The same 13,440,000 of overhead, five drivers instead of one, and a profitable part that turns out to lose 25.5 per cent.
Activity-based costing per unit takes each overhead pool, divides it by the count of the activity that drives it to get a rate, charges each product its own count times that rate, and divides by the product's units. On the same 13,440,000 of overhead, a low-volume aerospace bracket that costs 287.69 on a labour-hour rate costs 436.91 on five activity drivers, and a 17.3 per cent margin becomes a loss of 25.5 per cent.
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-hour rate is not wrong arithmetic. It is the wrong question: it assumes overhead moves with the time people spend on a part, when most of it moves with how often a part is set up, ordered, changed and inspected. Low-volume complex parts consume those activities far out of proportion to their labour hours.
The case is Calderbrook Engineering, the fictional machine shop in the companion files of Cost Accounting. Its overhead of 13,440,000 sits in five cost centres the ledger already has.
| Pool | Cost | Driver | Driver total | Rate |
|---|---|---|---|---|
| Setup and changeover | 3,510,000 | setups | 3,900 | 900.00 |
| Order handling and scheduling | 1,980,000 | production orders | 5,330 | 371.48 |
| Machine running | 4,620,000 | machine hours | 150,650 | 30.67 |
| Engineering and change notes | 1,610,000 | engineering changes | 980 | 1,642.86 |
| Quality and inspection | 1,720,000 | inspection events | 16,660 | 103.24 |
| Total | 13,440,000 | labour hours | 152,940 | 87.88 |
The aerospace bracket sells at 348.00, uses 104.00 of material and 1.54 labour hours at 31.40, and is made 19,500 times a year in 1,690 setups. It is 0.7 per cent of the factory's units, 19.6 per cent of its labour hours, 43.3 per cent of its setups and 70.4 per cent of its engineering changes.
Activity rate = pool cost ÷ driver total
Overhead per unit = Σ (product's driver count × activity rate) ÷ product units
=SUMPRODUCT(C2:C6,D2:D6)/B1, units in B1.| Activity | Count | Charge | Per unit |
|---|---|---|---|
| Setups | 1,690 | 1,521,000.00 | 78.00 |
| Production orders | 2,180 | 809,831.14 | 41.53 |
| Machine hours | 38,610 | 1,184,057.09 | 60.72 |
| Engineering changes | 690 | 1,133,571.43 | 58.13 |
| Inspection events | 8,720 | 900,264.11 | 46.17 |
| Overhead | 5,548,724 | 284.55 |
Unit cost on activity drivers is 104.00 of material, 48.36 of labour and 284.55 of overhead: 436.91. On the plant-wide rate the overhead is 1.54 hours × 87.88 = 135.33 and the unit cost 287.69.
| Family | Price | Cost, labour hours | Margin | Cost, activities | Margin | Shift |
|---|---|---|---|---|---|---|
| Standard bushings | 9.20 | 6.53 | 29.0% | 4.87 | 47.0% | −25.3% |
| Hydraulic fittings | 23.50 | 15.50 | 34.1% | 13.95 | 40.7% | −10.0% |
| Valve bodies | 78.00 | 54.53 | 30.1% | 64.22 | 17.7% | +17.8% |
| Aerospace brackets | 348.00 | 287.69 | 17.3% | 436.91 | −25.5% | +51.9% |
Both methods allocate exactly 13,440,000, so nothing is created: the cost only changes address. The bushings, made 5,967.7 at a time, were carrying overhead the brackets caused. The factory has been quoting its simplest parts too dear and its most complex too cheap, which is exactly the order book a competitor with better costing would leave it with.
Setups, orders and inspections are batch-level: they cost the same whether the run is ten units or a thousand. Hold the bracket's volume, machine time and engineering changes, and lengthen the run.
| Units a setup | Batch overhead a unit | Overhead a unit | Unit cost | Margin |
|---|---|---|---|---|
| 11.5 | 165.70 | 284.55 | 436.91 | −25.5% |
| 23.1 | 82.85 | 201.70 | 354.06 | −1.7% |
| 46.2 | 41.42 | 160.28 | 312.63 | 10.2% |
| 115.4 | 16.57 | 135.42 | 287.78 | 17.3% |
The labour-hour cost of 287.69 is only right if the bracket were run about ten times longer than it is. A plant-wide rate silently assumes batch-level overhead follows labour hours. For the bracket that assumption is off by an order of magnitude.
The free workbook for this case on the Cost Accounting companion page carries the five pools, the sixteen driver counts and the twenty charges, each footing back to 13,440,000. What the bushing's lower cost means for a make-or-buy quote is worked in should a factory buy a part quoted below its absorbed cost.
Activity rate equals the cost of the activity pool divided by the total count of its driver. A setup pool of 3,510,000 spread over 3,900 setups gives 900.00 a setup. A product's charge is its own count times that rate: 1,690 bracket setups cost 1,521,000, which is 78.00 a unit because each setup produces only 11.5 brackets.
Because setups, orders, inspections and engineering changes are incurred per batch or per product, not per unit. The aerospace bracket is 0.7 per cent of units but 43.3 per cent of setups, so it absorbs 284.55 of overhead a unit on activity drivers against 135.33 on labour hours.
No. Both methods allocate the same 13,440,000 and the four families' costs still foot to the same total. The bushings fall from 6.53 to 4.87 a unit and the brackets rise from 287.69 to 436.91. The cost changes address, which changes which quotes the factory should win.
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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