Break-Even Discount: Extra Volume You Need

Every discount asks the same question: how many more units do I have to sell to earn the same money I would have earned without it? The answer is a single fraction, and it is brutal at low margins. This page derives the break-even discount formula step by step, gives you a lookup table you can read without a calculator, and shows what the table leaves out so you do not trust it further than it deserves.

The formula

Start with one product. Let the price be 1 (call it 100 percent), the unit cost be c, and the gross margin be M = 1 − c, so M is your margin as a share of the original price. A discount of D, also as a share of the original price, lowers the price to 1 − D and leaves the cost unchanged, so the margin per unit falls to M − D.

Without the discount you sell Q0 units and earn M × Q0. With it you sell Q1 units and earn (M − D) × Q1. Break-even is the point where the two are equal:

M × Q0 = (M − D) × Q1

Divide both sides by (M − D) × Q0:

Q1 ÷ Q0 = M ÷ (M − D)

The required increase in volume is Q1 ÷ Q0 minus 1, which simplifies to:

Required volume increase = D ÷ (M − D)

A worked check. A product sells for 40 dollars and costs you 16 dollars, so M = 24 ÷ 40 = 60 percent. You run 20 percent off, so D = 20 percent. Required increase = 20 ÷ (60 − 20) = 50 percent. Verify with money: before, 100 units earn 100 × 24 = 2,400 dollars. After, the price is 32 dollars, the margin per unit is 16 dollars, and you need 2,400 ÷ 16 = 150 units. That is 50 percent more. The formula holds.

Two properties follow from the algebra, and both are worth knowing before you read the table:

• When D equals M, the denominator is zero: you earn nothing per unit, and no amount of extra volume recovers the margin. When D is larger than M, you lose money on every sale.
• The required increase grows faster than the discount. Going from 10 to 20 percent off at a 50 percent margin does not double the requirement, it takes it from 25 percent to 66.7 percent.

Lookup table: margin 20 to 70 percent vs discount 5 to 40 percent

Each cell is the extra unit volume, as a percentage of your current volume, you need to earn the same gross profit. "Never" means the discount equals or exceeds the margin. Cells are rounded to one decimal place.

Every cell is D ÷ (M − D) with the percentages written as numbers. The 60 percent row at 20 percent off reads 50 percent, matching the check above.

Reading the table

Find your gross margin in the left column, then the discount you are considering. The cell is the lift you must see just to stand still.

• Doubling is the line to notice. Any cell at 100 percent or above means you must sell at least twice as many units. At a 30 percent margin a 15 percent discount already needs that. At a 50 percent margin the same is true at 25 percent off.
• Low margins leave almost no room. At 20 percent margin, 5 percent off needs a third more volume, and 20 percent off or more can never be recovered by volume.
• Small discounts are cheap, big ones are not. At a 60 percent margin, 10 percent off asks for 20 percent more units. 30 percent off asks for double.
• Margin here is margin on the price you sell at now. Use the gross margin of the products that will actually be discounted, not your store-wide average, if the mix differs.

To use it before a sale: pick the product or collection, find its gross margin, find the discount, then ask whether you believe a lift of that size is plausible. Look at your own history, for example how much a past promotion on similar products moved unit sales, rather than a number from someone else's store. If the honest answer is "no", shrink the discount, add a threshold, or use a different mechanism, such as a gift, whose cost does not scale with the price.

What the table leaves out

The formula treats one thing, unit margin, and ignores several that usually make a discount cost more than the table says:

• Returns. If sold units come back at a higher rate during a sale, the extra volume is smaller than it looks. Count what a return costs you in your own process, such as outbound postage you do not recover.
• Payment fees. A percentage processing fee shrinks along with the price, but any fixed per-order fee does not. On low-priced orders that fixed piece takes a bigger bite after the discount. Check your own processor's fee schedule.
• Cannibalized full-price sales. The table assumes that the old volume would have sold anyway at the old price and counts only the extra as new. Buyers who would have paid full price and now pay less are the main hidden cost. The more loyal your customer base, the more of the discount goes to people who needed no nudge.
• Fixed and per-order costs. Pick-and-pack labor and shipping are spent per order. If you give a discount and do not change order size, they stay the same; if extra volume arrives as extra small orders, they rise.
• Stock. If the extra volume cannot be fulfilled, or sells down inventory you would have sold at full price later, the profit is not what the table promises.

Treat the table as a floor. The real requirement is the table value or higher.

Using it with a tiered cart discount

A cart discount changes the question slightly. When a discount applies to the whole order, the "volume" you need is order value, and the formula still holds with D as the discount on the cart and M as the margin on the added products.

Shopify's discount combinations help classes a discount that applies to cart subtotals as an order discount, as opposed to a product or shipping discount, and Freebies Engine by Log Studio Lab describes its cart template as "A discount on the whole cart that grows with spend." Take that template's own example shape: 5 percent off at one spend level and 10 percent off at a higher one. Assume a 50 percent gross margin across the cart. From the table, 5 percent off needs 11.1 percent more value in the baskets that earn it, and 10 percent off needs 25 percent more.

That turns into a rule for setting the tiers. If the lower tier starts at 100 dollars, the shopper who would have spent 90 dollars needs to be pulled up to 100 dollars, which is 11.1 percent more, to pay for the 5 percent off. If most of the shoppers who reach the tier would have spent 100 dollars or more anyway, the tier is a cost with no lift. So set the first tier above the typical basket, not at it, and check the second tier the same way: a shopper moving from 150 dollars to 200 dollars is a 33.3 percent step, comfortably above the 25 percent needed at 10 percent off in this example.

Then compare the plan with your data. How many baskets last month landed within the stretch distance below each tier, and how many were already above it? The first group is what the discount can win. The second is what it can only lose.

Build it

Once the numbers work, the Cart discount tiers template in Freebies Engine by Log Studio Lab builds the tiered cart discount. For the same math applied to a shipping promise, read Free Shipping Threshold: The Formula. The season where most stores break these rules is covered in the Black Friday Cyber Monday offer plan. Plan requirements are on the pricing page.