We show what a discount does to the volume you need - before you agree to it.
How much more you have to sell to break even on a discount
Ten percent off at a fifty percent margin needs twenty five percent more volume. The relationship is not linear, and it is not the one people guess.
The working
How this is worked out
A discount comes out of the price. Your cost of delivering the work does not move. So the whole discount comes out of gross profit, which is a much smaller number than revenue, and that is why the effect is larger than it looks.
New volume / old volume = m / (m + d) m = gross margin, as a decimal d = price change, as a decimal (negative for a discount)
Two consequences fall straight out of that formula.
The share of gross profit you give away is the discount divided by the margin. A 10% discount at a 50% margin costs you 20% of gross profit. At a 25% margin the same 10% discount costs 40% of it.
There is a discount no volume can repay. It is equal to your gross margin. At that price every unit contributes nothing at all, and selling more of them cannot restore a profit that no longer exists per unit. As you approach that point the required volume rises steeply rather than in a straight line, which is why a 30% discount is far worse than three times a 10% one.
A worked example
You sell something for £100. It costs you £50 to deliver, so your gross margin is 50%. You sell 100 units a month, making £5,000 of gross profit.
A customer asks for 10% off.
- New price: £90. Cost is still £50, so you now keep £40 per unit instead of £50.
- Your margin is now 44.4%, not 40%. The discount did not come off the margin percentage one for one.
- To make the same £5,000 of gross profit you need £5,000 / £40 = 125 units.
- That is 25% more volume, for the same money, from the same team.
Run it the other way and it becomes an argument for raising prices. At the same 50% margin, a 10% price rise means you can lose 16.7% of your customers and still make exactly the same gross profit. Most founders have never calculated that number, and it is usually much larger than the number of customers they are afraid of losing.
| Your gross margin | Extra volume needed for 10% off | Share of gross profit given away |
|---|---|---|
| 20% | 100% | 50% |
| 30% | 50% | 33% |
| 40% | 33.3% | 25% |
| 50% | 25% | 20% |
| 70% | 16.7% | 14% |
| 90% | 12.5% | 11% |
Why it is gross margin, not net margin
The formula uses gross margin, meaning revenue less the direct cost of delivering that revenue. It deliberately excludes rent, salaries, software and everything else that does not change when you sell one more unit.
That is not an approximation, it is the point. The question is what one additional sale contributes, and fixed costs do not respond to one additional sale. Using net margin would understate the contribution of extra volume and make every discount look unrecoverable.
The flip side is that this arithmetic only tells you about gross profit. It does not tell you whether the extra volume is deliverable, and it does not tell you whether your fixed costs are covered.
What changes your answer
- It assumes your unit cost stays flat. If you buy materials better at volume, the required uplift is smaller. If overtime and rush shipping kick in, it is larger.
- It ignores capacity. Needing 25% more volume is meaningless if you are already at 95% utilisation. In a service business the honest reading is often "this discount is not available to us at any volume".
- It is a single-period view. If a discount wins a customer who stays five years, the lifetime arithmetic is different from the arithmetic on the first order. The formula tells you what the discount costs, not whether it is worth it.
- Discounts are sticky. The volume assumption usually applies to one deal; the price usually applies to every renewal after it.
- It says nothing about your competitors. Holding price while a competitor cuts is a strategy with its own risks, and no formula settles it.