Promotion: calculating the incremental volume required before cutting the price.
Key distinctions
Three conditions before calculating.
A counterfactual baseline
The reference is not the previous week but the volume expected without the operation, corrected for season, distribution, trend, competition and calendar. A poor baseline turns seasonality into increment.
Margin per unit
The discount also applies to customers who would have bought at full price. The lower the promotional margin, the higher the uplift needed to preserve contribution.
Delayed effects
Stockpiling, purchase acceleration, learning the low price and repeat purchase change the value after the campaign. The window must include the post-promotion dip and, where possible, the acquired cohort.
Method
Assessing a promotion before, during and after the operation
- 01Estimate the volume without promotion
Build a forecast or a comparable group within the same distribution scope, and publish the uncertainty of that baseline rather than a single point.
- 02Calculate the threshold
Divide the reference contribution by the promotional unit margin, then add media, in-store feature, coupon, logistics and retailer funding costs.
- 03Decompose the volume
Separate new buyers, additional frequency, switching from another SKU, stockpiling and purchases brought forward from the following weeks.
- 04Measure the recovery
Track the return to full price, repeat purchase, cohort margin and post-operation volume; an acquisition promotion must be judged on the cohort, not on the initial basket.
The promotional break-even curve
The required volume rises quickly as the discount cuts the unit margin. The threshold is compared with the observed volume and with the volume corrected for pull-forward.
required volume = contribution without promotion ÷ promotional unit marginA 65% volume increase still destroys €3,750
The price falls from €100 to €80, the variable cost stays at €55, and the volume expected without promotion is 1,000 units. The reference contribution is €45,000.
The promotional margin is €25. It takes 45,000 ÷ 25 = 1,800 units, that is +80%, to match the contribution. With 1,650 units, contribution is only €41,250, before media costs and purchase acceleration.
The operation must be rejected or given a shallower discount. An uplift target below 80% is economically incompatible with maintaining the margin.
Acceptance conditions
What must be true to act.
- 01
The reference volume is estimated for the same scope and the same season.
- 02
The threshold includes every variable cost and every cost specific to the operation.
- 03
The volume is corrected for purchase acceleration and cannibalisation.
- 04
The return to full price and the repeat purchase are tracked after the campaign.
Limits
What this analysis does not prove.
- A promotion can serve a destocking or customer-acquisition objective that differs from immediate margin.
- The counterfactual becomes fragile during a competitor stock-out or a change of distribution.
- Reference-price and promotion-expectation effects need several cycles to be observed.
References
Works cited.
- Gupta, S. (1988), “Impact of Sales Promotions on When, What, and How Much to Buy”, Journal of Marketing Research.
- Bell, D. R., Chiang, J. & Padmanabhan, V. (1999), “The Decomposition of Promotional Response”, Marketing Science.
- Blattberg, R. C. & Neslin, S. A. (1990), Sales Promotion: Concepts, Methods, and Strategies.