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How do you calculate a price-volume-mix bridge on contribution?

Five effects, one check line that must read zero, and a volume year that turns out to be a price year.

Julian R. Sterling · from Pricing Strategy

A price-volume-mix bridge on contribution splits the change into five effects that must add back to the total: volume at last year's average contribution per unit, mix at last year's contribution per unit of each product, then price, commission and variable cost per unit at this year's volumes. In the worked case units rise 5.1 per cent and invoiced revenue 1.7 per cent, yet contribution falls 1,448,518.15, and price explains −1,089,991.39 of it, 3.31 times the damage done by mix.

Worked in full in Pricing Strategy by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →

A revenue bridge cannot answer the question a pricing review is really asking, which is where the profit went. The bridge has to run on contribution, and each effect has to be priced at the right year's figures, or the boxes overlap and stop closing.

The assumptions

The case is Ravensworth, the fictional adhesives maker in the companion files of Pricing Strategy, across its three product families. Pocket price is invoice price less every off-invoice deduction; contribution is pocket revenue less commission and variable cost.

Per-unit figures, year one to year two. Illustrative case.

Family	Units Y1	Units Y2	Pocket Y1	Pocket Y2	Var. cost Y1	Var. cost Y2	Contrib. a unit Y1
Structural adhesives	160,000	158,395	121.84	119.52	78.00	79.56	41.23
Sealants	420,000	457,803	48.62	47.72	36.00	36.72	11.58
Protective coatings	210,000	214,206	77.18	75.74	58.00	59.16	17.53
Total	790,000	830,404					19.16

Contribution was 15,139,362.59 in year one and 13,690,844.44 in year two. Sealants, the lowest-margin family, grew 9.0 per cent and rose from 53.2 to 55.1 per cent of units. Every family's pocket price fell 1.9 per cent and every variable cost rose about 2 per cent.

The calculation, step by step

The five effects. The check line must read zero.

Effect	Contribution
Volume	774,292.16
Mix	−329,158.64
Price (pocket, at year-two volumes)	−1,089,991.39
Commission	21,533.04
Variable cost	−825,193.32
Change in contribution	−1,448,518.15
Check: effects less change	0.00

The result

The sales review saw invoiced revenue up 1.7 per cent on 5.1 per cent more units and called it a volume year. Pocket revenue rose only 1.6 per cent and contribution fell 9.6 per cent. Price alone accounts for 75.2 per cent of the fall. The commission box is positive because commission is paid on the invoice, and a lower invoice pays less of it: a small offset, not a gain.

Read together, price and cost are −1,915,184.71. Pocket prices went down while costs went up, so the margin was squeezed from both sides, and the extra volume of 774,292.16 recovered well under half of it.

What if: how much price recovery would have changed the year

Change in contribution, year one to year two, all other effects (commission included) held as reported.

Scenario	Change in contribution
As happened: pocket prices down 1.9%	−1,448,518.15
Half the price erosion recovered	−903,522.46
Pocket prices held flat	−358,526.76
Prices held and cost inflation passed through	466,666.56

Passing through the cost increase needed about 0.99 a unit on average. Holding price and passing that on would have turned a fall of 1,448,518.15 into a rise of 466,666.56 on the same volume and the same mix.

The common mistakes

• Volume at each family's own margin. Pricing the extra units family by family gives 445,133.51 and makes the mix box vanish. It is the volume and mix effects added together, so the mix shift towards sealants disappears from view.
• Running the bridge on revenue. On pocket revenue the same data show volume of 2,870,445.06 and mix of −903,263.09 at an average pocket price of 71.04, with a net rise of 877,190.58. Revenue rose; profit fell. The boxes that matter for a pricing decision are on contribution.
• Treating the convention as neutral. Weighting the price change at year-one volumes gives −1,053,409.71 instead of −1,089,991.39, a difference of 36,581.68 or 3.4 per cent of the box. State the convention you use. The direction and the order of magnitude survive the choice; the exact figure does not.
• A bridge that does not close. If the five effects do not add to the change in contribution, one of them is double counting. Keep the check line on the page.

Takeaway

• Volume and mix at year-one contribution; price, commission and cost at year-two volume.
• Here: volume 774,292.16, mix −329,158.64, price −1,089,991.39, commission 21,533.04, cost −825,193.32.
• Price did 3.31 times the damage of mix. A volume year on the sales report was a price year on the contribution line.

The five-effect bridge with its check line is in the price bridge workbook on the Pricing Strategy companion page, built from every account line rather than from family totals. The price erosion itself starts in the waterfall, worked in how to calculate pocket price from list price, and an increase can be partly undone before it lands, as shown in how much of a price increase forward buying takes back.

Questions readers ask

What is the difference between the volume effect and the mix effect?

The volume effect prices the change in total units at last year's average contribution per unit: 40,404 extra units at 19.1638 give 774,292.16. The mix effect captures the shift between products at last year's per-product contribution. A shift towards lower-margin sealants gives -329,158.64, even though total units rose 5.1 per cent.

Should price effects be weighted at current or prior-year volumes?

Either is defensible if stated. Weighting at current-year volumes assigns the price-volume interaction to price; here that gives -1,089,991.39 against -1,053,409.71 at prior-year volumes, a 3.4 per cent difference. The bridge closes either way as long as the other effects use the matching convention.

Why run price-volume-mix on contribution rather than revenue?

Because revenue can rise while profit falls. On pocket revenue the same year shows a gain of 877,190.58; on contribution it shows a loss of 1,448,518.15, because lower prices and higher variable costs squeezed every unit. Pricing decisions are about margin, so the bridge must be.

Also on this site

• How do you calculate pocket price from list price?List less on-invoice discounts, then off-invoice deductions as a share of invoice: 148.00 list, 129.03 invoice, 112.51 pocket, 24.0 points below list.
• How much of a price increase does forward buying take back?Distributors buy 8.67 weeks ahead of a 2.5 per cent increase and take back 59,840.25, exactly a fifth of what they were due to pay. Then their volume falls 67 per cent.
• When does a commission plan reward a discount that loses money?A revenue commission pays a representative to discount from 4.55 extra units per hundred; the company needs 11.40. The 1.20 per cent rate cancels out.
• How do you calculate activity-based costing per unit?Pool over driver count gives the rate; counts times rates over units gives overhead a unit. A bracket costing 287.69 on labour hours costs 436.91 on activities.
• How do you calculate construction cost escalation to the midpoint?Compound the inflation rate from the base date to mid-construction: 24,000,000 escalated 21 months at 4.0 per cent adds 1,705,117, or 7.10 per cent.
• How do you convert a cycle service level into a fill rate?Fill rate is 1 minus sigma times G(z) over the order quantity. On part AF-7 a 98 per cent cycle service level is a 99.38 per cent fill rate.

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