How to calculate a discount break-even

Most promotions are approved on a feeling. The number looks like it needs help, 20 percent off sounds like it will move things, and the email goes out on Thursday.

The arithmetic that would have settled it takes about a minute, and it is two lines.

The two numbers you need

Your gross margin, as a percentage of the selling price. What is left of the price after the costs that scale with each unit: the product itself, the packaging, and whatever share of the postage you absorb. Rent, salaries and your Shopify subscription do not belong in here, because they do not change when you sell one more unit.

Your discount depth, as the percentage off that the customer will see.

That is it. The selling price is worth knowing because it turns the result into money, but it does not affect either answer.

Line one: what it costs you in profit

Profit lost = Discount / Gross margin

A product sells at £40 with a 50 percent margin. It costs you £20, so you keep £20.

Take 20 percent off. It now sells for £32. It still costs you £20, so you keep £12.

You cut the price by a fifth and your profit by 40 percent. Which is what the formula says: 20 divided by 50.

The same 20 percent discount behaves completely differently depending on where your margin sits:

• At a 60 percent margin, it costs you 33 percent of your profit.
• At a 50 percent margin, it costs you 40 percent.
• At a 40 percent margin, it costs you 50 percent.
• At a 30 percent margin, it costs you 67 percent.
• At a 20 percent margin, it costs you all of it.

This is worth sitting with if you run one promotional depth across a whole catalogue. A blanket 20 percent off is a mild trim on your best products and close to a wipeout on your thinnest ones, and nobody has decided that on purpose.

Line two: what it has to sell to stand still

Losing profit per unit is fine if enough extra units arrive. So the real question is how many.

Extra units needed = Margin / (Margin - Discount)

Back to the £40 product at a 50 percent margin with 20 percent off. That is 50 divided by 30, which is 1.67. You need to sell 67 percent more units than you would have sold anyway, just to end up in the same place.

Check it in money. Say you would have sold 100 units at full price: 100 times £20, so £2,000 profit. At the discounted price you make £12 a unit, so you need £2,000 divided by £12, which is 167 units. That is 67 more than 100.

Everything above 167 units is the promotion actually working. Everything below it is a busy week that cost you money.

The requirement accelerates

Here is the part that surprises people. Doubling the discount does considerably more than double the volume you need, because each additional point comes out of a slice that is already thinner.

On that 50 percent margin product:

• 10 percent off needs 25 percent more units.
• 20 percent off needs 67 percent more units.
• 30 percent off needs 150 percent more units.
• 40 percent off needs 400 percent more units.
• 50 percent off needs an infinite number, because there is nothing left per unit.

The jump from 10 to 20 adds 42 points of required volume. The jump from 30 to 40 adds 250. There is a depth for every margin where the promotion stops being a commercial decision and becomes a way of turning stock into cash, and it is usually shallower than people expect.

Where it goes wrong

Using net margin instead of gross. Loading fixed costs into the margin figure makes it look far worse than it is and produces break-even numbers nobody could hit. Only the costs that move with volume belong in this calculation.

Forgetting that discounted orders still cost you to fulfil. Payment processing, picking, packing and postage do not go down because the customer paid less. If you absorb postage, a deep discount on a low value item can put you below cost even when the margin arithmetic says otherwise. Include the per-unit share of those costs and the number tells the truth.

Comparing to zero instead of to baseline. The promotion does not need to beat nothing, it needs to beat what you would have sold that week anyway. A sale that shifts 167 units in a week where you would have sold 140 at full price has not cleared its break-even, it has lost you money while looking like your best week of the quarter. Take the four weeks before the promotion as your baseline and measure the difference.

Counting the customers you would have kept. Some of the people who bought at 20 percent off were going to buy at full price. Every one of them is pure margin given away, and they are usually your most loyal customers, because they are the ones reading your emails.

What to do with the answer

You now have a number: the extra volume this promotion needs. Hold it against what your last three promotions actually did.

If the last comparable sale lifted volume by 30 percent and this one needs 67 percent, the decision is made and it took a minute. If it needs 150 percent, it was never going to work at any depth of enthusiasm.

If the number is plausible, run it, and then check afterwards whether it landed. That last step is the one everybody skips, and it is the one that stops the same optimistic promotion running again next quarter.

And if the answer is that the promotion cannot pay for itself, the underlying problem was probably never price. What to run instead of a discount covers the options that do not cost you margin, and the wider case on discounting covers the two costs that do not show up in this arithmetic at all.