A factory's direct labour line split into a rate and an efficiency variance, then the overhead variance a labour-hour absorption base drags along with every excess hour.
The labour rate variance is (actual rate − standard rate) × actual hours, and the labour efficiency variance is (actual hours − standard hours for the actual output) × standard rate. A factory that paid 4,802,316 for 152,940 hours, 31.40 an hour, against a standard of 148,500 hours at 30.80 has a rate variance of 91,764 adverse and an efficiency variance of 136,752 adverse: 228,516 in all. Under labour-hour absorption, the same 4,440 excess hours also report 372,960 of adverse overhead variance.
Worked in full in Cost Accounting by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The labour line here is the one in the worked case of the book, 152,940 direct labour hours costing 4,802,316. The standards below are illustrative additions, chosen to show how the split works and what it hides.
| Input | Value |
|---|---|
| Actual direct labour hours worked | 152,940 |
| Actual direct labour cost | 4,802,316 |
| Standard rate per hour | 30.80 |
| Standard hours allowed for the output actually produced | 148,500 |
| Predetermined overhead rate per labour hour | 84.00 |
Step 0: standard hours allowed. The 148,500 is not a budget figure. It is the output actually produced, family by family, multiplied by the standard hours per unit on each cost card, then summed. It flexes with volume and with mix: a month that makes more of the labour-heavy parts earns more standard hours, so a crew is never blamed for hours the output genuinely required.
Step 1: the actual rate. 4,802,316 ÷ 152,940 = 31.40 an hour, 0.60 above standard.
Step 2: build the three figures the variances sit between.
Actual hours × actual rate = 152,940 × 31.40 = 4,802,316
Actual hours × standard rate = 152,940 × 30.80 = 4,710,552
Standard hours × standard rate = 148,500 × 30.80 = 4,573,800
Step 3: the two variances. The rate variance is the gap between the first two lines, the efficiency variance the gap between the last two.
Rate variance = (31.40 − 30.80) × 152,940 = 91,764 adverse
Efficiency variance = (152,940 − 148,500) × 30.80 = 4,440 × 30.80 = 136,752 adverse
Total = 4,802,316 − 4,573,800 = 228,516 adverse
Excel: =(ActCost/ActHrs-StdRate)*ActHrs and =(ActHrs-StdHrs)*StdRate
The rule that keeps the split clean is the same as for materials: the price effect is measured on the actual quantity, the quantity effect at the standard price. Reverse either and the two no longer add to the total.
The crew worked at 97.1 per cent efficiency and cost 0.60 an hour more than planned. Of the 228,516, 40.2 per cent is rate and 59.8 per cent is hours. That would normally end the analysis. In a factory that absorbs its overhead on labour hours, it should not, because every excess hour is also charged 84.00 of overhead in the overhead efficiency variance.
Overhead efficiency variance = 4,440 × 84.00 = 372,960 adverse
The overhead figure is 2.73 times the labour efficiency variance it comes from, and the reported adverse variance attached to labour performance rises to 601,476.
The two figures usually belong to different people. The rate variance sits with whoever sets pay, grades and overtime; the efficiency variance with production. A rate variance is often overtime in disguise: if the whole 0.60 an hour came from a time-and-a-half premium of 15.40, it would represent 5,959 overtime hours, 3.9 per cent of the hours worked. That is a scheduling question as much as a pay question, and it is why the two variances should be read together rather than sent to two different desks.
| Scenario | Rate | Hours | Rate var. | Efficiency var. | Labour total | Overhead eff. |
|---|---|---|---|---|---|---|
| On standard | 30.80 | 148,500 | 0 | 0 | 0 | 0 |
| Actual year | 31.40 | 152,940 | 91,764 | 136,752 | 228,516 | 372,960 |
| Cheaper, slower crew | 29.90 | 158,000 | −142,200 | 292,600 | 150,400 | 798,000 |
| Overtime to hold the schedule | 32.60 | 149,800 | 269,640 | 40,040 | 309,680 | 109,200 |
Positive figures are adverse. On labour alone, the cheaper crew is the best of the three and overtime the worst. Add the overhead efficiency variance and the ranking flips: overtime reports 418,880 in all, the cheaper crew 948,400. Which ranking is right depends on a question the variance report cannot answer: does the overhead actually rise when labour hours rise?
If the overhead pool moves with setups, orders, machine hours and inspections rather than labour hours, most of the overhead efficiency variance is an artefact of the absorption base. It is not cash, and a supervisor judged on it will avoid a cheaper crew for the wrong reason.
The same factory costed on labour hours and again on five activity drivers, with every figure on a live formula, is in the free workbook for this case. The material side of the same analysis is in how to calculate material price and usage variances.
(Actual hours minus standard hours allowed for the actual output) times the standard rate. With 152,940 hours worked against 148,500 allowed at a standard of 30.80, the variance is 4,440 times 30.80, or 136,752 adverse. The standard hours must be those for what was actually produced, not the budget.
Because a cheaper crew often works more slowly. At 29.90 an hour over 158,000 hours the rate variance is 142,200 favourable, but the efficiency variance is 292,600 adverse, and under labour-hour absorption the extra hours also report 798,000 of adverse overhead efficiency variance.
Only for the part of overhead that genuinely moves with labour hours. With overhead absorbed at 84.00 a labour hour, 4,440 excess hours report 372,960 adverse. If the pool is driven by setups, orders and machine time instead, most of that figure is a product of the absorption base, not cash spent.
This article is one calculation from Cost Accounting. 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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