A favourable payroll line is usually empty roles sitting on top of a rising cost per head. The three-way split into headcount, grade mix and pay shows which is which.
Split a payroll variance into headcount and rate by pricing the difference in heads at the budgeted average cost, and the difference in average cost at the actual heads. An illustrative quarter budgeted at 3,000,000 for 120 people came in at 2,949,840 for 112: 50,160 favourable, made of 200,000 of vacancies and 149,840 of higher cost per head. Split the rate further by grade and 92,000 of it is a richer mix, 57,840 an unbudgeted pay rise, and with all 120 roles filled at today's average cost per head the quarter runs 160,543 over.
Worked in full in Financial Planning and Analysis by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Payroll is the largest controllable line in most budgets and the one most often reported as a single favourable number. A favourable payroll variance usually means unfilled roles, which is a timing benefit that reverses, sitting on top of a cost per head that is drifting upwards, which does not. Reporting them as one figure hides the second behind the first.
| Grade | Budget FTE | Budget cost per FTE | Actual FTE | Actual cost per FTE |
|---|---|---|---|---|
| Junior | 60 | 18,000 | 50 | 18,360 |
| Mid | 45 | 28,000 | 46 | 28,560 |
| Senior | 15 | 44,000 | 16 | 44,880 |
| Total | 120 | 25,000 avg | 112 | 26,338 avg |
FTE are averages over the quarter, not period-end heads: a hire in the last week of the quarter adds almost nothing to cost. Actual pay is 2.0 per cent above budget in every grade, an increase the budget did not include. What a fully loaded cost per FTE contains is set out in the fully loaded cost of an employee.
Step 1: the totals. Budget 120 × 25,000 = 3,000,000. Actual 918,000 + 1,313,760 + 718,080 = 2,949,840, an average of 26,338 per FTE. Total variance 50,160 favourable.
Step 2: the two-way split.
Headcount variance = (actual FTE − budget FTE) × budget average = (112 − 120) × 25,000 = 200,000 favourable
Rate variance = (actual average − budget average) × actual FTE = (26,337.86 − 25,000) × 112 = 149,840 adverse
Excel: =(ActFTE-BudFTE)*BudAvg and =(ActAvg-BudAvg)*ActFTE
The average cost per head rose 5.35 per cent, but pay rose only 2.0. The rest is the mix.
Step 3: split the rate into mix and pay. Price the actual heads at the budget cost of their own grade:
Actual FTE at budget grade rates = 50 × 18,000 + 46 × 28,000 + 16 × 44,000 = 2,892,000
Mix variance = 2,892,000 − 112 × 25,000 = 92,000 adverse
Pay variance = 2,949,840 − 2,892,000 = 57,840 adverse
The three pieces add back to the total: 200,000 favourable less 92,000 and 57,840 adverse is 50,160 favourable. The structure is the same as the price and usage split in material price and usage variances, with heads in place of kilograms.
| Grade | FTE vs budget | Heads at grade rate | Pay variance |
|---|---|---|---|
| Junior | −10 | −180,000 | 18,000 |
| Mid | +1 | 28,000 | 25,760 |
| Senior | +1 | 44,000 | 14,080 |
| Total | −8 | −108,000 | 57,840 |
All the vacancies are junior roles; the department is over budget at mid and senior grades. The heads column at grade rates, 108,000 favourable, is the headcount and mix variances together: 200,000 less 92,000. A manager who has hired senior people into a junior budget looks under budget for as long as the junior roles stay empty.
| Eight hires at | Quarter cost | Over budget, quarter | Over budget, year |
|---|---|---|---|
| Junior | 3,096,720 | 96,720 | 386,880 |
| Mid | 3,178,320 | 178,320 | 713,280 |
| Senior | 3,308,880 | 308,880 | 1,235,520 |
Even the cheapest refill leaves the department 96,720 a quarter over budget. A reforecast that keeps 120 heads at the actual average of 26,338 lands at 3,160,543 a quarter, 160,543 over, or 642,171 for a year. To come back to budget it must also restore the budgeted mix and find the 60,000 a quarter that the 2.0 per cent pay rise costs at full headcount.
The mistake is to compute the rate variance on budget heads, or the headcount variance at actual average cost, and so produce a pair that does not add up, or to stop at two lines. A two-way split tells you that cost per head rose 5.35 per cent; only the three-way split tells you that most of the rise is who was hired, which a hiring decision can reverse, rather than what they are paid, which it cannot.
Fourteen empty roles behind a favourable research and development line, and what the slip they cause defers, are worked in the free workbook for this case.
The difference between actual and budgeted average FTE, multiplied by the budgeted average cost per FTE. Eight vacancies against a budget of 120 at 25,000 a quarter each is a 200,000 favourable headcount variance. Use average FTE over the period, not period-end heads.
Because the mix of grades changed. If the vacancies are junior and the hires senior, the average rises even at budget pay rates. Here the average rose 5.35 per cent, from 25,000 to 26,338: 92,000 of the rate variance was mix and 57,840 was the 2.0 per cent pay rise.
Only the part that will not reverse. Vacancies are timing: once filled, the cost returns at the current cost per head. A department 50,160 under budget with 112 of 120 roles filled runs 160,543 over a quarter at full headcount and its current average cost per head, 642,171 a year, because its average cost per head has risen.
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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