Cannibalisation: When Your New Product Eats Your Old One

A new line that takes sales from the old one has not lost those sales, it has moved them. Whether the move pays turns on one ratio: the new line's contribution a unit over the old line's. The ratio names the share of new sales that may come out of the old line before the business is worse off, and neither price appears in it anywhere.

A stall adds a cheaper plate and six regulars switch. Is that a problem?

The question almost never arrives as arithmetic. A business is already selling something. The business puts a second thing on the counter beside the first. People buy the second thing. Some of those people, had the second thing not existed, would have walked out with the first one instead. Somebody at a table then asks the one question everything turns on: is that a problem?

Take it out of the office and put it on a footpath. A stall outside one office building sells one plate of food at one price, and it has been selling it for years. The stall adds a cheaper plate beside it. Over a week, ten people buy the cheaper plate. Six of them are regulars who, every previous week, took the usual plate. The usual plate cost more than the other four wanted to spend on lunch, so those four had never stopped at the stall at all, though they work on the same street.

Nobody walked away. Nobody ate twice. The stall lost six sales of the usual plate and gained ten of the new one, and that sentence on its own decides nothing at all. The sentence describes what happened completely and it still contains no answer. The answer depends on a quantity nobody has mentioned yet.

The two prices are the two numbers printed on the two things, so the mind goes straight to them. Everybody at the table knows them, nobody has to look them up, and dividing one by the other produces a tidy figure in about four seconds. The instinct to divide the two prices is the whole trouble on this subject.

So what does the whole subject rest on?

A displaced sale is not a lost sale, and every mistake on this subject starts by treating the two as the same event. The buyer still bought. The buyer still bought from the same business. The money still crossed the counter. The only change is which of the two lines the money crossed through. So the question is never how many sales were displaced, taken on its own. The question is what the difference between the two lines was worth on each displaced sale. The difference is a far smaller quantity than the sale itself, and it is the only quantity that moved at all.

A displaced unit was never made, so what it destroys is its contribution and not its price. The old line's unit that nobody bought consumed no materials and took up no carriage. The business gave up the price and saved the variable costCost that rises when one more unit is made and falls when one fewer is made. Materials and carriage behave this way; rent does not. in the very same instant, and the difference between those two amounts is exactly the contribution a unitThe amount a single unit adds to the pot once everything that rises and falls with it is settled. A separate part of these notes assembles it.. Every price is a distraction for that reason, and two of them are printed anyway so the wrong test can be watched being run on them.

Setting the gain against the loss leaves a ratio of the two contributions and nothing else in the expression. Sell one unit of the new line and the business gains that line's contribution. If some share of new units displaces old units one for one, it gives up that share of the old line's contribution. The two are equal when the share equals the new contribution divided by the old one, and no other term survives the cancellation. One division, two inputs, and both inputs are things the business already knows about itself without asking anybody.

A cost that is the same at every answer cannot change the answer, which is why the standing base is absent from a test everybody expects it in. Rent, salaries and space sit exactly where they sat whether the buyer took the old line or the new one, so they appear on both sides of the comparison and cancel out of it. The test is a contribution test rather than a profit test for that reason alone. Where a new line brings standing costSpending that turns up at the same size whatever the week's selling does. Rent and wages are the everyday examples of it. of its own, that is a separate subtraction from the total the business keeps, and it leaves the displacement threshold precisely where it was.

Which two questions keep getting confused?

There are two questions in this subject and they wear similar clothes. The first is how much the new line sold. The second is how much of what it sold came out of the old line. The first question is answered by the till and the second is answered by nobody.

Look at what the second one is actually asking, in the buyer's terms rather than the business's. Of the people who bought the new thing, how many would have bought the old thing today if the new thing did not exist? The answer is not a fact about a transaction. The answer is a counterfactualA statement about what would have happened in a situation that did not occur. It cannot be observed directly, because the situation it describes never took place. about a person's intention in a world that did not happen, and no record anywhere in the business contains it. The till knows what was bought. The till does not know what would have been bought instead.

The difficulty is real, and naming it early keeps it from becoming a surprise. The first move is to establish what the number would mean if somebody produced it. Who can produce one, and what producing it costs, is settled below.

Where does the one ratio actually come from?

Build it in words before any symbols arrive, one step at a time, and stop after each step to check that it is still obviously true.

Step one. One unit of the new line sells, and the business gains the new line's contribution a unit. Nothing else has happened yet.

Step two. Suppose that sale displaced one unit of the old line. The displaced unit was never made and its materials were never bought, so the business gives up the old line's contribution a unit and gives up nothing else whatsoever.

Step three. Not every new sale displaces an old one. Some new buyers are genuinely new, like the four people on the street outside that office. Write the share of new sales that does displace as the displacement rateThe share of the new line's sales that came out of the old line rather than from buying that would never have happened..

Step four. So, per new unit sold, the business is ahead by the new line's contribution less the displacement rate multiplied by the old line's contribution.

Step five. Set that expression to zero and ask which displacement rate balances it. The balancing rate is the new contribution divided by the old contribution. The threshold is the ratio of the two contributions, and nothing else survives the cancellation.

The arithmetic ends there. One division. Everything printed around it exists because the division is easy and using it honestly is not.

What do the figures look like when somebody prints them?

One label governs all four figures below. The four are arithmetic demonstrating a property rather than a business. The construction carries no name, no trade, no country and no year, and it says unit everywhere a real case would say what the thing actually is.

The old line's contribution is Rs 46.20/- a unit, a figure published in these notes under how one works turns paper into finished goods. The old line's realised priceWhat the seller actually received a unit after any discount, rather than the price on the list. is Rs 108.00/- a unit, published in the same place. The new line's contribution is a demonstration figureA figure invented so that an arithmetic property can be watched. It carries no business behind it and describes nothing that happened. of Rs 34.65/- a unit, invented so the property can be seen. The new line's price is a second demonstration figure of Rs 86.40/- a unit, and it carries nothing behind it either.

Now the division. Rs 34.65/- over Rs 46.20/- is 0.75, so the threshold is 75.00 per cent. Three quarters of the new line's sales may be buying switched out of the old line before this business is worse off than it was.

One honesty line, and it is what makes a construction respectable rather than merely convenient. The two demonstration figures were chosen so the division lands on exact numbers, and the property does not depend on that in any way at all. Two untidy figures produce an untidy ratio that behaves identically. Worth noting in passing: the new line's contribution is 40.10 per cent of its price while the old line's published contribution is 42.78 per cent of its own. The small difference in shape is the entire reason the two tests below disagree.

What does the threshold look like in money, on either side of it?

A boundary that has to be taken on trust is worth very little, so it is priced here. A hundred units of the new line bring in Rs 3,465.00/- of contribution however the displacement falls, and three settings of the rate run underneath that.

Read the outer two rows together. The relationship is a straight line and not a cliff, so fifteen points either side of the threshold is the same Rs 693.00/-. Nothing dramatic happens at 75.00 per cent. The line simply crosses zero there, on its way from one side to the other, at a steady Rs 46.20/- of swing for every point of displacement across a hundred new units.

The straight line buys something worth having. There is no rate at which the new line suddenly becomes a disaster, and there is no rate below which it is safe. The threshold is a crossing point rather than a limit, and anybody who converts it into a rule saying that some level is unacceptable has added a judgement that the arithmetic did not supply.

A household version, and the shape is the same one. One earner in a household takes a job closer to home at a lower salary. The saving on the fare offsets the cut exactly at one number of travelling days a week, and at no other. Below that number the household is behind, above it the household is ahead, and the amount by which it is ahead or behind grows steadily with distance from that one number. Nobody in the household experiences a cliff. The household experiences a slope with a break-evenThe setting at which two opposing amounts are exactly equal, so the net effect is nothing. Past it the sign flips. somewhere on it.

Why the two contributions and never the two prices?

Run the wrong test in full, and let it look as reasonable as it genuinely does. The two prices are Rs 86.40/- and Rs 108.00/-. Rs 86.40/- over Rs 108.00/- is 0.80. So the tolerance is 80.00 per cent. The figure is clean, it is correctly divided, and it is the answer to a question nobody asked.

When a new sale displaces an old one, the old unit is not made. Nobody buys paper for it. Nobody pays carriage on it. The business never spends the Rs 61.80/- that the old unit would have cost it, so the business never gives up the Rs 108.00/- that the old unit would have brought in either. The business gives up the gap between the two, Rs 46.20/-, and the price test compares a quantity that was never at stake. The cost not incurred on the unit that was never made is the whole of why the price test is wrong.

A general warning is worth much less than a stated bias, so name the direction of the error too. When the new line carries the thinner margin, as it does in this construction, the price version reports more room than the business actually carries: 80.00 per cent against a real 75.00 per cent. Only that direction is worked here. Turn it round, give the new line the fatter margin, and the price version runs the other way and condemns a line that would have paid. The price version is the same arithmetic read from the other end.

Where do the rent and the salaries go?

One question is still open at this point. A business carries rent, salaries, space and a great deal else that arrives whether anybody buys anything at all. Where does that go in this test?

The standing base goes nowhere. A cost that does not change with the answer cannot change the answer. The rent is the same amount if the buyer takes the old line and the same amount if the buyer takes the new one, so it appears on both sides of the comparison and cancels straight out of it. The test is a contribution test and not a profit test for that reason, and arithmetic about whether a swap pays can run its whole length without a single standing figure appearing in it.

Now the honest exception, handled properly rather than waved away. Suppose the new line brings standing costs of its own: another shift supervisor, another rented space, another machine sitting there whether it runs or not. The extra spending is real and it comes out of the total the business keeps, as a separate subtraction. The threshold compares what each unit leaves behind, and a standing cost leaves nothing behind on any unit at all, so the extra spending does not move the displacement threshold by a single point. Two questions, two answers, and folding them into one ratio is how a clear test turns into a muddle.

One assumption is held throughout and it is worth stating outright. The standing base is held fixed through every setting here, in the table, in the drawings and inside the panel. A standing cost, and how it differs from one that moves, is covered separately under Fixed Costs vs Variable Costs. There is one more inheritance worth naming: the source that publishes Rs 46.20/- states the split between what moves and what stands still as a judgement made by somebody, rather than as something a filing disclosed, so any work borrowing that figure borrows the judgement along with it.

Can anybody outside the business see any of this?

No, and the reason is structural rather than a gap somebody could close by disclosing more carefully.

A published revenue line is an addition. Units, revenue and contribution are all sums taken across both lines, and the sum is exactly the same whether every new buyer switched out of the old line or every one of them was somebody who had never bought before. Published accounts show the sum and never the split. Two businesses with wildly different displacement rates and the same total will file the same figure, and nothing in the filing distinguishes them.

There is a second trap sitting beside that one. A fall in the old line's units is not evidence of displacement either. A falling line is equally consistent with fewer buyers overall, with one large account going elsewhere, with an order pattern that shifted a month across a year end, and with all three at once. The accounts contain nothing whatsoever that separates them, so reading a cause out of a falling line is reading something that is not printed.

The same limit has already appeared once, on the spending side. Money spent on something new and money spent on more of the same reach the outside as one line, and the accounts alone cannot tell the two apart. The identical problem shows up here on the volume side. Same limit, different column.

So what is the honest output? A statement that the split is not disclosed, followed by the short list that would have to reach the outside before anybody could compute it: what each line sold, and what each line's contribution a unit was, both by line and both covering the same period. The list is short, and no filing anywhere asks for it. Naming it is worth far more than a figure assembled out of the things that happen to have been printed.

What would the business itself have to do?

Move inside the building and half the problem disappears. The business knows its own prices and its own costs that move, so it already knows both contributions. The threshold costs it one division and about a minute.

The displacement rate is the one thing the business does not hold, and cannot hold by looking harder at its own records. The rate is a statement about what buyers would have done rather than about what they did, so no ledger produces one. Three routes exist and each is worth something different.

Ask the buyer at the point of sale. Asking produces an answer quickly, and it produces it from the person who actually knows, and the speed is the attraction. Accuracy is what asking does not produce. People answer a question about their own counterfactual intention in about a second and a half, and they answer it agreeably.

Compare buyers who could reach the new line with buyers who could not. Where the new line is available in some places and not others, the difference between the two groups says something about displacement that no single group can say. Comparing two groups produces a difference rather than a count, and it needs the two groups to be alike in the ways that matter.

Watch the old line's units and attribute the whole movement to the new line. Watching the old line's units needs no fieldwork and no design, so it is the route that requires the fewest steps and the most assumption, and by a distance the most common. Everything said above about a falling line applies to it in full.

The threshold is arithmetic and the rate is evidence, and only one of the two can be produced at a desk. The sentence names exactly where the effort has to go, and exactly which half of the answer somebody skipped when the work arrives finished.