How Many Extra Sales Does a Discount Need to Pay for Itself?

Why profit falls faster than the price

Take an item that sells for 50 and costs 30 to supply. The profit is 20 per unit, which is a 40% margin. Now offer 10% off. The new price is 45, the cost is still 30, and the profit drops to 15.

The price fell by 10%, but the profit per unit fell from 20 to 15, a drop of 25%. Because the cost stays put, the whole discount comes out of the profit, so the cut in profit is far bigger than the discount suggests.

The break-even volume formula

Let the margin be m and the discount be d, both as a share of the original price. The new profit per unit is m − d of the original price, so you need to sell m ÷ (m − d) times as many units as before.

required increase in units = d ÷ (m − d)m is the original margin, d is the discount, both as decimals. It only works while d is smaller than m.

For the 50 item: m = 0.40 and d = 0.10, so the increase is 0.10 ÷ 0.30 = 33.3%.

Worked example: the shop sells 200 units a month at a profit of 20 each, which is 4,000. After the discount each unit earns 15, so it needs 4,000 ÷ 15 = 266.7, or 267 units, to match. That is 67 extra sales a month, a third more, just to earn what it earned before.

Reference table

The increase in sales volume needed to keep total profit unchanged, by original margin and discount:

Notice how quickly the requirement grows when margin is thin. At a 20% margin, a 10% discount means you must double your sales. At 50%, the same discount needs only a quarter more.

Worked example for a thin margin: an item costs 16 and sells for 20, a 20% margin and 4 of profit. A 10% discount drops the price to 18 and the profit to 2, so each sale now earns half as much. You need twice the volume, a 100% increase, simply to stay level.

The same logic works for price rises

The calculation runs the other way too. A price rise adds profit to every unit, so you can lose some customers and still come out ahead. If the price rises by p (as a share of the old price) and the margin was m, the share of volume you can lose before profit falls is p ÷ (m + p).

Worked example: the 50 item with a 20 profit goes up by 10% to 55, so profit per unit becomes 25. Selling 200 units earned 4,000 before, so 4,000 ÷ 25 = 160 units earns the same. You can lose 20% of your volume and break even. For discounts, a price cut that needs 33% more customers is a hard bet. For rises, a price change that loses a fifth of customers merely matches the old profit.

Using the result to decide

• Ask whether the extra volume is believable. Needing 33% more sales from a promotion is plausible for some products and fanciful for others.
• Count the other effects. Existing customers who would have paid full price now pay less, and some promotions simply pull future sales forward.
• Look for benefits outside this formula. Clearing old stock, winning repeat customers or using spare capacity can justify a discount even when the break-even volume is hard to reach.
• Consider alternatives. A bundle, a free add-on or a small gift can feel generous while costing less than a price cut, because the add-on costs you less than its apparent value.

The formula assumes your cost per unit and fixed costs stay constant, which is a fair approximation for small changes. To check a discounted price, use the discount calculator, and use the margin calculator to see the margin you have left.

This is general education about a simple formula, not business or financial advice. Real demand responses vary, so test promotions against your own sales data.