Head-to-head
Discount vs Markup
Discounts and markups are mirror images, but they are not symmetric. A markup is applied to cost and moves the price up; a discount is applied to price and moves it down. Because the two percentages sit on different bases, equal-looking numbers do not cancel.
The relationship is exact: a discount of d exactly undoes a markup of m when (1 + m)(1 − d) = 1. For a 25% markup, the cancelling discount is 20%, not 25%. For a 50% markup it is 33.3%. The discount needed is always smaller than the markup it removes, which is why discounting feels more powerful than it is — and why it destroys margin faster than most pricing sheets assume.
The practical consequence is that discount authority should be expressed in margin points, not percent off. A 10% discount on a 33% margin product removes 30% of the profit, not 10%. That is the single most useful number for anyone who approves discounts.
It also explains a pattern that looks like bad faith in retail: a product marked up 100% and then sold at half price is not being sold at a loss, it is being sold at cost. The discount feels enormous and the margin is zero, which is exactly the arithmetic that makes permanent sales possible.
Discount
How To Calculate A Discount
A discount is a percentage taken off the price before tax, so the sale price and the money saved are two separate numbers that the tag never prints. On an original price of 120 with 25 per cent off, the saving is 30.0, the sale price is 90.0, and with 8 per cent tax the bill is 97.2.
Markup
How To Calculate Markup
Markup is the amount loaded on top of cost to reach a selling price, expressed as a percentage of that cost. Margin divides the very same profit by the price instead, which is why a 40% markup on a cost of 60 produces a price of 84 but a margin of only 28.5714%.
How They Differ
| Attribute | Discount | Markup |
|---|---|---|
| Applied to | The selling price | The cost |
| Direction | Reduces revenue | Increases price above cost |
| Formula | Sale price = Price × (1 − d) | Price = Cost × (1 + m) |
| Cancels out | A markup of d ÷ (1 − d) | A discount of m ÷ (1 + m) |
| Effect on margin | Falls faster than the discount rate | Sets the margin before any discount |
| Who decides it | Sales and marketing, often under time pressure | Finance and pricing, usually in advance |
| Common mistake | Assuming 20% off and 20% on cancel | Assuming the markup percentage equals the margin |
The Same Numbers, Both Ways
An item that costs $80, priced at $100, then discounted 20%.
- Cost
- $80
- List price
- $100
- Discount
- 20%
| Line | Discount | Markup |
|---|---|---|
| Rate | 20.0% | 25.0% |
| Reference point | List price ($100.00) | Cost ($80.00) |
| Price after applying it | $80.00 | $100.00 |
| Profit per unit | $0.00 | $20.00 |
| Discount that cancels this markup | — | 20.0% |
A 25.0% markup takes $80.00 to $100.00. A 20.0% discount takes $100.00 straight back to $80.00, leaving $0.00 of profit — exactly nothing. The discount that cancels a 25.0% markup is 20.0%, not 25.0%.
When To Use Each
Discount
- You are running a promotion and need to know what it costs in margin, not just revenue.
- You are comparing two offers — 20% off versus $15 off — on the same product.
- You are stacking discounts, where the effective rate is multiplicative, not additive.
Markup
- You are setting a price from a known landed cost.
- You are deciding how much room there is for a discount before profit disappears.
- You are quoting a trade price to a reseller who expects a standard markup.
Common Questions
Does a 20% discount cancel a 20% markup?
No, and this is the classic error. A 20% markup on $80 gives $96; a 20% discount on $96 gives $76.80 — below cost. You need a 16.7% discount to cancel a 20% markup.
How do I know how much discount I can afford?
Convert the discount into margin points. If your margin is 30% and you give 10% off, your new margin is (0.30 − 0.10) ÷ 0.90 = 22.2%, a loss of 7.8 points — 26% of your profit.
Do two 10% discounts equal 20% off?
No. They compound: 0.9 × 0.9 = 0.81, which is 19% off. Stacked discounts always cost slightly less than the sum, which is why 'extra 10% off sale prices' is cheaper than it sounds.
Why is the markup always bigger than the discount that cancels it?
Because the markup is a fraction of the smaller number. The same dollar amount is a larger percentage of cost than of price, so removing it takes a smaller percentage of the larger base.
What discount is safe?
The one that leaves a positive contribution margin after variable costs. If gross margin is 25%, a 15% discount leaves 11.8% — still positive, but it has removed more than half the profit on that unit.
More Comparisons
- Markup vs Margin
Markup divides profit by cost; margin divides it by price. The same $20 profit is 50% markup and 33.3% margin — and the gap widens as the rate rises.
- ROI vs CAGR
ROI measures the whole return; CAGR turns it into a compound annual rate. A 100% return over five years is 20% a year by division but 14.87% a year in reality.
- Simple Interest vs Compound Interest
Simple interest charges the principal only; compound interest charges the balance. On $10,000 at 5% over 10 years that gap is $1,288.95 — here is where it comes from.
Sources
- Pricing your products — discounts and margin — U.S. Small Business Administration
- Retail trade — gross margin and markdown data — U.S. Census Bureau, Annual Retail Trade Survey
- Consumer prices and promotional pricing — U.S. Bureau of Labor Statistics
Both methods sit in Finance.