Divide overhead by actual hours and the cost of an empty shift disappears into every part the factory did make.
The cost of unused capacity is the idle hours times an overhead rate struck on practical capacity: (practical hours − actual hours) × (overhead pool ÷ practical hours). A factory with 13,440,000 of overhead, 168,000 practical labour hours and 152,940 actual hours has 15,060 idle hours at 80.00, so 1,204,800, 9.0 per cent of the pool, is the cost of capacity it owned and did not use. Struck on actual hours instead, the rate is 87.88 and that 1,204,800 is buried in the cost of every part that was made.
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The choice of denominator looks like a technicality. It decides whether the cost of an empty shift shows up as a line management can act on, or as a higher unit cost that sales then tries to pass on to customers.
The case is Calderbrook Engineering, the fictional machine shop in the companion files of Cost Accounting, which absorbs its whole overhead on direct labour hours.
| Input | Value |
|---|---|
| Factory overhead pool | 13,440,000 |
| Practical capacity, labour hours (normal shift pattern) | 168,000 |
| Actual labour hours worked | 152,940 |
| Utilisation | 91.0% |
| Direct labour rate, loaded | 31.40 |
Practical capacity is what the factory can do on its normal shifts, allowing for maintenance and changeovers. It is not theoretical capacity running every hour of the year, and it is not this year's budget. It is a judgement, and it should be written down as one.
Rate on practical capacity = pool ÷ practical hours
Cost of unused capacity = (practical − actual hours) × practical rate
=(B3-B4)*B2/B3 with the pool in B2, practical hours in B3 and actual hours in B4.Every hour now carries 7.88 less overhead. That gap, times each family's hours, is the idle cost each family was being charged for work that was not done.
| Family | Hours a unit | Cost, actual-hour rate | Cost, practical rate | Margin before | Margin after | Idle cost carried |
|---|---|---|---|---|---|---|
| Standard bushings | 0.030 | 6.53 | 6.29 | 29.0% | 31.6% | 437,207 |
| Hydraulic fittings | 0.062 | 15.50 | 15.01 | 34.1% | 36.1% | 312,583 |
| Valve bodies | 0.235 | 54.53 | 52.68 | 30.1% | 32.5% | 218,446 |
| Aerospace brackets | 1.540 | 287.69 | 275.56 | 17.3% | 20.8% | 236,564 |
| Total | 1,204,800 |
The company's profit does not change: the 1,204,800 is still spent. What changes is where it is reported. Product costs now describe what a part costs when the factory is run as designed, and the idle line describes a capacity decision, which is a question for the operations director rather than for the price list.
Overhead is mostly fixed in the short run. Watch what each denominator does when volume drops across the board.
| Volume fall | Actual hours | Utilisation | Rate, actual hours | Rate, practical | Idle cost | Bracket cost, actual-hour rate |
|---|---|---|---|---|---|---|
| 0% | 152,940 | 91.0% | 87.88 | 80.00 | 1,204,800 | 287.69 |
| 10% | 137,646 | 81.9% | 97.64 | 80.00 | 2,428,320 | 302.72 |
| 20% | 122,352 | 72.8% | 109.85 | 80.00 | 3,651,840 | 321.52 |
| 30% | 107,058 | 63.7% | 125.54 | 80.00 | 4,875,360 | 345.69 |
On actual hours, a 30 per cent volume fall lifts the bracket's cost from 287.69 to 345.69 although nothing about how the bracket is made has changed. On practical capacity the bracket stays at 275.56 and the idle line grows to 4,875,360, 36.3 per cent of the pool, which is the number that should be on the board's table.
This is the death spiral. Volume falls, the actual-hour rate rises, quoted prices rise to cover it, more volume is lost, and the rate rises again. A rate struck on practical capacity breaks the loop, because a lost order no longer makes every other order look more expensive.
Practical capacity is an input cell in the free workbook for this case on the Cost Accounting companion page, so the idle line moves as soon as your own judgement does. The same factory's overhead is re-costed on activity drivers in how to calculate activity-based costing per unit, and the make-or-buy consequence of the labour-hour cost is in should a factory buy a part quoted below its absorbed cost.
Practical capacity, if the rate is used for pricing and product decisions. A rate on budgeted or actual volume charges products for idle time: here 87.88 an hour on 152,940 actual hours, against 80.00 on 168,000 practical hours. The 7.88 difference is the cost of capacity not used, which belongs on its own line.
It is what happens when fixed overhead is spread over falling volume. If hours fall 30 per cent, the actual-hour rate rises from 87.88 to 125.54 and a bracket's cost from 287.69 to 345.69. Higher quotes lose more volume, which raises the rate again. A practical-capacity rate keeps the bracket at 275.56 and shows the problem as idle cost.
No. The 13,440,000 is spent either way: 12,235,200 is absorbed into products at 80.00 an hour and 1,204,800 is reported as idle capacity. What changes is the information. Product costs stop depending on how busy the factory was, and the idle line shows a capacity decision that management can act on.
The capacity sheet is part of the workbook for chapters 4 and 8 of 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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