The formulas
- Sales you can lose after a price rise = rise ÷ (margin + rise).
- Extra sales a discount needs = discount ÷ (margin − discount).
- New gross margin = (margin + change) ÷ (1 + change).
All figures as decimals (40% = 0.4). They assume the cost of each sale stays the same and only the price moves.
A worked example
A business sells $50,000 a month at a 40% gross margin, so it makes $20,000 of gross profit. (Made-up figures to show the arithmetic.)
| Prices up 10% | 10% discount | |
|---|---|---|
| Gross profit per $100 of today's sales | $50 | $30 |
| Volume change for the same gross profit | 20% fewer | 33.3% more |
| New gross margin | 45.5% | 33.3% |
| Gross profit a month if volume does not change | $25,000 | $15,000 |
The same 10% moves gross profit by a quarter either way, because it all lands on the $40 of profit in every $100, not on the $100. Press "Load the worked example" above to see it in the calculator.
Charge by the hour and not sure what the new rate should be? The charge-out rate calculator works it out from the pay you want, your overheads and the hours you can really bill.
Volume change for the same gross profit
| Gross margin | Prices up 5% | Prices up 10% | 5% discount | 10% discount |
|---|---|---|---|---|
| 20% | 20% fewer | 33.3% fewer | 33.3% more | 100% more |
| 30% | 14.3% fewer | 25% fewer | 20% more | 50% more |
| 40% | 11.1% fewer | 20% fewer | 14.3% more | 33.3% more |
| 50% | 9.1% fewer | 16.7% fewer | 11.1% more | 25% more |
| 60% | 7.7% fewer | 14.3% fewer | 9.1% more | 20% more |
After the price change: check it worked
Compare the next two or three months with the months before on the Profit and Loss in Xero: did total trading income hold up, and did gross margin rise by roughly what the table says? If margin did not move, check for old prices still on repeating invoices or quotes. The guide to reading a Profit and Loss walks through it, the margin and markup calculator sets the price for a target margin, and the break-even calculator shows the sales that margin needs to cover your overheads. A year on, the sales growth calculator takes the rise back out of this year's sales, so you can see whether you sold more or only charged more.
To make that check a habit, P&L management for small business sets out a monthly routine against a budget, with a kitchen fitter whose materials crept from 35% to 40% of sales and a 5% rise on new quotes that won the lost profit back.
Questions
- If I raise my prices, how many customers can I afford to lose?
- It depends on your gross margin. Volume you can lose = price rise ÷ (margin + price rise). At a 40% margin, a 10% rise lets you lose 10 ÷ 50 = 20% of sales and still make the same gross profit. At a 20% margin the same rise lets you lose 33%.
- How many more sales does a discount need?
- Extra volume needed = discount ÷ (margin − discount). At a 40% margin, a 20% discount needs 20 ÷ 20 = 100% more sales: twice as many, just to make the same gross profit. If the discount is as big as your margin, every sale loses money and no volume pays for it.
- Why does a low margin make discounts so expensive?
- The discount comes entirely out of your gross profit, because the cost of what you sell does not change. Take 10% off at a 30% margin and a third of the profit on each sale is gone, so you need half as many sales again to make it back.
- Where do I find my gross margin in Xero?
- On the Profit and Loss, divide Gross Profit by Total Trading Income. If your Profit and Loss has no cost of sales section, your gross margin may show as 100%: estimate the direct cost of each sale (materials, subcontractors, stock) instead.
- Does this include overheads?
- No, and it does not need to. Rent, wages and software stay the same whether you raise prices or not, so the question is only whether gross profit goes up or down. The break-even calculator shows the sales you need to cover overheads.
- Are my figures stored or sent anywhere?
- No. The calculation runs in your browser. Nothing you type is saved or sent to our server or anyone else. The only exception is if you ask us to email you the result: then your email address and a short summary of the result are stored, and nothing is sent until you confirm.
- How is this different from ReportPilot's weekly email?
- This calculator answers one what-if question. ReportPilot reads your Xero figures and sends a Monday email comparing sales, gross margin and profit with last month and last year, so after a price change you can see whether sales held up and the margin moved the way you expected.
No Xero needed
Get a sample Monday email for a business like yours
Pick your kind of business, rough sales and country. We email you the Monday email ReportPilot would write for a business like that: cash, sales and profit against last month, who owes money and one thing to do. Made-up figures, clearly labelled as a sample, from the same engine as the real one.
We email a link to confirm first; nothing else is sent until you press it. Then the sample, a few related emails over three weeks and a monthly cash check. One click to unsubscribe.
This calculator gives an estimate from the figures you enter. It is not financial advice. Xero is a trademark of Xero Limited. This tool and ReportPilot are independent and are not made or endorsed by Xero.