Discount cascade calculator — stacked discounts and margin
Chain up to four sequential discounts to see the net price, the effective single discount, and the gross margin left at every step of the cascade.
Free · no signup · runs in your browser·Updated
Short answer
Stacked discounts multiply, they do not add. Chaining 20%, 7.5%, 5% and 2% off a $1,250 list price gives 0.80 × 0.925 × 0.95 × 0.98 = 0.68894, so the net price is $861.18 and the effective single discount is 31.1% — not the 34.5% the four rates sum to. At a $780 cost, gross margin falls from 37.6% to 9.4%.
Real prices rarely come off a single discount. A distributor rate, a volume break, a quarterly promotion and a payment-terms deduction each take a slice, and each one takes it from what the previous slice left. The result is a net price nobody in the room predicted.
Enter the list price, your unit cost and up to four discounts. The calculator shows the price and gross margin after every step, the effective single discount, how many points compounding saved you, and the largest total discount your floor margin can absorb.
Your numbers
$
$
Landed cost, not standard cost with overhead in it.
%
%
%
%
%
The lowest margin you will approve. Sets the maximum total discount off list.
Result
Effective single discount
31.1%
Net price $861.18 · 9.4% gross margin · the rates sum to 34.5%
Net price after the cascade$861.18
Gross profit per unit$81.17
Gross margin at net price9.4%
Points saved by compounding3.4
Max discount at a 15% floor26.6%
Volume needed to hold gross profit5.79×
Each step is taken off the price the step above it left.
Step
Off
Price
GP/unit
Margin
Cumulative
List price
—
$1,250.00
$470.00
37.6%
0.0%
Distributor discount
20.0%
$1,000.00
$220.00
22.0%
20.0%
Volume break
7.5%
$925.00
$145.00
15.7%
26.0%
Promotion
5.0%
$878.75
$98.75
11.2%
29.7%
Payment terms
2.0%
$861.18
$81.17
9.4%
31.1%
$1,250.00 × 0.800 × 0.925 × 0.950 × 0.980
= $861.18 net price (combined factor 0.68894)
Effective discount = 1 − 0.68894 = 31.1% · rates sum to 34.5%
Floor: $780.00 ÷ 0.85 = $917.65 → 26.6% is the most you can give
31.1% effective discount is 4.5 points past your 15% floor, which caps you at 26.6% off list ($917.65). Margin is 9.4% and holding gross profit would take 5.79× the volume.
Everything is computed in your browser. Nothing you type is sent anywhere or stored.
The formula
Net price = List × (1 − d₁) × (1 − d₂) × (1 − d₃) × (1 − d₄) · Effective discount = 1 − Net ÷ List
List
Published list or book price before any deduction.
d₁ … d₄
Each discount in the chain, applied in sequence to the price that survived the step before it.
Net price
What the customer is actually invoiced per unit.
Effective discount
The single discount that would produce the same net price. Always less than the sum of the rates.
Discounts compound because every step after the first is taken off an already-reduced base. Order does not change the net price — multiplication is commutative — but it does change the margin shown at each intermediate step, which matters when you are deciding which concession to withdraw.
Worked example
List price
$1,250.00
Unit cost
$780.00
Distributor discount
20%
Volume break
7.5%
Promotion
5%
Payment terms
2%
Result
Net $861.18 · 31.1% effective discount · 9.4% gross margin
$1,250.00 × 0.80 = $1,000.00, × 0.925 = $925.00, × 0.95 = $878.75, × 0.98 = $861.18. The multipliers combine to 0.68894, so the effective single discount is 31.1% while the four rates sum to 34.5% — compounding saved 3.4 points. Margin is the real casualty: gross profit per unit drops from $470.00 at list to $81.18, so margin falls from 37.6% to 9.4% and you would need 5.79 times the volume to hold the same gross profit.
Why a discount cascade beats the sum of its rates
Adding the rates always overstates the discount. Ten percent off $1,000 leaves $900; a second ten percent takes $90, not $100. The gap widens with the number of steps and with the size of each rate, which is why a four-step cascade of small concessions feels harmless and a two-step cascade of large ones does not.
Discount chain
Sum of the rates
Effective single discount
Points saved by compounding
20% + 10%
30.0%
28.0%
2.0
20% + 7.5% + 5% + 2%
34.5%
31.1%
3.4
10% + 10% + 10% + 10%
40.0%
34.4%
5.6
30% + 15% + 5%
50.0%
43.5%
6.5
The sum is never the answer. Use it as a ceiling estimate only.
Margin falls much faster than price
Price fell 31.1% in the worked example. Gross profit fell 82.7%, from $470.00 to $81.18 per unit, because the cost stayed at $780.00 the whole way down. That is the arithmetic behind every uncomfortable quarter-end conversation: the discount looks like a third off, the profit behaves like a wipeout. The volume test makes it concrete — to earn the same gross profit at the net price you would need 5.79 times the units, which sales rarely promises and the plant usually cannot supply. Check the contribution side of the same trade with the contribution margin calculator.
Where cascades come from in ERP pricing
Price level or customer group — the standing rate attached to the account, often set years ago and never revisited.
Quantity breaks on the item or price group, which fire automatically once a line crosses a threshold.
Promotions and campaign codes applied at order entry, frequently on top of the break rather than instead of it.
Payment-terms deductions, taken by the customer whether or not they paid early.
Off-invoice items — rebates, freight allowances, co-op marketing, year-end volume bonuses. These do not show on the quote at all but they come out of the same margin.
Set a floor, not a policy document
A floor margin converts into a single number sales can hold in their head. At $780 cost and a 15% minimum margin, the lowest defensible price is $780 ÷ 0.85 = $917.65, which is 26.6% off a $1,250 list. Anything past 26.6% needs approval, whatever combination of steps produced it. The worked cascade reaches 31.1%, so it is 4.5 points past the floor — and sequential rates hide breaches like that because no single step looks unreasonable. Convert price to margin with the gross margin calculator, and read margin vs markup if your price list is built on markup.
Finding the cascades you did not know about
The discounts on the quote are the easy part. Realised price — list minus every deduction including credits, rebates and unearned terms — usually lives across four tables and nobody owns the join. That is why the average discount reported to the board is lower than the one the bank statement implies. Ask ERPray for it directly: "average realised discount off list by customer group last quarter, including credit memos". It writes the query against your own schema and shows it, so you can argue with the definition instead of the number.
Frequently asked questions
Do stacked discounts add up?
No. Each discount applies to the price left after the previous one, so they multiply. A 20% and a 10% discount give 1 − (0.80 × 0.90) = 28%, not 30%. Adding the rates always overstates the total, by more points as the chain gets longer or the rates get larger.
How do you calculate the effective single discount?
Multiply the surviving fractions together and subtract from one. For 20%, 7.5%, 5% and 2%: 0.80 × 0.925 × 0.95 × 0.98 = 0.68894, so the effective single discount is 31.1%. Equivalently, divide the net price by the list price and subtract from one.
Does the order of discounts matter?
Not for the net price — multiplying the same factors in any order gives the same result. Order does change the price and margin shown at each intermediate step, which matters when you are negotiating concession by concession or deciding which discount to withdraw first.
Why does a small extra discount cost so much margin?
Because it comes out of gross profit, not revenue. On a 9.4% margin, another 5% off price removes more than half the remaining profit, since the cost does not move. The lower your margin, the more destructive each additional point becomes — this is why floors are set on margin rather than on discount.
How much extra volume does a discount need to pay for itself?
Divide the gross profit per unit before the discount by the gross profit per unit after it. Going from $470.00 to $81.18 of profit needs 5.79 times the volume to break even on gross profit. Any discount justified by "we will sell more" should be checked against that multiple first.
Should rebates be part of the discount cascade?
Include them if you want realised price. Off-invoice rebates, freight allowances and co-op marketing never appear on the quote but they reduce the same margin, so leaving them out produces a net price that looks healthier than your bank balance. Model them as one more step in the chain.
This calculator needs you to find the inputs first. ERPray pulls them from your own ERP account and computes the answer live — with the exact query shown so you can check it.