Strike the rate, apply it to actual hours, then split what is left into spending and volume before deciding where it goes.
The predetermined overhead rate is budgeted factory overhead divided by the budgeted level of the allocation base, set before the year starts. On an illustrative budget of 13,440,000 of overhead over 160,000 direct labour hours, the rate is 84.00 an hour. If the factory then works only 152,940 hours and spends 13,610,000, it applies 12,846,960 and is left with 763,040 under-applied, which splits into a 275,900 spending variance and a 487,140 volume 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 rate exists because a quotation, a job card or a monthly inventory valuation cannot wait for the year-end ledger. It is struck once, used all year, and the difference between what it applies and what was actually spent is settled at the close. Both halves of that process are arithmetic, and both are where costing errors start.
| Input | Value |
|---|---|
| Budgeted variable overhead | 2,400,000 |
| Budgeted fixed overhead | 11,040,000 |
| Budgeted factory overhead | 13,440,000 |
| Budgeted direct labour hours (the denominator) | 160,000 |
| Practical capacity, hours | 168,000 |
| Actual direct labour hours worked | 152,940 |
| Actual factory overhead incurred | 13,610,000 |
Predetermined overhead rate = budgeted overhead ÷ budgeted allocation base
13,440,000 ÷ 160,000 = 84.00 an hour, of which 15.00 variable and 69.00 fixed.
In Excel, with budgeted overhead in B1 and budgeted hours in B2: =B1/B2. Keep the variable and fixed parts as separate rates (=B3/B2 and =B4/B2): the variance split in step 4 needs them.
Every job now carries overhead at 84.00 for each labour hour it consumes. A job that takes 120 hours absorbs 10,080.00 of overhead on top of its material and labour, whatever the factory actually spends that month.
Applied overhead = predetermined rate × actual hours
84.00 × 152,940 = 12,846,960
The rate is predetermined; the hours are not. Applied overhead is what has been charged to work in progress through the year, job by job.
| Line | Amount |
|---|---|
| Actual overhead incurred (debits) | 13,610,000 |
| Overhead applied to jobs (credits) | 12,846,960 |
| Under-applied overhead | 763,040 |
Under-applied means the jobs were costed too cheaply: 763,040, or 5.6 per cent of the actual spend, never reached a product. Had actual overhead been lower than applied, the balance would be over-applied and the jobs would have been costed too dear.
A single balance tells you nothing about cause. Split it with a flexible budget, which is what overhead should have been at the hours actually worked: the fixed 11,040,000 plus 15.00 on 152,940 hours, or 2,294,100, giving 13,334,100.
| Variance | Formula | Amount |
|---|---|---|
| Spending | Actual overhead minus flexible budget | 275,900 |
| Volume | Fixed rate × (budgeted hours minus actual hours) | 487,140 |
| Under-applied | 763,040 |
The spending variance is a cost problem: the factory paid more for its overhead than the budget allowed at this activity. The volume variance is not a cost problem at all. It is 7,060 hours that were budgeted and not worked, each of which was supposed to carry 69.00 of fixed cost. Nobody overspent on that 487,140; the denominator was simply wrong.
Where the balance is immaterial, it goes straight to cost of goods sold. Where it is material, prorate it across the accounts that hold the applied overhead, so that inventory is carried at something close to actual cost.
| Account | Share | Applied overhead | Under-applied allocated |
|---|---|---|---|
| Work in progress | 8% | 1,027,757 | 61,043 |
| Finished goods | 12% | 1,541,635 | 91,565 |
| Cost of goods sold | 80% | 10,277,568 | 610,432 |
| Total | 100% | 12,846,960 | 763,040 |
Writing it all off to cost of sales lowers this year's profit by 152,608 more than proration does; that is the slice proration leaves in inventory until those units are sold. Under the usual inventory standards, the part caused by idle capacity should not be capitalised into stock at all, which is an argument for expensing the volume variance and prorating only the spending variance.
The numerator is a budget; the denominator is a judgement. The same 13,440,000 struck over three different hour counts gives three different rates and three different job costs.
| Denominator | Hours | Rate | 120-hour job | Applied | Under-applied |
|---|---|---|---|---|---|
| Actual hours (known only at year end, budgeted pool) | 152,940 | 87.88 | 10,545.31 | 13,440,000 | 170,000 |
| Budgeted hours | 160,000 | 84.00 | 10,080.00 | 12,846,960 | 763,040 |
| Practical capacity | 168,000 | 80.00 | 9,600.00 | 12,235,200 | 1,374,800 |
The higher the denominator, the cheaper every job looks and the bigger the year-end balance. Practical capacity leaves 1,374,800 unabsorbed: 170,000 of overspending against the budgeted pool and 1,204,800 for 15,060 idle hours at 80.00. That second part is deliberate: it is the cost of capacity the factory paid for and did not use, kept out of product cost so that customers are not quoted for idleness. The arithmetic of that choice is worked in how to calculate the cost of unused capacity.
Activity moves the balance as hard as the denominator does. Keeping the budgeted rate and the same spending overrun, 140,000 actual hours leave 1,655,900 under-applied, of which 1,380,000 is volume. At exactly 160,000 hours the volume variance is zero and only the 275,900 of spending remains. At 168,000 hours the factory over-applies by 276,100, because the fixed rate absorbs 552,000 more than the fixed budget.
The most damaging one is re-striking the rate on actual hours when volume falls. Fewer hours over the same fixed cost push the rate up, quotations rise, orders are lost, hours fall again and the rate climbs further. The volume variance is the factory telling you capacity is idle; loading it into the next year's rate passes the idleness to the customers most likely to leave. The other frequent mistake is quoting the plant-wide rate as if it measured what a product consumes. A labour-hour rate is a convenient base, not a cause, and when most of the pool moves with setups and machine time it can misprice whole families: see activity-based costing per unit.
Rate = budgeted overhead over budgeted base, 84.00 an hour. Applied = rate times actual hours, 12,846,960. The 763,040 left over is two different stories, 275,900 of spending and 487,140 of volume, and only the first is an overspend. Cost Accounting runs one factory's overhead pool through both a labour-hour rate and five activity drivers, and the free workbook for this case sets the rate on actual and practical hours side by side.
Under-applied overhead means actual overhead exceeded the overhead charged to jobs at the predetermined rate, so products were costed too cheaply. Over-applied is the reverse. With a rate of 84.00 an hour, 152,940 hours apply 12,846,960; against 13,610,000 actually spent, 763,040 is under-applied and must be charged to cost of sales or prorated across inventory and cost of sales.
Actual overhead and actual hours are only known at the year end, but jobs must be quoted, costed and valued in inventory every month. A predetermined rate also stops unit costs swinging with seasonal volume. The actual rate in the example, 13,610,000 over 152,940 hours or 88.99 an hour, would only be available after the close, by which point every quotation has gone out at the budgeted 84.00.
Budgeted hours absorb the full pool if the budget is met. Practical capacity gives a lower rate, 80.00 instead of 84.00 in the example, and leaves a larger year-end balance, 1,374,800 here, of which 1,204,800 is the cost of 15,060 idle hours, as a separate period expense rather than burying it in product cost. That keeps quotations from rising every time volume falls.
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.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: business operations: cost, contracts, pricing and supply chain → · All 681 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.