A gross margin percentage bridge for a three-segment business, the two conventions in use, and why they disagree by 0.31 points.
To split a change in gross margin percentage, recompute the margin on actual volumes at budget prices and budget unit margins. The gap between that margin and the budget is mix; the gap between it and actual is rate. In an illustrative quarter the margin fell from 45.61 to 42.61 per cent: 1.57 points of mix and 1.43 points of price, so even with no discount at all the margin would have been 1.57 points short.
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A gross profit bridge in money answers "how much did we lose?". The board usually asks a different question: "why is the margin lower?". The answer in points is not the money bridge divided by revenue. It needs its own step, a hypothetical quarter that sells what was actually sold at the prices and margins that were budgeted.
| Segment | Budget revenue | Actual revenue | Budget margin | Actual margin |
|---|---|---|---|---|
| Instruments (1,200 units budget, 1,380 actual) | 110,400,000 | 121,440,000 | 32.00% | 28.91% |
| Consumables | 68,000,000 | 62,500,000 | 68.00% | 68.00% |
| Service | 31,600,000 | 32,400,000 | 45.00% | 45.00% |
| Group | 210,000,000 | 216,340,000 | 45.61% | 42.61% |
Instruments were budgeted at 92,000 a unit and sold at 88,000, a discount of 4.35 per cent, against a standard cost of 62,560. Revenue beat budget by 6,340,000; gross profit missed it by 3,600,800.
=GP_mid/Rev_mid-GP_bud/Rev_bud for mix and =GP_act/Rev_act-GP_mid/Rev_mid for rate.The two effects are roughly equal, and the mix effect is the larger. The quarter sold 180 more instruments at a 32.00 per cent margin and fewer consumables at 68.00 per cent. That shift alone takes 1.57 points off the group margin, even though at budget prices it adds 1,919,200 of gross profit. The discount takes 1.43 points and 5,520,000 of gross profit: 1,380 instruments at 4,000 less each. Points and money do not translate one for one, which is why each needs its own bridge.
The finding that matters: remove the discount and the margin is still 1.57 points below budget. Whoever owns pricing can explain only half of the movement. The other half belongs to whoever owns the sales mix: more instruments, fewer consumables.
Holding volumes as they were and varying only the instrument price:
| Instrument price | Actual margin | Mix (pts) | Price (pts) | Total (pts) | GP vs budget |
|---|---|---|---|---|---|
| 92,000 | 44.04% | −1.57 | 0.00 | −1.57 | +1,919,200 |
| 90,000 | 43.34% | −1.57 | −0.70 | −2.28 | −840,800 |
| 88,000 | 42.61% | −1.57 | −1.43 | −3.00 | −3,600,800 |
| 86,000 | 41.87% | −1.57 | −2.17 | −3.74 | −6,360,800 |
At full price gross profit beats budget by 1,919,200 while the margin is still 1.57 points light. A pack that reports only gross profit in money would call that quarter a success; one that reports only margin would call it a failure. Both are true, which is why the bridge has to be shown in money and in points side by side.
The second convention in common use weights each segment by its actual revenue share: mix is the change in share times the budget margin, rate is the actual share times the change in margin.
| Segment | Budget share | Actual share | Mix | Rate |
|---|---|---|---|---|
| Instruments | 52.57% | 56.13% | +1.14 | −1.74 |
| Consumables | 32.38% | 28.89% | −2.37 | 0.00 |
| Service | 15.05% | 14.98% | −0.03 | 0.00 |
| Group | −1.27 | −1.74 |
The total is the same −3.00 points, but 0.31 points have moved from mix to rate. The discount lowered instrument revenue, so instruments' actual share is smaller than it would have been at full price, and part of the mix shows up as rate. Neither convention is wrong. Changing between them from one quarter to the next is, because the movement in the bridge is then the analyst's, not the business's. The same base problem appears in the money bridge, set out in the price-volume-mix bridge on contribution.
A second trap: running the mix step on revenue alone. A flexible budget restates costs at actual volume but, on a single line, cannot see mix at all. With several lines, mix appears only when margins are weighted, so build the middle column on gross profit, not revenue.
The bridge in money and in points, with the discount as an input, is live in the free workbook for this case.
The change in the overall margin caused by selling relatively more of the low-margin lines, with every line's own margin held at budget. In the illustrative quarter, at budget prices, instruments at 32.00 per cent rose from 52.57 to 57.23 per cent of revenue while consumables at 68.00 per cent fell from 32.38 to 28.17 per cent, costing 1.57 points of margin before any discount.
Because the extra revenue came at a lower margin. Revenue was 6,340,000 above budget, 3.02 per cent, yet gross profit was 3,600,800 below it, down 3.76 per cent: 180 extra instruments were sold at a 4.35 per cent discount while high-margin consumables fell short. A revenue bridge alone will never show it.
Either, provided the pack says which and keeps it. Weighting by actual revenue shares lets the discount shrink the instruments' share, so the same quarter reads 1.27 points of mix and 1.74 of rate instead of 1.57 and 1.43. The 0.31 points that move between the lines are a convention, not a finding.
This article is one calculation from Financial Planning and Analysis. 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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