How discounts affect margin, and the volume needed to recover
A discount comes entirely out of gross profit. A 10% price cut on a 40% margin product removes a quarter of the profit on every unit, so volume has to rise by a third just to stand still. This guide shows the arithmetic and a table you can reuse.
Worked example (illustrative)
A product sells for $100 and costs $60: gross profit $40, gross margin 40%. You offer 10% off.
- New price = $90; cost is unchanged at $60.
- New gross profit = $30 per unit, down 25%. New margin = $30 ÷ $90 = 33.33%.
- To earn the same total gross profit, units must rise by $40 ÷ $30 − 1 = 33.33%. If you sold 300 units before ($12,000 of gross profit), you now need 400 units to make $12,000 again.
The formula
(discount and margin both as fractions of the original price)
Check with the example: 0.10 ÷ (0.40 − 0.10) = 0.10 ÷ 0.30 = 33.33%. If the discount is equal to or larger than the margin, no volume increase can recover the profit, because each sale no longer makes any gross profit at all.
Lookup table: discounts
| Starting gross margin | 5% discount | 10% discount | 15% discount | 20% discount | 25% discount |
|---|---|---|---|---|---|
| 30% starting margin | +20.0% | +50.0% | +100.0% | +200.0% | +500.0% |
| 40% starting margin | +14.3% | +33.3% | +60.0% | +100.0% | +166.7% |
| 50% starting margin | +11.1% | +25.0% | +42.9% | +66.7% | +100.0% |
The lower the starting margin, the more painful a discount is. At a 30% margin a 15% discount needs double the volume; at a 50% margin the same discount needs about 43% more.
The other direction: price increases
Raising the $100 price 10% to $110 lifts gross profit to $50. You could sell 20% fewer units (0.10 ÷ 0.50) and earn the same total gross profit.
| Starting gross margin | 5% price increase | 10% price increase | 15% price increase |
|---|---|---|---|
| 30% starting margin | −14.3% | −25.0% | −33.3% |
| 40% starting margin | −11.1% | −20.0% | −27.3% |
| 50% starting margin | −9.1% | −16.7% | −23.1% |
What the arithmetic leaves out
- Demand. The tables say how much volume you need, not whether you will get it.
- Variable selling costs. If a fee or commission is a percentage of price, it falls with the discount, which helps slightly; if it is per unit, the extra volume adds more of it.
- Capacity and overhead. Extra volume may need extra staff or space, which are fixed-cost steps (see fixed vs variable costs on our sibling site).
- Customer expectations. Customers who bought at a discount may wait for the next one.
Checklist before you discount
- Write the starting gross margin as a fraction of price.
- Compute the required volume increase from the table or formula.
- Compare it with the volume lift you can reasonably expect, and say where that expectation comes from.
- Set an end date and measure units and gross profit dollars, not just revenue.
Sources for definitions
- OpenStax, Principles of Accounting Vol. 1 §6.6: Gross margin
- OpenStax, Managerial Accounting §3.3: Sensitivity analysis under changing business situations
Definitions follow standard accounting usage as presented in the sources above. All dollar figures on this page are our own illustrative arithmetic.
Educational arithmetic only. Results do not set a suitable price or establish suitability for any lending, investment or business decision. See Use & limitations.