The rebate cliff worked on one account: the effective price of the units that cross the tier, the two thresholds where they become free or loss-making, and what an incremental scheme changes.
A retroactive rebate pays the higher rate on every unit of the year once the tier is reached, so the real price of the units that cross it is (extra revenue − extra rebate on the whole year) ÷ extra units. For account DIR-075, 640 units short of a 3.5 per cent tier, the last units bring 53,351.82 but trigger 13,571.37 of extra rebate: an effective price of 62.16 against an invoice price of 83.36. After variable cost, commission and other deductions they contribute 4,967.52, about 7.76 a unit instead of the usual 27.30.
Worked in full in Pricing Strategy by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Rebate tiers are presented as a reward for volume. Retroactive ones are also a cliff. Just below each threshold the marginal price collapses, sometimes below zero, and the customer's buyer knows it better than the seller's pricing team.
| Input | Value |
|---|---|
| Units bought this year | 9,360 |
| Invoiced purchases | 780,270.35 |
| Blended invoice price per unit | 83.36 |
| Variable cost per unit | 50.98 |
| Next tier, units | 10,000 |
| Rebate rate now / at the tier | 2.0% / 3.5% |
| Sales commission, share of invoice | 2% |
| Other off-invoice deductions on this account | 2.1% |
=(B3*B4-(B7*(B2+B3*B4)-B6*B2))/B3 for the effective price, with invoiced purchases in B2, units short in B3, price in B4 and the two rates in B6 and B7Sold at the account's normal 2 per cent rebate, the same 640 units would contribute 17,471.85. The tier takes 72 per cent of that away. The customer sees the mirror image: the 640 units cost it 39,780.45 net, against 53,351.82 at its normal invoice price, which is a strong reason to move them from a second supplier.
The extra rebate is almost fixed, because it is mostly the re-rating of units already bought. The extra revenue shrinks with the distance. So the closer an account is to the tier, the worse the last units become.
| Units short | Extra revenue | Extra rebate | Effective price | Contribution |
|---|---|---|---|---|
| 650 | 54,185.44 | 13,588.04 | 62.46 | 5,240.52 |
| 640 | 53,351.82 | 13,571.37 | 62.16 | 4,967.52 |
| 400 | 33,344.89 | 13,171.23 | 50.43 | -1,584.42 |
| 200 | 16,672.44 | 12,837.78 | 19.17 | -7,044.38 |
| 145 | 12,087.52 | 12,746.08 | -4.54 | -8,545.87 |
| 100 | 8,336.22 | 12,671.06 | -43.35 | -9,774.36 |
| 50 | 4,168.11 | 12,587.69 | -168.39 | -11,139.34 |
Two thresholds fall out in closed form. The last units stop covering their variable cost, commission and other deductions when the account is 458.04 units short:
Inside 153.06 units the customer is paid to take the goods: an account 100 units short gets them at minus 43.35 a unit.
Across Ravensworth's whole book, 17 accounts sit within 15 per cent below a tier, 9,961 units short in total. If every one crossed, the rebate bill would rise by 187,091.56 on volume the company largely already has.
Pricing the tier at its headline rate. A 3.5 per cent rebate sounds like 3.5 per cent off. On the units that cross the tier it is 25.4 per cent off, because they carry the re-rating of the whole year.
Leaving out the account's other deductions. DIR-075 also takes freight allowances, returns and claims worth 2.1 per cent of invoice, and the extra units carry them too. Without them the contribution looks like 6,087.91 instead of 4,967.52, and the loss-making threshold moves.
Treating incremental as a free fix. Paying each rate only on the units inside its band removes the cliff: the last 640 units then contribute 17,471.85. But on Ravensworth's current volumes the same published rates paid incrementally would cost 951,505.97 instead of 1,604,149.89, taking 652,643.92 out of customers' pockets. Converting is a price increase in disguise, to be planned as one.
The free workbook for this case, on the Pricing Strategy companion page, carries the rebate cliff with both thresholds solved and a blank version for your own tiers. Where rebates sit in the cascade from list to pocket is worked in how to calculate pocket price from list price.
A retroactive, or all-units, rebate pays the tier rate on every unit of the year once the threshold is reached. An incremental rebate pays each rate only on the units inside its band. On account DIR-075 the last 640 units before a 10,000-unit tier contribute 4,967.52 under the retroactive scheme and 17,471.85 under an incremental one at the same published rates.
When the extra rebate on the whole year exceeds the invoice value of the units that cross the tier. With a 2 per cent rate below and 3.5 per cent at 10,000 units, that happens 153.06 units short of the tier. Below that distance the customer is paid to take the goods, and the account's effective price on those units is negative.
They are common, but retroactive, all-units rebates that pull the last units of a customer's requirement away from a competitor are the shape competition authorities scrutinise most closely when the seller holds a strong position. Changing a published rebate scheme also needs the notice set out in the conditions of sale. Price the scheme, then take it to counsel; this is a calculation, not legal advice.
This article is one calculation from Pricing Strategy. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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