How much can you discount before you lose money?

For one product, the most you can discount and still make anything on each sale is its margin: price minus what it costs you to make and deliver, as a share of the price. For the business as a whole, at the volume you are selling now, the across-the-board discount that takes the entire profit is profit divided by revenue. Both are ceilings, not answers. The useful number is smaller: a discount comes out of the contribution, not the price, so ten per cent off a product with a forty per cent margin is a quarter of the profit on it, and to stand still that product has to sell a third more units.

Margin, not price, is what a discount comes out of

Take a product that sells for 25 and costs 15 to make, so each one contributes 10 towards the overheads and, once those are covered, the profit. Ten per cent off is 2.50 off the price. The customer sees 2.50 off 25. The business sees 2.50 off 10: a quarter of what the sale was worth. That is the whole trick of the question, and it is why the intuitive answer — “we have a forty per cent margin, ten per cent is fine” — is off by a factor of two and a half.

The same discount costs different products very different shares of their contribution, which is the first thing worth knowing before a promotion is planned. On BREAKEVEN's example of three products:

Discounting the thin-margin product is the expensive choice and the one most often made, because it is the one that feels safe to discount.

The volume that pays for a discount

A discount is worth giving if it brings in enough extra sales to replace the contribution it gives away. How many extra is a single division: margin over margin-less-discount. With a forty per cent margin and ten per cent off, that is 40 over 30, so a third more units just to make what you were making before. Not a third more revenue — a third more units, sold at the lower price.

Extra units needed to make the same contribution as before the discount. The table is the reason a twenty per cent sale on a thirty per cent margin needs three times the volume, and why promotions that “did really well” in units so often show up as a worse month.

The floor for the whole business

Across every product at once, at the volume you are selling now, there is a discount at which the year's profit is exactly nothing. It is profit divided by revenue, because an across-the-board price cut comes entirely out of contribution and the overheads do not move. On the example — revenue of 1,530,000, contribution of 888,000, overheads of 240,000, profit of 648,000 — that is 42.4%. Any across-the-board cut deeper than that, without more volume, is a year spent working for nothing.

That figure is a ceiling and it is a long way above the sensible answer. Ten per cent off everything on that example takes the profit from 648,000 to 495,000, which is 23.6% of it gone, and to earn that back the business has to sell 20.8% more of everything at the lower prices. BREAKEVEN puts those side by side as the levers: on this mix, ten per cent on price moves profit by 23.6%, ten per cent on volume by 13.7%, ten per cent on unit cost by 9.9%, and ten per cent on overheads by 3.7%. Price is the strongest lever in both directions, and almost nobody guesses that before seeing it.

Why it is never quite that simple

• Overheads do not move, which is what operating leverage measures: on the example a one per cent change in volume moves profit by 1.37 per cent. A discount that brings volume also brings the leverage with it, in both directions.
• The mix changes. A discount sells more of the discounted product and, usually, less of whatever it was competing with on your own shelf. The break-even for the business is computed on the mix as it stands, and a promotion changes the mix.
• Some of the extra sales are not extra. The customers who would have bought at full price and now buy at the discount are the promotion's real cost, and no arithmetic on this page can see them. The tables above assume every extra unit is genuinely extra, which is the most generous assumption there is.
• A discount is remembered. The next full-price month is measured against it. That is a pricing question, not an arithmetic one, and it is worth more thought than the sums.

What BREAKEVEN does and does not do

BREAKEVEN takes the overheads, the profit you want, and each product's price, cost and share of the mix, and works out break-even on that mix, the margin of safety, operating leverage, the discount that ends the profit, and the four levers moved by the same amount so they can be compared. It runs in your browser; nothing is uploaded, and it works with the connection off.

It does not know which of your extra sales would have happened anyway, what the discount does to the mix, or what your customers will expect next month. It gives the arithmetic, exactly, so that the judgement is made on top of the right numbers rather than instead of them.