Can we afford this discount? How many more units must we sell to break even?
A discount cuts the margin on every unit, so the volume has to rise by more than the discount itself. This shows how much more you must sell to end up with the same contribution — and, the other way round, how much volume a price increase of the same size can lose before it stops paying.
Your assumptions
Worked-example values — replace with yoursAssumes the unit cost stays the same at the higher volume.
This is an estimate. Check it on your own data.
The break-even tells you what volume you would need. It cannot tell you whether the discount actually brought that volume. Checking realised discounts against real invoices is what the free Margin Scan and a Starter workspace do.
Your inputs travel with you into the request, or into the free Margin Scan. Nothing is sent to ADEXMA until you submit a form.
The formula
- contribution per unit today = price − variable cost
- contribution per unit after = price × (1 − discount) − variable cost
- extra units needed (%) = contribution today ÷ contribution after − 1
- volume you can lose after an increase of the same % = 1 − contribution today ÷ (price × (1 + increase) − variable cost)
Worked example · the values pre-filled above
Current selling price: $100 per unit · Variable cost: $70 per unit · Discount you are considering: 5 % of price · Units sold today: 10,000 units
- Contribution today = $100 − $70 = $30 a unit, × 10,000 units = $300,000 a year.
- A 5% discount takes the price to $95, so contribution falls to $95 − $70 = $25 a unit.
- Extra units needed = 30 ÷ 25 − 1 = 20%, so 12,000 units a year instead of 10,000.
- Contribution is $300,000 either way. If you raised price by 5% instead, you could lose 14.3% of volume.
Result: 20.0% more units
What this assumes
- Variable cost per unit does not change with volume.
- Fixed costs are unchanged, so contribution is the right yardstick.
- The discount applies to every unit, including units you would have sold at full price anyway.
- It is an estimate from your own inputs. Results from different tools overlap and must never be added together into one savings figure.
Sources
- Nagle, T., Hogan, J. & Zale, J., The Strategy and Tactics of Pricing (Routledge, 6th ed.) — Break-even sales change for a price change, expressed through contribution margin.
- Marn, M. & Rosiello, R., “Managing Price, Gaining Profit”, Harvard Business Review, Sept–Oct 1992 — Why a small price move outweighs the same move in volume or cost.
Questions people ask
How many more units do I need to sell to pay for a 5% discount?
It depends on your unit margin, not on the discount alone. With a $100 price and $70 variable cost, a 5% discount needs 20% more units to keep the same contribution.
Why is the required volume bigger than the discount?
Because the discount comes off the margin, not off the price. A 5% cut in price is a 16.7% cut in a $30 unit margin ($5 of $30).
Does this include fixed costs?
No. Fixed costs do not change with volume, so contribution per unit is the right yardstick for a short-term discount decision.
Related tools
On your own data, Margot picks up this finding in a workspace and your advisor confirms it. See what each plan adds →