Note

Why the mix number depends on the method

Two conventions for the same bridge, both reconciling to the same change of 520: one says units were flat and mix cost 200; the other says volume cost 200 and has no mix line at all. Neither is wrong, because they answer different questions, and almost nobody says which one they asked. A third bridge on the same file also reconciles and puts mix at +220, and that one is wrong: its mix is whatever was left over. What follows is the arithmetic on a book small enough to check in your head, both conventions written out, the ways a bridge quietly stops being true, and how to put the method in front of a board instead of underneath it.

One book, two answers

A price/volume/mix bridge explains a change in sales as a small number of causes: we sold more, we sold a different shape of thing, we charged more, we launched, we lost. It is the chart behind most of the sentences a commercial review produces, and it is the first chart anybody from outside your finance team rebuilds for themselves.

It also has no single definition. There are at least two conventions in common use, both taught, both defensible, and they do not agree. Put them side by side on one book and the line labelled Volume can read 0 under one and −200 under the other, on the same sales, in the same currency, for the same twelve months.

This is not a rounding argument. Adding up is the easy part. The hard part is saying which question you answered.

The notation, once

Per group g — a product, a brand, a customer, whatever the bridge is grouped by:

• V = volume, in whatever unit the file carries
• S = value: net sales, or gross profit
• P = S ÷ V, the achieved price per unit

PY is last year, CY is this year. A group is comparable when it carries volume in both years. Membership is decided on volume, not on value and not on the row being present.

The book

Five lines. The numbers are small on purpose: you can check every one of them in your head.

Net sales are up 520, or 14 per cent. Three facts to hold on to:

• The two continuing lines sold 200 units last year and 200 units this year. In aggregate, continuing volume is flat.
• Both of them raised their prices: A from 10.00 to 12.00, B from 20.00 to 21.00.
• The 20 units A gained are cheap units. The 20 units B lost are dear ones.

The prior-year average price across the comparable lines is 3,000 ÷ 200 = 15.00.

Convention one — Volume / Mix / Price

The consumer-goods convention. It is the one in revenue decks and board packs, and it is the one that can say we grew, but the growth was in the cheap end. Mix is isolated at last year's average price.

Read as a sentence: units were flat; the shape of what we sold moved 200 against us because the growth was in the cheap line; higher prices added 320; a launch added 600 and a delisting took 400; and 200 of the change has no units behind it at all.

Convention two — Price / Volume variance, with the joint effect

The controller's convention, straight out of standard-cost variance analysis: a rate variance measured on base quantity, a quantity variance at base price, and the rectangle where both moved on its own line. There is no mix line. Mix is not lost — it sits inside Volume, because each group's units are valued at that group's own prior-year price.

Read as a sentence: the units we shifted cost us 200 at last year's own prices; we took 300 of price on last year's quantities; 20 arose where price and quantity moved together; launch, loss and the unsplittable as before.

Side by side

Three things to notice.

The totals are identical, and they always are. Prior year, current year and the change do not move when the method changes. Only the middle bars divide that same change differently. If your two bridges disagree on the total, you have a data problem, not a method problem — a different question entirely, and a worse one.

The word Volume means two different things. Under the second convention Volume reads −200 in a year when the continuing lines sold exactly as many units as last year. That is not an error: each line's own units are valued at its own price, so a swap of dear units for cheap ones shows up as volume. But it is not what a commercial director means when he says volume, and on this book that −200 is entirely mix.

The two conventions are the same three numbers, regrouped. This is arithmetic you can verify on the table above rather than take from us, and it holds generally over the comparable groups:

Which means choosing the first convention is a decision that the joint rectangle belongs to price. Choosing the second is a decision to show it on its own line and to let mix hide inside volume. Neither is a discovery about your business. Both are conventions, and a convention that nobody states is a convention nobody can argue with.

Which one to use, and for what

Use Volume / Mix / Price when the question is commercial. Did we sell more, sell richer, or charge more? It is the only one of the two that can put a number on we grew into the cheap end, which is the sentence that starts most useful margin conversations. It is the convention of revenue-growth management and of most board packs, and it is this software's default on every screen that draws the bridge.

Use Price / Volume with a joint line when the question is control. When the audience already lives in rate and quantity variances, when the bridge has to sit beside standard-cost variance reporting and use the same words, or when somebody needs each row to reconcile on its own. That last point is a real difference and it catches people out: under the first convention the per-group rows reconcile only in total, because Volume and Mix are defined against one blended prior-year price; under the second they reconcile row by row, by construction. A reader who adds up a single row under convention one, finds it short, and concludes the numbers are wrong is not being careless. He was not told.

And know what each cannot say. The second convention cannot answer did we sell richer?, because it has no mix line to answer with. The first cannot be laid beside a standard-cost variance report without a translation, because it has already given the joint rectangle to price.

Trap one — mix as the balancing figure

The commonest defect in the wild, and the hardest to see, is a bridge in which mix is not computed at all. It is the plug: the difference between the total change and everything else.

Watch what that does to this book. Take the second convention's computed lines — Volume −200, Price +300, New +600, Lost −400 — and derive the remainder: 520 − 300 = +220. Label it Mix, and the chart reconciles perfectly.

So on one book, from one file, the line called Mix reads −200 under a convention that computes it and +220 under one that plugs it. Same word, opposite sign, 420 apart on a change of 520. A board that hears the first is told the portfolio got cheaper. A board that hears the second is told it got richer. One of those is a conclusion; the other is the leftovers with a label on.

How to test it in thirty seconds. Ask for the formula for the mix line. If the answer is it is the difference, it isn't mix. Or open the workbook and set an unrelated cell wrong: a computed line moves only when its own inputs move; a plug moves whenever anything at all moves, and swallows every error in the model without changing colour.

The rule the software holds to. Every line on a bridge is computed independently, and whatever is left over after all of them is called what it is — a residual, shown on the face, with its own name, and expected to be rounding.

Trap two — launches and delistings dropping out

The second commonest defect is a bridge built only on the lines present in both years — an inner join, usually written without anyone deciding to write it.

On this book that would leave A and B: 3,000 last year, 3,120 this year. The bridge would explain +120, and it would reconcile beautifully to +120, while the profit and loss account says +520. Four hundred of the change — more than three-quarters of it — would be nowhere on the chart, and nothing on the page would look wrong, because a bridge drawn on a smaller book still ties. It describes a different business from the one named in its own title.

The fix is two lines that many bridges do not carry:

• New = Σ SCY for groups with no prior-year volume: +600
• Lost = − Σ SPY for groups with no current-year volume: −400

And then the residue nobody expects: a launch that still carried a little value last year, or a delisting that still carries some this year. Those amounts cannot go in New or Lost without misstating them, so they go on the unsplittable line rather than evaporating.

There is a second way rows drop out, and it is worse because it looks like completeness. Build the same bridge on gross profit where some rows carry no cost, and the groups that cannot be measured are silently dropped from one side. The chart ties perfectly and covers a smaller book than the heading claims. The rule here is to drop such a group from both years, count it, and name it — or refuse to draw the chart at all and say which groups are missing.

Trap three — the check that cannot fail

Every bridge carries a reconciliation check: PY + effects = CY. It is the control the whole artefact rests on, and where one line is the plug, it is a tautology. It passes for any volume and any price whatsoever, including zero. It cannot fail. It never told you anything.

It is easy to miss. A set of automated tests can assert the reconciliation on every run and stay green while pinning not one effect value: swap the convention overnight and nothing goes red.

Two things follow, and both apply just as well to a finance team's own month-end checks.

• A control that cannot fail is not a control. If your month-end check is the bridge ties, establish first whether any line in it is derived from the others. If one is, your check tests subtraction.
• Pin values, not identities. Keep a small book with known answers — five rows is enough, as above — and re-run it whenever the model changes. If an effect moves and nobody meant it to, you find out in the file, not in the meeting.

Once every line is computed, the reconciliation becomes a real test, and the residual is free to mean what it should: float rounding, and nothing else, because every other cause now has a line of its own.

Trap four — value with no volume

The Service line: 300 last year, 500 this year, no units in either. You cannot speak of a price change for something that never had a price, and you cannot speak of a volume change for something that has no quantity. It is 200 of a 520 change — 38 per cent — with no price/volume story available at any level of effort.

In a real file these rows are not exotic. They are rebates and listing fees booked against a customer with no quantity; service, co-packing and freight recharges; credit notes keyed without a quantity; anything that is money but not kilos.

In many reports that 200 hides, in a bar labelled Residual — rounding or in a bar labelled Mix. Both are lies of the mild, ordinary kind that nobody gets sacked for. It belongs on a line of its own, Not split (no volume), with the groups responsible printed beside it, up to four by name and then a count.

The extreme case belongs here too, because it is the one that produces a confident chart out of nothing: a file with no quantity column at all. Every price is then 0 ÷ 0, so there is nothing anywhere to decompose and the entire year-on-year change is unsplittable. The right behaviour is to refuse the chart and say which column is missing, rather than to draw one anonymous bar and let a reader believe it means something.

Trap five — the grain nobody states

Volume and Mix depend on the level at which the bridge is grouped. Change the grouping, or the number of rows shown before the rest is pooled, and the split between volume and mix changes — although the total does not.

The reason is mechanical. At product level, a customer moving from a 500g pack to a 200g pack is mix: two groups, two prior-year prices, units shifting between them. At brand level those two packs are one group with one blended price, so the same movement has nowhere to go as mix and reappears as a price effect, because the smaller pack sells at more per kilo and the brand's achieved price per kilo has risen. Nothing has been miscalculated. The bridge was asked a different question.

Two habits follow. State the grain on the chart, beside the method. And keep it fixed: a bridge drawn at product level in March and at brand level in April has told the board two different stories about the same portfolio, and neither month's chart carries a mark to say so. If you want to know whether a mix number is doing real work, draw it at two grains and see how much of it survives.

Presenting it to a board

The method has to be on the table, not under it. In practice that is six small disciplines, and none of them costs anything:

• Name the method on the chart, in the caption, with its one-line definition beside it — mix separated at last year's average price, or classic variance analysis, price measured on last year's quantity. In this software that name rides on the waterfall, the table's formula column, the help panel and both exports, so a chart cannot circulate without it.
• Print the check line under the chart: Volume + Mix + Price + New + Lost = Δ Total. Where anything was unsplittable, it is part of that sum too and appears as its own bar.
• Say the invariant out loud once: changing the method never changes prior year, current year or the total change — only how the middle bars divide it. It is the sentence that stops a director distrusting both charts after seeing two.
• Show New, Lost and Not split even when they are small, and name the groups on the Not split line. A line nobody can trace is a line nobody trusts, and the first question from the sharpest person in the room will be about the one bar you hoped to skip.
• Answer for the residual before you are asked. It should be rounding. If it is not, something with a name has gone into it.
• Do not change convention mid-year. If you must, restate the prior period on the new convention in the same pack, side by side, and say why. And never circulate two bridges built on different conventions in the same pack — that is the failure that starts the argument this note exists to prevent.

One more, from the finance seat rather than from the software. When a business raises its prices to recover an input cost, the price line on this bridge stops being an achievement and becomes a recovery measurement. The board's question is no longer how much did the higher prices add, but how much of the cost did the price cover, and what did the volume and mix cost us to get it. A bridge whose mix is a plug cannot answer that, because the plug absorbs precisely the thing being asked about.

And assume the bridge will one day be rebuilt by somebody who did not draw it: your auditor, the controller who takes the job after you, a customer's buyer asking why the price moved. An outsider treats an unexplained mix line as exactly that: unexplained. Whatever it contains gets tested, the burden of proof sits with you, and until it is explained it does not count as an explanation of anything.

The checklist, if you read nothing else

Ten questions to put to any bridge, including your own:

1. Which convention is this drawn in, and where does the chart say so?
2. Is the mix line computed, or is it the difference?
3. At what grain is it grouped, and was it the same grain last month?
4. Do prior year, current year and the total change match the P&L, exactly?
5. Where are the launches, and are they measured at this year's value?
6. Where are the delistings, and are they measured at last year's value?
7. What happened to rows with value and no quantity — are they named?
8. What happened to rows the measure could not be computed for at all?
9. What is the residual, and what is it made of?
10. If somebody swapped the method overnight, which of your checks would go red?

If question 10 has no answer, the reconciliation on that chart is decoration.

What the software does about it

Two conventions, both computed, named in finance language, chosen by the reader and stamped on everything that leaves the screen: the chart, the table, the help panel, the Excel export and the image. The choice follows the reader from screen to screen, because a convention that changes silently between two screens is exactly the failure the control exists to prevent. No line is a plug, so the reconciliation is a real test; anything that cannot be split lands on its own named line with its groups listed; and the calculations are checked, effect by effect, against the five-line book above.

Price, volume and mix is one analysis among many in the commercial analytics we build, alongside gross to net, customer and product profitability, pricing, promotions, and trade and marketing spend.