One variance is an overspend someone can explain; the other is output that never absorbed a cost already paid.
The fixed overhead spending variance is actual fixed overhead minus budgeted fixed overhead; the volume variance is (budgeted hours minus standard hours allowed for the actual output) times the fixed overhead rate. A factory that budgeted 11,040,000 of fixed overhead over 160,000 hours, spent 11,193,548 and produced only 148,500 standard hours has a spending variance of 153,548 adverse and a volume variance of 793,500 adverse: 947,048 under-absorbed, of which 83.8 per cent is not overspending at all.
Worked in full in Cost Accounting by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The case is the same illustrative machining factory used for the variable overhead and labour variances on this site, so the four overhead variances can be read together and reconciled to the overhead control account. The 69.00 fixed rate is the fixed part of its 84.00 predetermined overhead rate.
| Input | Value |
|---|---|
| Budgeted fixed overhead (supervision, depreciation, rent, insurance) | 11,040,000 |
| Budgeted direct labour hours (the denominator) | 160,000 |
| Fixed overhead rate per labour hour | 69.00 |
| Actual direct labour hours worked | 152,940 |
| Standard hours allowed for the actual output | 148,500 |
| Actual factory overhead incurred | 13,610,000 |
| of which variable overhead | 2,416,452 |
| Actual fixed overhead | 11,193,548 |
The fixed rate is the budget divided by the denominator: 11,040,000 over 160,000 hours is 69.00. The variable part of the rate, 15.00, comes from 2,400,000 of variable overhead over the same hours, which is how the predetermined rate reaches 84.00.
Actual fixed overhead = 11,193,548
Budgeted fixed overhead = 11,040,000
Applied fixed overhead = standard hours × fixed rate = 148,500 × 69.00 = 10,246,500
Spending (budget) variance = 11,193,548 − 11,040,000 = 153,548 adverse
Volume variance = (160,000 − 148,500) × 69.00 = 11,500 × 69.00 = 793,500 adverse
Under-absorbed fixed overhead = 11,193,548 − 10,246,500 = 947,048
Excel: =ActFOH-BudFOH and =(BudHrs-StdHrs)*BudFOH/BudHrs
Notice what is missing from the fixed overhead calculation: there is no flexible budget that moves with hours. For variable overhead the flexible budget is actual hours times the standard rate. For fixed overhead the flexible budget is the budget itself, 11,040,000, at any level of activity inside the relevant range. That is why the spending variance compares actual cost with the original budget, and why the whole effect of activity lands in the volume variance.
The spending variance is a real overspend. The factory paid 153,548, or 1.4 per cent, more for its fixed costs than budgeted: a rent review, a supervisor hired mid-year, a higher insurance premium. Someone can be asked about it.
The volume variance is not money spent. The factory still paid 11,040,000 of budgeted fixed cost (plus the overspend). What it did not do was produce enough output to absorb it: 148,500 standard hours against 160,000 budgeted, 92.8 per cent of the plan. Each of the 11,500 missing standard hours was supposed to carry 69.00 of fixed cost into a product. It did not, so 793,500 sits in the overhead account instead of in inventory and cost of sales.
The 11,500 hour shortfall has two causes, and the actual hours separate them.
| Variance | Formula | Hours | Amount |
|---|---|---|---|
| Spending | Actual less budget | 153,548 | |
| Capacity (idle time) | (Budgeted − actual hours) × 69.00 | 7,060 | 487,140 |
| Fixed overhead efficiency | (Actual − standard hours) × 69.00 | 4,440 | 306,360 |
| Under-absorbed | 11,500 | 947,048 |
The capacity part, 487,140, is the 7,060 budgeted hours that were never worked. The efficiency part, 306,360, is the 4,440 hours that were worked but produced nothing a standard recognises. Neither changed the fixed cost bill by a penny.
Put the fixed analysis beside the variable overhead variances and the whole overhead account closes.
| Variance | Amount |
|---|---|
| Variable overhead spending | 122,352 |
| Variable overhead efficiency | 66,600 |
| Fixed overhead spending | 153,548 |
| Fixed overhead volume | 793,500 |
| Total under-applied, all adverse | 1,136,000 |
The two spending variances add to 275,900, the spending figure in how to calculate the predetermined overhead rate. That article applies overhead on actual hours (12,846,960) and reports 763,040 under-applied; the difference to 1,136,000 is the 372,960 of overhead efficiency on 4,440 excess hours at 84.00. The four-way view shows that only 66,600 of that efficiency effect was variable cost. The other 306,360 is fixed.
The spending variance does not move with output. The volume variance moves with every standard hour.
| Standard hours | Of budget | Applied | Volume variance | Under (over) absorbed |
|---|---|---|---|---|
| 140,000 | 87.5% | 9,660,000 | 1,380,000 A | 1,533,548 |
| 148,500 | 92.8% | 10,246,500 | 793,500 A | 947,048 |
| 155,000 | 96.9% | 10,695,000 | 345,000 A | 498,548 |
| 160,000 | 100.0% | 11,040,000 | 0 | 153,548 |
| 168,000 | 105.0% | 11,592,000 | 552,000 F | (398,452) |
At exactly budgeted output only the spending variance remains. Above it the volume variance turns favourable and the factory over-absorbs, which flatters profit for no reason other than volume.
The denominator matters as much. Strike the fixed rate on the 168,000 hours of practical capacity and it falls to 65.71. Applied fixed overhead becomes 9,758,571 and the volume variance grows to 1,281,429 on 19,500 hours, because the benchmark is now what the plant could do rather than what the budget expected. That larger figure is the logic behind the cost of unused capacity.
The volume variance is a signal about output, not a cost to cut. A manager asked to "recover" 793,500 by cutting fixed spend is chasing a number that no saving can reach. The only things that close it are more output or a different denominator.
Split under-absorbed fixed overhead before anyone reacts to it. Here 153,548 is a spending question for the budget holder and 793,500 is a volume question for sales and operations, of which 306,360 traces back to labour efficiency. The free workbook for this case, with the overhead pool and its drivers, is on the Cost Accounting companion page.
No. The fixed cost is paid whatever the output; the volume variance measures how much of it failed to reach products because output fell short of the denominator. In the worked case 11,500 missing standard hours at 69.00 leave 793,500 unabsorbed, while the actual overspend on fixed costs is only 153,548. Cutting fixed spend cannot close a volume variance; only output or a different denominator can.
In the two-way split the efficiency effect is inside the volume variance, because the volume variance uses standard hours allowed for the output. Splitting it with actual hours gives a capacity variance of 487,140 on 7,060 idle hours and a fixed efficiency variance of 306,360 on 4,440 excess hours. Together they make the 793,500 volume variance.
They are the same thing under two names. Both compare actual fixed overhead with the budgeted lump sum, not with a flexed figure, because fixed cost does not change with activity. In the case, 11,193,548 actual against 11,040,000 budgeted is 153,548 adverse, or 1.4 per cent of the budget.
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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