has already committed that bill before the first sale of the year, so every rupee of contribution that arrives or fails to arrive lands on profit whole. A committed bill and a moving contribution is the whole mechanism. The mechanism is arithmetic, not a policy anyone adopted.

Anjani Stationers runs a shed on rent, employs people on salaries, insures the premises, pays an audit fee and took a second warehouse during year two. None of those costs asks how many notebooks left the building. Set that Rs 74,00,000 of standing cost against year two EBIT of Rs 41,50,000 and the shape of the answer is already visible: the standing bill is nearly twice the profit, so the profit is the thin slice left after a thick one has been paid, and thin slices move in large percentages.

Why does contribution divided by profit give the multiple?

The formula is short and the reasoning behind it is shorter still, so it is worth doing properly once rather than memorising. EBIT is contribution less fixed cost. Fixed cost does not move when revenue moves. Therefore any change in EBIT is exactly and only the change in contribution, rupee for rupee, with nothing lost on the way.

Contribution, meanwhile, is a constant percentage of revenue, so a 10 per cent revenue movement is a 10 per cent contribution movement. Taking the two together, a 10 per cent revenue movement produces a change in EBIT of one tenth of contribution. Expressed as a percentage of EBIT, that change is one tenth of the ratio contribution over EBIT. Contribution over EBIT is therefore not a formula to be taken on trust but the direct consequence of fixed cost standing still, and that single ratio converts any percentage revenue movement into a percentage profit movement.

The ratio contribution over EBIT has a name. The degree of operating leverageThe number by which a percentage change in revenue is multiplied to get the percentage change in operating profit. Computed as contribution divided by operating profit at a stated level of revenue. is contribution divided by EBIT, computed at a stated level of revenue. Notice what the ratio contains and what it does not. The ratio contains no forecast, no view about the future and no judgement. It is a description of a cost structure at one point, and it is as true of a bad year as a good one.

What is the degree of operating leverage for Anjani Stationers in both years?

Both years are computed below from the split already established, with the inputs restated so the arithmetic can be checked in place. Everything in the table reconciles to the published operating profit in both columns.

The movement between the last two rows is the finding, so read them together rather than one at a time. The numerator rose 12.6 per cent while the denominator fell 21.7 per cent. A ratio whose top rises while its bottom falls moves further than either of its parts, and so 1.94 became 2.78 and not something modest. Contribution went from Rs 1,02,60,000 to Rs 1,15,50,000 because the business sold more. EBIT went from Rs 53,00,000 to Rs 41,50,000 because the standing bill grew faster than the extra contribution. The multiple rose 43.8 per cent on the back of those two opposite movements.

No Indian statutory filing splits costs into the ones that move and the ones that do not, so the Rs 74,00,000 is an estimate an analyst has to build. Two careful readers of the same statements reach two fixed totals and therefore two multiples, neither of them a mistake. A multiple is therefore quoted with its split, every time.

What does a multiple of 2.78 do to a revenue movement in each direction?

Now the part most treatments skip over. A multiple describes amplificationThe enlargement of a movement as it passes from one measure to another. A revenue movement arrives at profit larger than it started, and the enlargement works on falls exactly as it works on rises. and amplification has no preferred direction. The same 2.78 that turns a 10 per cent revenue rise into a 27.8 per cent profit rise turns a 10 per cent revenue fall into a 27.8 per cent profit fall, and it does so by exactly the same arithmetic with exactly the same numbers, only with the sign reversed.

Computing both sides in rupees is the only way to see that nothing has been smuggled in, so work both sides rather than trusting the multiple. Revenue up 10 per cent is Rs 2,97,00,000. Contribution at 42.8 per cent is Rs 1,27,05,000, and taking off the unchanged Rs 74,00,000 leaves EBIT of Rs 53,05,000. EBIT is Rs 11,55,000 higher, or 27.83 per cent. Revenue down 10 per cent is Rs 2,43,00,000. Contribution is Rs 1,03,95,000, and taking off the same unchanged Rs 74,00,000 leaves EBIT of Rs 29,95,000. EBIT is Rs 11,55,000 lower, or 27.83 per cent. The rupee amount is identical on both sides because contribution moved by the same Rs 11,55,000 in each case, and a reader who has only tested the upside has read half of a two-sided measure and formed a whole opinion on it.

Each row below was computed in rupees first and only then checked back against the multiple.

What pushed the multiple from 1.94 to 2.78?

Two things could in principle move the multiple: the share of each rupee left behind by a sale, and the size of the standing bill. Only one of them moved. Contribution marginThe share of every rupee of revenue that survives the costs moving with volume, and is therefore available to cover the costs that do not move. held at 42.8 per cent across both years, 42.75 per cent the first year against 42.78 per cent the second, three hundredths of a point apart. The fixed cost base closed the year at Rs 74,00,000 against Rs 49,60,000, so Rs 24,40,000 was added to it, a rise of 49.2 per cent set against revenue growth of 12.5 per cent.

The loose version of this attribution gets the direction wrong, so do it properly. Hold the fixed base at year one's Rs 49,60,000 and apply year two's revenue and contribution: EBIT would have been Rs 65,90,000 and the multiple would have been 1.75. Revenue growth on its own was pushing the multiple down from 1.94 to 1.75. The fixed cost rise then carried it all the way from 1.75 to 2.78. The standing bill did more than the whole of the work. The profit denominator grows while the bill stays put, so growing revenue against an unchanged standing bill always reduces operating leverage. Anjani Stationers got the opposite result only because the bill grew four times faster than revenue did.

The split is not on the face of the statement, but the components of the Rs 24,40,000 are, so name where each sits. Employee benefits rose Rs 6,00,000. The fixed part of other operating costs rose Rs 11,40,000, mostly the second warehouse taken during the year. Depreciation and amortisation rose Rs 7,00,000 on the assets bought. Not one of those three decisions was a decision about operating leverage, and yet together they raised it by 44 per cent. A multiple that rises 44 per cent on the back of three decisions about something else is a consequence rather than a choice. A business that puts capacity in place before the volume arrives raises its own amplification mechanically, on the way to doing something else entirely.

Why is this the same finding as the margin of safety, upside down?

The margin of safety here is the cost accounting one, the distance between revenue achieved and break-even revenue. The phrase also names the margin of safety in value investing, the sense Benjamin Graham gave it, where it measures how far under an estimate of worth a price has been paid. The two measures have nothing in common but the words.

One relationship prevents one fact being counted twice, and it is worth checking rather than believing. Anjani Stationers' margin of safety was 51.7 per cent in year one against a multiple of 1.94, and 35.9 per cent in year two against a multiple of 2.78. Multiplied out on the figures behind the display, rather than on the printed ones, each pair gives one. Not approximately one. Exactly one, at every level of revenue and every level of fixed cost. Multiplying the printed readings instead gives 0.999998 for year two. The shortfall is the rounding in the two displays, and none of it is in the arithmetic.

The algebra is three lines and worth following once. Break-even revenue is fixed cost divided by the contribution margin. Take revenue less break-even and divide by revenue, and that is the margin of safety; it equals one less break-even over revenue, and therefore one less fixed cost over contribution. One less fixed cost over contribution is contribution less fixed cost, over contribution, and contribution less fixed cost is EBIT. So the margin of safety is EBIT over contribution, and the degree of operating leverage is contribution over EBIT. The two are the same fraction the two ways up. A margin of safety and a degree of operating leverage are one finding stated twice, never two items of evidence.

Two things follow. Either figure computes the other with no further input, so a business at a 25 per cent margin of safety has a multiple of 4 and a business at a multiple of 5 has a margin of safety of 20 per cent. And a note quoting both, as though a thin cushion and a high multiple were two observations pointing the same way, has doubled the weight of a single fact. Say it once, and say which way up.

Three positions of the standing bill are worth knowing by heart. At the published year two, revenue Rs 2,70,00,000 and standing bill Rs 74,00,000, the multiple is 2.78 and the margin of safety 35.93 per cent. Pull the standing bill down to Rs 50,00,000 and EBIT rises to Rs 65,50,000, the multiple falls to 1.76 and the margin of safety widens to 56.71 per cent, and the two still multiply to exactly one. Push it to Rs 1,00,00,000 and EBIT is Rs 15,50,000, the multiple is 7.45 and the cushion is 13.42 per cent. A movement cannot be expressed as a percentage of nothing, so at a standing bill of exactly Rs 1,15,50,000, where the whole of contribution is consumed and EBIT is nil, the multiple has no value at all. Push past that point and the arithmetic still returns a number, now negative, and it no longer means amplification of anything: EBIT is a loss, the base revenue sits below break-even rather than above it, and the honest report is that the measure does not apply here rather than that leverage has turned negative.

Where does the measure stop working?

Three limits follow, and every one of them bounds whether the number describes anything at all, rather than qualifying how precisely it does so. The first is the relevant rangeThe span of activity over which a cost really does behave the way the split assumes. Push the arithmetic outside that span and the fixed total in it is no longer the right fixed total.. Fixed costs are only flat over a band. A shed fills, a shift is added, a second warehouse is taken, and beyond the band fixed costs move in jumps rather than in slopes. Anjani Stationers took its second warehouse during year two and its monthly standing cost jumped by Rs 50,000 the moment it did. The Rs 50,000 jump is a step costA cost that stays flat over a range of activity and then jumps to a new flat level, rather than rising smoothly. A second warehouse or an extra shift adds one in a single move., and pushing the plus 30 per cent row of the amplification table through a cost structure that would have stepped somewhere before it is an arithmetic exercise rather than a reading.

The second is that the multiple is computed at a point. The multiple is contribution over EBIT at one stated revenue. The moment revenue moves, EBIT has moved, and the multiple moves with it. At Anjani Stationers' plus 10 per cent row, the multiple recomputed at Rs 2,97,00,000 is Rs 1,27,05,000 over Rs 53,05,000, or 2.39, not 2.78. The multiple describes the next small movement from the stated position, not a property the business carries with it, so a large movement computed off a single multiple overstates the far end of the range in both directions. Use it for the first step and recompute after.

The third is the one that should be printed alongside every quoted figure. The split behind the multiple is an estimate, so the multiple is an estimate. Writing it as 2.78313 when the fixed total behind it was a judgement about which part of other operating costs moves with cartons is false precisionStating a result to more decimal places than its inputs can support, so the figure looks measured when the number behind it was estimated.: five figures of apparent measurement resting on one figure of judgement. Two decimals on a multiple whose denominator came from an assumption tells the reader the answer is measured when it is estimated, and the fix is not fewer decimals but the assumption printed next to the answer.

Where in a filing does each input sit?

Field notes, and they say where a figure is found rather than what it means. EBIT is not a line item in the Schedule III format, so it has to be built: profit before tax is taken off the face of the statement and the finance cost added back. Anjani Stationers' year two profit before tax of Rs 38,00,000 plus finance cost of Rs 3,50,000 gives Rs 41,50,000, the EBIT behind every multiple above. Revenue is revenue from operations, on the face of the same statement, taken before other income.

Contribution is not in the filing at all and has to be assembled from lines that are. The materials line, employee benefits, other expenses and depreciation are each printed on the face, and it is the note to other expenses that pulls carriage outward, packing, rent, insurance and the audit fee apart from one another. A degree of operating leverage without its revenue point is a number with no address, so record which year's revenue the multiple was computed at, in the same line as the multiple itself.

Who computes operating leverage, and what do they do with it?

Three people open the same statements in the same week and put the multiple to three different uses, none of which is admiring it.

A lender uses the multiple to size how far revenue can fall before interest stops being covered, an equity analyst uses it to decide how much of a profit movement to attribute to the sale and how much to the structure, and Vaidehi Rao uses it to know what a slow quarter will do to the year before the quarter happens. Watch the lender first. Interest of Rs 3,50,000 has to be covered as well as the Rs 74,00,000 standing bill, so the lender is not asking where profit reaches zero but where it reaches Rs 3,50,000. The revenue at that point is Rs 77,50,000 divided by 42.78 per cent, or Rs 1,81,16,883, and it leaves 32.9 per cent of revenue as room rather than 35.9. The multiple told the lender how quickly the room closes: a 10 per cent revenue fall does not remove a tenth of the cushion, it removes more than a quarter of the profit sitting on top of it.

The analyst's use is a discipline rather than a number. EBIT fell 21.7 per cent while revenue rose. Revenue moved the wrong way to explain that fall, and an analyst who knows the multiple sees at once that the explanation must be elsewhere. The enquiry goes straight to the structure, where the Rs 24,40,000 was. And Vaidehi Rao, as the finance controller, uses the multiple in the one direction the outside world cannot: forward, on a monthly cash view, where knowing that a 10 per cent shortfall against plan costs Rs 11,55,000 of operating profit rather than Rs 4,15,000 is the difference between noticing early and noticing at the audit.

One boundary belongs with all three uses. Operating leverage says how hard a movement will land and says nothing whatever about how likely the movement is. A stationery business selling into schools has a revenue pattern set by a school year, and a multiple of 2.78 knows nothing about that pattern. Pairing the multiple with a view on how volatile revenue actually is takes two separate jobs, and only the first of them is arithmetic.

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