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Price-Volume-Mix Analysis

Price-volume-mix analysis splits a change in revenue or margin into the parts caused by price, volume, and mix, so the story behind the number is clear.

The questionOf this change in revenue or margin, how much came from price, how much from volume, and how much from selling a different mix?

PVM. Also called a PVM bridge, a sales variance bridge, or price-volume-mix.

Formula · Management accounting practice, 20th century

Change in revenue

Price New prices on current volume

Volume More or fewer units, prior mix

Mix Shift among products, prior prices

FX Translation, if relevant

Simplified bridge from last period's revenue to this one. FX is used when results are translated.

When to use it

Revenue or gross margin moved, and the board is being told "volume was up" when price, mix, and currency may have done the work.
Two products or two channels moved in opposite directions, and a single growth rate is hiding which one.
A budget-versus-actual review needs one bridge that finance, sales, and the general manager will all argue from.
A price increase was taken and you need to see how much of the extra revenue is still there after volume and mix moved.

When to avoid it

There is only one product and one currency. Price and volume are enough, and mix is empty by construction.
The data cannot separate price from discounting, or units from a change in pack size. The bars will be artifacts of the file, not of the business.
You need to know which activities caused the cost side to move. Activity-based costing follows the work. PVM follows the selling-price and unit story.
A one-off item, such as a large catch-up invoice or a destocking, dominates the gap. Split that out first or it will land in mix.

Overview

Price-volume-mix analysis splits a change in revenue, or in contribution, into the part that came from selling at different prices, the part that came from selling more or fewer units of the old mix, and the part that came from selling a different blend. A fourth bar, FX, holds translation when the books are in another currency. The choice it supports is which of those stories is true, before anyone acts on “volume was up.”

The bars add to the gap only if the convention is fixed. This note puts price on current units so that price and volume do not leave a leftover interaction. Mix is a share shift at old prices, not a dumping ground. Rebuild the same bridge on contribution before treating a richer revenue mix as a better business.

The four effects

Price

The change in selling price, including list, mix of discount, and surcharge, holding the current basket of units fixed. A price bar can be positive while unit prices on the hero product fell, if a surcharge elsewhere rose. Always show it by product, not only in total.

Volume

The change in total units, priced at last period's mix and last period's prices. It answers "if we had sold more of the same thing." Growth that comes from adding a cheap product does not belong here. That is mix.

Mix

The shift in the share of products, channels, or customers, valued at last period's prices. Selling more of a higher-priced item, and less of a lower-priced one, raises revenue with no price increase and no extra total units. The same bar on a margin bridge uses contribution per unit, not price.

FX

The translation effect when local prices and volumes are reported in another currency. Compute price, volume, and mix in constant currency first, then put the spot-rate movement in its own bar. Folding FX into price makes a weak dollar look like a price increase.

What it is not

A full profit bridge. This split explains revenue, or gross margin if you rebuild it on contribution. Cost bars, such as input prices and efficiency, are a different bridge.
A unique algebra. Two teams can both be right and still put the interaction of price and volume in different bars. Write the convention on the chart.

The steps

Lock the perimeter and the convention

State what is being bridged, revenue or contribution, from which period or budget, in which currency, and whether price uses current units or prior units. Write that on the chart. If FX matters, do the first three bars in constant currency.
Get units, prices, and groups that add up

Pull units and net selling prices by product, or by the grouping you will explain, such as channel. Reconcile to reported revenue before you split anything. A bridge that does not add back to the accounts is not usable.
Compute the three, then FX

Calculate price on current units, volume as total-unit change at prior mix and prior prices, and mix as the rest at prior prices. Add FX last. Show the bars in money and as a share of the gap.
Go one level down on the bar that matters

Split the largest bar by product or channel. A positive price total can hide a cut on the hero SKU. A positive mix can be one customer leaving a cheap line.
Write the story as causes, not as bars

Each bar becomes a hypothesis, such as discount leakage, destocking, or a shift to a smaller pack. The output is those questions, with the dollars attached, for sales and operations, not the chart as the finding.

The formula

ΔRevenue = Price + Volume + Mix [+ FX], with Price = Σ (P1 − P0) × Q1, Volume = (Q1 total − Q0 total) × prior mix-weighted price, Mix = Σ P0 × (Q1 − Q0 scaled to the new total)

The change in revenue is the sum of a price effect on the units you actually sold, a volume effect as if the old mix had grown or shrunk in one piece, and a mix effect from selling a different blend at old prices. Add FX only after those three are done in constant currency.

P0, P1: selling price of each product (or channel) in the prior period and this one, in constant currency.
Q0, Q1: units of each product in the prior period and this one.
Prior mix-weighted price: prior revenue divided by prior total units, or equivalently each prior price times its prior share.
Q0 scaled to the new total: each product's prior share times Q1 total, which is the constant-mix basket.
FX: this period's local-currency result translated at this period's rate, minus the same result translated at the prior rate. Leave it out in a single-currency book.

In practice

A drinks company reports revenue of $110 million last year and $126.6 million this year, up $16.6 million, and the sales story is "volume and a price increase." Two products. Last year: cola 40 million units at $2.00, sparkling 10 million at $3.00. This year: cola 42 million at $2.10, sparkling 12 million at $3.20. Price, using this year's units: cola (2.10 − 2.00) × 42 million = $4.2 million, sparkling (3.20 − 3.00) × 12 million = $2.4 million, so price is +$6.6 million. Total units went from 50 million to 54 million. At last year's mix, 80 percent cola, that extra 4 million units would have been 3.2 million cola and 0.8 million sparkling. Volume at last year's prices is 3.2 × 2.00 + 0.8 × 3.00 = $8.8 million.

Mix is this year's basket against that constant-mix basket, at last year's prices. Cola is 42 million against 43.2 million, a shortfall of 1.2 million units at $2.00, −$2.4 million. Sparkling is 12 million against 10.8 million, an extra 1.2 million at $3.00, +$3.6 million. Mix is +$1.2 million. The three bars sum to 6.6 + 8.8 + 1.2 = $16.6 million, which is the whole gap. About 40 percent of the increase is price, 53 percent is more units of the old mix, and 7 percent is a richer mix. The board pack that said "volume" was giving mix and a price rise to the volume line. If the same bridge is rebuilt on contribution, and sparkling carries twice cola's contribution per unit, mix would do more of the margin work than of the revenue work, which is the next slide, not a reason to skip this one.

What you leave with

A bridge from prior, or from budget, to actual, with price, volume, mix, and FX if used, adding to the reported gap.
The convention written on the chart, including whether price used current or prior units.
The same bridge by product or channel for the bar that dominates.
A short list of causes to test, each tagged to a bar.

Failure points

Volume meaning "everything that is not list price"

Mix, extra units, pack-size changes, and destocking are all labeled volume. The conversation then goes to capacity when the actual issue is discounting or a richer basket.

Interaction dumped into mix

Price is computed on old units, volume and mix on old prices, and the leftover ΔP × ΔQ is called mix. Mix then moves when prices move, and the story is wrong.

FX inside price

A reporting-currency increase is read as a price rise. Local prices were flat, and the dollar moved. Separate constant-currency PVM from translation.

Packs treated as units

A shift from a 12-pack to a 6-pack doubles unit count at a lower price and manufactures a volume boom and a price crash. Define the unit as the comparable item, or add a pack-mix bar.

Stopping at revenue

The revenue bridge looks healthy because mix shifted to a high-price, low-contribution item. Rebuild the same bars on contribution before you congratulate sales.

The failures above are usually Commercial Acumen: the work was not tied to money, for the client and/or for you.

Origin

Splitting a sales gap into price and volume is standard-costing work, taught as sales price variance and sales volume variance. When the "volume" line still hides a shift from cheap products to dear ones, or the reverse, that volume variance is split again into a quantity effect at the old mix and a mix effect at old prices. Textbooks such as Horngren's cost-accounting line set out the algebra. Consulting and FP&A teams use the same split as a bridge from last period, or from budget, to this period, and they often add a foreign-exchange bar when local-currency results are translated into the reporting currency.

There is no trademark and no founding paper that consultants are expected to cite. What has to be cited, in the work itself, is the convention used for the interaction of price and volume, because that choice moves the bars. This note uses current volume for the price bar, so there is no leftover interaction term, and prior prices for volume and mix.