The formula is one line. The input most teams get wrong is the margin, and the error always runs in the dangerous direction.
A price increase stops adding EBITDA when the volume it loses reaches price rise ÷ (contribution margin + price rise). For a 4 per cent increase in a business with a 40 per cent contribution margin, that is 9.09 per cent of volume. Use the EBITDA margin instead of the contribution margin and you get 21.1 per cent, and a plan that can lose money while the model says it is safe.
Worked in full in The Private Equity Operating Partner by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Pricing is the first lever most operating partners pull after a buyout, because every point of price that sticks drops straight to EBITDA. The question the board asks is how many customers the company can afford to lose. The answer is a one-line formula, and the only input people get wrong is the margin.
| Input | Value |
|---|---|
| Revenue | 120.0 |
| Variable costs (60% of revenue) | 72.0 |
| Contribution | 48.0 |
| Fixed costs | 30.0 |
| EBITDA | 18.0 |
| Contribution margin | 40% |
| EBITDA margin | 15% |
| Proposed price increase | 4% |
If no customer leaves, the whole increase is profit: 4 per cent of 120.0 is 4.80 of extra EBITDA. Each unit of volume that leaves takes away its new price and saves its variable cost. Set the new contribution equal to the old one and solve for the volume loss L:
(1 + p)(1 − L) − v(1 − L) = 1 − v ⇒ L = p ÷ (c + p)
where p is the price rise, v the variable cost ratio and c = 1 − v the contribution margin.
=B8/(B6+B8) with the contribution margin in B6 and the price rise in B8.Fixed costs drop out of the equation because they do not change. That is why the formula needs the contribution margin, not the EBITDA margin: only the costs that leave with the customer belong in it.
Suppose the commercial team estimates 3 per cent of volume will walk.
| Line | Before | After 4% price, 3% volume lost |
|---|---|---|
| Revenue | 120.0 | 121.056 |
| Variable costs | 72.0 | 69.84 |
| Contribution | 48.0 | 51.216 |
| Fixed costs | 30.0 | 30.0 |
| EBITDA | 18.0 | 21.216 |
EBITDA rises by 3.216, against 4.80 on the no-loss plan. Each point of volume lost costs 0.528 of EBITDA. At a 10.0× exit multiple the 3.216 is worth 32.16 of enterprise value, which is why this lever appears in almost every value creation plan.
First, the same 4 per cent increase at different levels of churn:
| Volume lost | EBITDA | Change vs 18.0 |
|---|---|---|
| 0.0% | 22.80 | 4.80 |
| 2.0% | 21.74 | 3.74 |
| 3.0% | 21.22 | 3.22 |
| 5.0% | 20.16 | 2.16 |
| 9.1% | 18.00 | 0.00 |
| 12.0% | 16.46 | −1.54 |
Then the break-even itself, across contribution margins and sizes of increase:
| Contribution margin | +2% price | +4% price | +6% price | +10% price |
|---|---|---|---|---|
| 25% | 7.4% | 13.8% | 19.4% | 28.6% |
| 40% | 4.8% | 9.1% | 13.0% | 20.0% |
| 60% | 3.2% | 6.2% | 9.1% | 14.3% |
| 75% | 2.6% | 5.1% | 7.4% | 11.8% |
The counter-intuitive row is the bottom one. A software or services business with a 75 per cent contribution margin can lose only 5.1 per cent of volume on a 4 per cent increase, against 13.8 per cent for a distributor at 25 per cent. The higher the margin, the more each lost customer was worth, and the less churn a price rise can absorb. The same arithmetic run backwards says a 4 per cent price cut at a 40 per cent margin needs 11.1 per cent more volume just to stand still.
Teams often plug the EBITDA margin into the formula because it is the margin on the board pack. Here that gives 0.04 ÷ (0.15 + 0.04) = 21.1 per cent, more than twice the true break-even. A plan that loses 12 per cent of volume passes that test comfortably and actually cuts EBITDA by 1.54. The error always runs in the dangerous direction, because the EBITDA margin is lower than the contribution margin by the whole fixed cost base.
The second mistake is to assume the break-even equals the price rise: "we can lose 4 per cent of customers on a 4 per cent increase." It is never exact. With no variable costs at all it is slightly too generous, and at any realistic contribution margin it is too cautious.
The third is to treat volume loss as one number. A blanket increase loses volume where the company is already priced at or above the market, and a segmented increase that moves only the underpriced customers usually loses far less. The formula tells you the loss you can afford; segmentation decides the loss you will get.
The free workbook for this case at the companion page takes the comparison one step further, a blanket increase against a segmented one, and shows the churn at which the ranking flips. Pricing interacts with customer behaviour in other ways too: see how much of a price increase forward buying takes back, and for what the operating gain is worth at exit, how to split EBITDA growth and multiple expansion in a value bridge.
Break-even volume loss equals the price rise divided by the contribution margin plus the price rise. A 4 per cent increase at a 40 per cent contribution margin breaks even at 9.09 per cent of volume lost. Fixed costs drop out because they do not change when customers leave, so the margin in the formula must be contribution margin, not EBITDA margin.
Because each lost customer took more profit with it. At a 75 per cent contribution margin a 4 per cent increase breaks even at 5.1 per cent volume loss, against 13.8 per cent at a 25 per cent margin. Software and services companies therefore need more precise targeting of price increases than distributors, not less.
The required gain is the price cut divided by the contribution margin minus the cut. At a 40 per cent contribution margin, a 4 per cent price cut needs 11.1 per cent more volume just to leave EBITDA unchanged, which is why discount-led growth plans rarely survive an operating review.
The companion files of The Private Equity Operating Partner work a blanket against a segmented price rise as a case drawn from chapter 8. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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