A discount authority matrix built from the extra volume each discount needs, instead of flat 5, 10 and 15 per cent bands.
Set discount approval levels from the extra volume each discount needs to break even, d / (m − d), not from round percentages. If a sales rep may approve any discount that needs no more than 15 per cent extra volume to pay for itself, the rep's limit is 2.61 per cent on a 20 per cent margin product, 3.91 per cent at 30 and 5.22 per cent at 40. A flat 5 per cent limit across all three lets the rep give away a discount that needs a third more volume on the low-margin line.
Worked in full in Pricing Strategy by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Most discount approval matrices look like this: up to 5 per cent the rep decides, up to 10 per cent the manager, up to 15 per cent the director, anything above goes to finance. The bands are the same for every product, so they treat a point of discount as if it cost the same everywhere. It does not. A discount comes straight out of contribution, and the thinner the margin, the larger the share of contribution it removes and the more extra volume the deal must bring to leave profit where it was.
The fix is to fix what each approver may risk, expressed as the volume uplift the deal must deliver, and let the discount limit fall out of the margin.
| Input | Value |
|---|---|
| Contribution margin at pocket price, family A / B / C | 20% / 30% / 40% |
| Maximum break-even volume uplift a sales rep may accept | 15% |
| Maximum for a sales manager | 35% |
| Maximum for a sales director | 60% |
| Example deal: order value at current pocket price, and discount requested | 200,000, 8% |
The margin is contribution after every on-invoice and off-invoice deduction the customer already takes, not the gross margin on list. Starting from list overstates it, as how to calculate pocket price from list price shows.
Step 1, the break-even uplift. A discount d on a product with margin m leaves unit contribution of m − d. To earn the same contribution, volume must rise by d / (m − d).
| Discount | Margin 20% | Margin 30% | Margin 40% |
|---|---|---|---|
| 2% | 11.1% | 7.1% | 5.3% |
| 3% | 17.6% | 11.1% | 8.1% |
| 5% | 33.3% | 20.0% | 14.3% |
| 8% | 66.7% | 36.4% | 25.0% |
| 10% | 100.0% | 50.0% | 33.3% |
| 15% | 300.0% | 100.0% | 60.0% |
Step 2, invert it. Fix the uplift k each approver may accept and solve for the discount:
k = d / (m − d) ⇒ dmax = k × m / (1 + k)
Sales rep, margin 30%: 0.15 × 0.30 / 1.15 = 3.91%
Excel, with the margins in row 1 and the uplift limits in column A: =$A2*B$1/(1+$A2)
| Approver (uplift limit) | Family A, 20% | Family B, 30% | Family C, 40% |
|---|---|---|---|
| Sales rep (15%) | 2.61% | 3.91% | 5.22% |
| Sales manager (35%) | 5.19% | 7.78% | 10.37% |
| Sales director (60%) | 7.50% | 11.25% | 15.00% |
| Above that | Pricing committee or finance | ||
Every cell carries the same risk: a deal at the limit has to bring the same proportional volume uplift to pay. On the high-margin family the derived matrix is close to the familiar 5, 10 and 15. On the low-margin family it is roughly half.
| Flat limit | Family A, 20% | Family B, 30% | Family C, 40% |
|---|---|---|---|
| Rep, 5% | 33.3% | 20.0% | 14.3% |
| Manager, 10% | 100.0% | 50.0% | 33.3% |
| Director, 15% | 300.0% | 100.0% | 60.0% |
Under the flat matrix a manager on family A can approve a discount that needs the customer to double its volume, and a director one that needs it to quadruple. Nobody would sign that off if the number were on the request form, which is why it should be.
An order worth 200,000 at the current pocket price with a further 8 per cent discount gives away 16,000 whichever family it is in. On family A that is 40.0 per cent of the 40,000 contribution, and the deal needs 66.7 per cent more volume, 133,333 more revenue at the undiscounted price, to break even: above the director's 60 per cent, so it goes to the pricing committee. On family C it is 20.0 per cent of 80,000 of contribution and needs 25.0 per cent more volume: a manager's decision. Under the flat matrix both would have been a manager's decision.
Delegate risk, not percentages. Choose the volume uplift each level may accept, 15, 35 and 60 per cent here, and derive the discount limit as k × m / (1 + k) for each margin. Print the break-even uplift on every discount request. The discount calculator in the free workbooks for this book builds the authority matrix with the break-even volume beside each band.
A table that says who may approve which discount. Built from break-even volume, it fixes the volume uplift each level may accept, for example 15, 35 and 60 per cent, and derives the discount limit per product. At a 30 per cent margin those give limits of 3.91, 7.78 and 11.25 per cent.
Discount divided by margin less discount. A 5 per cent discount needs 33.3 per cent more volume at a 20 per cent contribution margin, 20.0 per cent at 30 and 14.3 per cent at 40. The margin must be measured at pocket price, after the deductions the customer already takes.
Yes, whenever margins differ. The same 8 per cent discount on a 200,000 order costs 16,000 either way, but that is 40.0 per cent of contribution on a 20 per cent margin product and 20.0 per cent on a 40 per cent margin product, needing 66.7 against 25.0 per cent more volume.
The authority matrix, with the break-even volume beside each band, is built in chapter 17 of 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.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: business operations: cost, contracts, pricing and supply chain → · All 1340 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.