A price increase reduces the number of sales you need to earn the same contribution, and a discount raises it. The exact break-even is one formula: volume change = −price change ÷ (contribution margin + price change), with all three figures as decimals. At a 40% contribution margin, a 5% increase lets you lose up to 11.1% of volume before contribution falls; a 10% discount needs 33.3% more volume just to stand still.
This guide explains where the formula comes from, gives a table you can read off for your own margin, works through a hypothetical Canadian example, and sets out a careful way to test a change before rolling it out. It supports the pricing analysis in our growth strategy engagements.
The one input you need: contribution margin
Contribution margin is what is left from each sale after the costs that rise and fall with that sale. It is not the same as gross margin on your financial statements, which may include or exclude different costs depending on how your books are set up.
- Take the average pre-tax price of the product, job or contract you are changing.
- Subtract the variable costs per unit: direct labour paid by the job or hour, materials, subcontractors, shipping, card and financing fees, commissions.
- Divide what is left by the price. That is your contribution margin as a percentage.
If the business sells several lines with very different margins, run the math for each line separately. Our margin by service line guide walks through the split. Your CPA can help reconcile the result with your statements; this guide is business analysis, not accounting or tax advice.
Where the formula comes from
The formula simply holds total contribution constant before and after the change. Here is the proof with round numbers.
Say a unit sells for $100, variable cost is $60, so contribution is $40 (40%). You sell 100 units, earning $4,000 of contribution.
- Raise the price 5% to $105. Variable cost stays $60, so contribution becomes $45.
- Units needed for the same $4,000: $4,000 ÷ $45 = 88.9 units.
- Volume you can lose: 100 − 88.9 = 11.1 units, or 11.1%.
Now the formula: −0.05 ÷ (0.40 + 0.05) = −0.05 ÷ 0.45 = −0.111, or −11.1%. Same answer.
For a discount, the price change is negative. A 10% discount at a 40% margin: −(−0.10) ÷ (0.40 − 0.10) = 0.10 ÷ 0.30 = +0.333. You need 33.3% more volume to earn the same contribution.
The break-even table
Read across from your contribution margin to see the break-even volume change for common price moves. Negative numbers are the most volume you can lose; positive numbers are the extra volume you must win.
| Contribution margin | +3% price | +5% price | +10% price | −5% price | −10% price |
|---|---|---|---|---|---|
| 20% | −13.0% | −20.0% | −33.3% | +33.3% | +100.0% |
| 30% | −9.1% | −14.3% | −25.0% | +20.0% | +50.0% |
| 40% | −7.0% | −11.1% | −20.0% | +14.3% | +33.3% |
| 50% | −5.7% | −9.1% | −16.7% | +11.1% | +25.0% |
| 60% | −4.8% | −7.7% | −14.3% | +9.1% | +20.0% |
Two patterns stand out. First, the lower your margin, the more a price increase protects you, and the more a discount hurts. A business at 20% contribution has to double its volume to survive a 10% price cut. Second, at every margin level, discounts cost more volume than increases save. That asymmetry is why we treat broad discounting as a last resort in growth planning.
A worked Canadian example
Consider a hypothetical 14-person commercial cleaning company serving offices on monthly contracts. The figures are illustrative.
- Average contract: $2,400 a month, before GST/HST
- Variable cost per contract (cleaning labour, supplies, travel): $1,632
- Contribution per contract: $2,400 − $1,632 = $768, or 32%
- Active contracts: 120
- Monthly contribution: 120 × $768 = $92,160
Wages have risen, and the owner is considering a 6% increase at renewal.
- New price: $2,400 × 1.06 = $2,544
- New contribution per contract: $2,544 − $1,632 = $912
- Contracts needed for the same $92,160: $92,160 ÷ $912 = 101.1
- Contracts the business could lose: 120 − 101.1 = 18.9, or 15.8%
The formula agrees: −0.06 ÷ (0.32 + 0.06) = −0.06 ÷ 0.38 = −15.8%.
So the owner could lose almost 19 of 120 clients and still earn the same contribution, with fewer crews to manage. In practice, losing even five is unusual when an increase is explained well and the service is reliable. If the company keeps 115 contracts, monthly contribution becomes 115 × $912 = $104,880, an extra $12,720 a month.
Compare a competitor's suggestion to offer 10% off to win new accounts. At 32% margin, the formula says 0.10 ÷ (0.32 − 0.10) = 0.10 ÷ 0.22 = +45.5%. The company would need about 175 contracts at the discounted price to match today's contribution, and would need the crews to service them.
Remember that sales tax sits on top. A client in Ontario pays 13% HST on the $2,544; a client in Alberta pays 5% GST. The tax does not change your contribution, but it does change what the client sees on the invoice, so quote clearly.
How to test a price change safely
A test limits the downside while you learn how your customers actually respond. A careful sequence looks like this:
- Calculate your break-even first. Know the volume you can lose before you see any customer reaction, so the result is judged against a number, not a feeling.
- Start with new customers or new quotes. Existing clients have context and loyalty; new prospects tell you whether the market accepts the price.
- Change one segment at a time. For example, one service line, one region or one customer size band.
- Track the quote win rate weekly. If you won 34 of every 100 quotes before the change, decide in advance what rate would worry you.
- Run it long enough. For most businesses that means eight to twelve weeks, or at least 40 to 50 quotes, so one unusual week does not decide the outcome.
- Give existing clients notice and a reason. A written explanation at renewal, with a clear effective date, keeps the conversation about value.
- Review contribution, not revenue. A month with slightly lower revenue but higher contribution is the change working.
Whatever you advertise must be the price a customer actually pays, with every mandatory fee included. Ask a lawyer if you are unsure how advertising rules apply to your offer.
Common mistakes in pricing decisions
- Using gross margin from the statements without checking it. If it includes fixed costs, your break-even will be wrong. Rebuild contribution from variable costs.
- Averaging across very different lines. A blended 35% can hide one line at 15% and another at 55%, each needing a different decision.
- Discounting to fill capacity without a time limit. Temporary discounts tend to become the new list price.
- Raising prices only after costs have already eaten the margin. Smaller, regular adjustments are easier to explain than a large overdue one.
- Judging the test on the first two weeks. Early reactions are noisy; wait for the sample size you set.
- Forgetting capacity. Winning volume with a discount only helps if you can deliver it without overtime or new hires.
A short checklist
- Contribution margin calculated per line, from variable costs
- Break-even volume change worked out with the formula
- A test segment and a start date chosen
- A win-rate threshold written down before the test begins
- Customer notice drafted with a reason and an effective date
- Pre-tax and tax-inclusive prices both checked for each province you sell into
- A review date for contribution, not revenue
Putting the math to work
The formula tells you what the change must achieve; it does not tell you how customers will respond. That part comes from segment data, win rates and the strength of your service. In a growth strategy engagement we combine the two: margin by line, a pricing test plan and the capacity check. If you want the numbers checked first, start with financial clarity, or read how a business diagnostic fits pricing into the wider picture. Call, text or email to discuss it, by video call or in person; texting (604) 632-4959 with your margin and the change you are weighing is a fine first step.
Frequently asked questions
Does this formula work for service businesses?
Yes, as long as you can separate costs that rise with each job or contract (direct labour, materials, subcontractors, card fees) from costs that stay put (rent, salaried staff, software). The formula only needs the contribution margin percentage.
Should the calculation use prices before or after GST/HST?
Before. GST, HST and QST are collected on behalf of government and are not your revenue. Run the math on your pre-tax price, then add the tax for your customer's province on top.
What if fixed costs change with the price?
Then the simple formula understates or overstates the answer. If a price change lets you drop a shift or forces you to add one, model the new fixed costs separately and compare total profit, not just contribution.
How often should we review prices?
At least once a year, and whenever a major cost such as wages, materials or fuel moves by more than a few percent. Small, regular adjustments are usually easier for customers to absorb than one large catch-up.