Four things a price increase can protect, four different rates, and the volume each one can afford to lose.
To offset cost inflation in money, raise price by the cost increase per unit divided by the current price; to hold your margin percentage, raise it by the cost inflation rate itself. On an illustrative product at 100.00 whose costs rise by 5.10 a unit, that is 5.10 per cent to keep operating profit at 8,000,000, and 6.07 per cent to keep the 16.0 per cent margin. Raise by 4.30 per cent, the variable cost increase alone, and profit still falls by 400,000.
Worked in full in Pricing Strategy by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
"Costs are up 6 per cent, so prices go up 6 per cent" is the sentence heard in most pricing meetings in an inflationary year. Sometimes it is right. More often it answers a question nobody asked, because there are four different things a price increase can be meant to protect, and each needs a different rate. The calculation takes five minutes and should be done before the letter to customers is drafted, not after.
| Cost line per unit | Today | Inflation | Increase |
|---|---|---|---|
| Material | 40.00 | 6% | 2.40 |
| Direct labour | 14.00 | 5% | 0.70 |
| Energy and freight | 10.00 | 12% | 1.20 |
| Variable cost | 64.00 | 6.72% | 4.30 |
| Fixed cost, at current volume | 20.00 | 4% | 0.80 |
| Total cost | 84.00 | 6.07% | 5.10 |
The price is 100.00, so contribution is 36.00 a unit, a 36.0 per cent contribution margin, and operating profit 16.00, a 16.0 per cent operating margin. On 500,000 units: revenue 50,000,000, fixed costs 10,000,000, operating profit 8,000,000. The year's cost increase is 2,150,000 on variable cost and 400,000 on fixed cost, 2,550,000 in all. Do nothing and operating profit falls to 5,450,000, down 31.9 per cent.
=B2/B3 to hold money, =B2/B4 to hold the percentage.The two families of answer differ for one reason. Holding money needs the price to rise by the cost increase in money, which is a smaller percentage of price than of cost. Holding a percentage margin needs every line, price and cost, to rise by the same proportion, so the profit in money grows with it.
| Price rise | New price | Contribution per unit | Contribution margin | Operating margin | Operating profit |
|---|---|---|---|---|---|
| 4.30%: contribution per unit | 104.30 | 36.00 | 34.5% | 14.57% | 7,600,000 |
| 5.10%: profit in money | 105.10 | 36.80 | 35.0% | 15.22% | 8,000,000 |
| 6.07%: operating margin | 106.07 | 37.77 | 35.6% | 16.00% | 8,485,714 |
| 6.72%: contribution margin | 106.72 | 38.42 | 36.0% | 16.51% | 8,809,375 |
Which row is right depends on what the business has promised. A lender or a budget fixed in money needs 5.10 per cent. A board that reports margin percentages, or an investor valuing the company on a margin multiple, needs 6.07. In real terms, holding profit in money is a cut: if general inflation runs near the 6.07 per cent of this cost base, the same 8,000,000 buys about 6 per cent less than it did. That is the honest argument for the higher rate, and it should be made in those words rather than hidden in a cost-plus formula.
The variable-cost-only figure, 4.30 per cent, is the most common answer in practice because purchasing reports material and energy inflation and nobody reports the fixed cost line. Here it leaves operating profit 400,000 short, which is exactly the fixed cost inflation nobody priced.
Every rate above assumes no customer reacts. They do. The volume each rise can lose before operating profit falls below 8,000,000 is the money gained over the new contribution per unit:
| Price rise | 0% lost | 2% lost | 4% lost | 6% lost |
|---|---|---|---|---|
| 5.10% | 8,000,000 | 7,632,000 | 7,264,000 | 6,896,000 |
| 6.07% | 8,485,714 | 8,108,000 | 7,730,286 | 7,352,571 |
| 6.72% | 8,809,375 | 8,425,188 | 8,041,000 | 7,656,812 |
| 8.00% | 9,450,000 | 9,053,000 | 8,656,000 | 8,259,000 |
At 5.10 per cent there is no room at all: any lost unit takes profit below last year. At 6.07 per cent the business can lose 2.57 per cent of volume and still hold 8,000,000; at 6.72 per cent, 4.21 per cent. At 4.30 per cent it would need to sell 2.22 per cent more units to get back to last year, in a year when its customers are seeing a price increase.
Then there is realisation. If, as is typical, only part of the announced rate is collected because of negotiated exceptions and later effective dates, the letter must say more than the target. At an illustrative 60 per cent realisation, holding profit in money needs 8.50 per cent announced, holding the margin 10.12 per cent.
The common mistake is applying the variable cost inflation rate, 6.72 per cent, and calling it "passing on costs". It does pass them on, and then some: it holds the contribution margin percentage, which lifts operating profit by 809,375 above last year. That may be the right target, but a customer who asks for the cost breakdown will see that the cost increase was 4.30 a unit and the price increase 6.72. The reverse error, raising by 4.30 per cent because that is the material and energy bill, quietly absorbs the fixed cost inflation. Decide which number you are protecting, then compute the rate for it.
The free workbook for this case on the Pricing Strategy companion page sets a real price increase, segment by segment, against the cost increase it was meant to cover. How much of an announced rate is actually collected is worked in how to calculate price realisation on a price increase, and the weight of one point of price against one of volume in what a 1 per cent price increase is worth in operating profit.
Only if the aim is to keep the margin percentage. Costs rising 6.07 per cent need a 6.07 per cent price rise to hold a 16.0 per cent operating margin. To hold profit in money the rise is smaller: the 5.10 cost increase per unit over the 100.00 price, 5.10 per cent. Decide which one the business has promised before choosing.
Compute the cost increase per unit, including fixed costs spread over volume, and divide by price. Here material, labour and energy add 4.30 and fixed costs 0.80, so a 5.10 per cent rise passes on the cost exactly. Then gross it up for the share of the increase you expect to collect: at 60 per cent realisation, announce 8.50 per cent.
Less than in a normal year, because part of the rise only covers cost. A 5.10 per cent rise that just offsets inflation can lose nothing before operating profit falls below 8,000,000. At 6.07 per cent the product can lose 2.57 per cent of its volume; at 6.72 per cent, 4.21 per cent.
The book's own price increase is set against the cost inflation it was meant to cover in chapter 10 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.
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