One machine, five fixed costs, two running costs and the choice of hours that decides the answer.
A machine hour rate is the machine's annual fixed costs divided by its productive hours, plus its running costs per hour. For an illustrative CNC machining centre carrying 93,200 of fixed cost over 3,400 productive hours, with 6.27 an hour of power and tooling, the rate is 33.68 a machine hour. Divide by the 4,160 clock hours instead and the rate falls to 28.68, leaving 17,027 a year unrecovered.
Worked in full in Cost Accounting by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Where a part spends most of its time on a machine and very little with an operator, a labour-hour overhead rate charges it for the wrong thing. The machine hour rate is the usual correction: one rate per machine or per group of similar machines, built from what that machine costs to own and to run. The arithmetic is simple. The choices inside it, which costs go in and which hours go underneath, are where most rates go wrong.
| Input | Value |
|---|---|
| Purchase cost | 480,000 |
| Residual value after 10 years | 30,000 |
| Maintenance contract, per year | 18,000 |
| Floor space, m2, at 95 per m2 | 120 |
| Insurance, share of cost | 1% |
| Share of supervision and indirect support | 14,000 |
| Rated power, kW, at 70% average load | 22 |
| Electricity, per kWh | 0.18 |
| Tooling and coolant, per running hour | 3.50 |
| Clock hours: 52 weeks, 2 shifts of 40 hours | 4,160 |
| Less planned maintenance, hours | 160 |
| Less setups and changeovers, hours | 600 |
The operator is not in the list. In this factory operators are paid as direct labour and charged to jobs on their own timesheets, so their wages already reach the product cost by another route.
Step 1: the fixed costs of owning the machine. These are incurred whether the spindle turns or not.
| Fixed cost | Basis | Per year |
|---|---|---|
| Depreciation | (480,000 − 30,000) ÷ 10 | 45,000 |
| Maintenance contract | as contracted | 18,000 |
| Floor space | 120 m2 × 95 | 11,400 |
| Insurance | 1% × 480,000 | 4,800 |
| Supervision and support | allocated | 14,000 |
| Total fixed | 93,200 |
Step 2: the running costs per hour. Power is 22 kW × 70% × 0.18 = 2.77 an hour. Add 3.50 of tooling and coolant and the machine costs 6.27 for every hour it actually cuts.
Step 3: the productive hours. Two shifts give 4,160 clock hours. Planned maintenance takes 160 and setups take 600, leaving 3,400 hours in which the machine can make parts, 81.7 per cent of the clock. Setups are left out of the denominator because the machine makes nothing while it is being changed over: their cost is recovered through the rate on the running hours.
Machine hour rate = fixed costs ÷ productive hours + running cost per hour
= 93,200 ÷ 3,400 + 6.27 = 27.41 + 6.27 = 33.68
In Excel, with fixed costs in B7, productive hours in B12 and running cost per hour in B9: =B7/B12+B9. Keep the two parts in separate cells: the fixed part moves with the hours you choose, the running part does not.
The machine costs 33.68 for each productive hour, and 81.4 per cent of that is fixed. A job of 40 parts at 0.25 machine hours each takes 10.0 hours and carries 336.84 of machine cost, 8.42 a part.
Charged instead on an illustrative plant-wide rate of 87.88 a labour hour, the same job, which needs 3.5 hours of operator time because one operator tends the machine while it runs, would carry 307.58, or 7.69 a part. The two answers look close on this job. They diverge on every job where the ratio of machine time to labour time differs from the factory average, which is the reason for having a machine rate at all.
| Hours used | Hours | Fixed per hour | Rate |
|---|---|---|---|
| Low demand year | 2,500 | 37.28 | 43.55 |
| Budgeted hours this year | 3,000 | 31.07 | 37.34 |
| Practical capacity (productive hours) | 3,400 | 27.41 | 33.68 |
| Clock hours | 4,160 | 22.40 | 28.68 |
The denominator moves the rate far more than any cost line does. Electricity at 0.12 or 0.30 a kWh gives 32.76 or 35.53; load at 50 or 90 per cent gives 32.89 or 34.48. Moving from 3,400 to 3,000 hours adds 3.65 an hour on its own.
Strike the rate on practical capacity, not on the hours you expect to sell. If only the budgeted 3,000 hours are worked, the 400 idle hours leave 10,965 of fixed cost unabsorbed. That is the cost of capacity nobody used, and it should be reported as such rather than loaded onto the parts that were made.
Using budgeted hours does the opposite: in a quiet year it raises the rate, raises the quoted price, and makes the next quiet year more likely. The arithmetic of that cost is set out in how to calculate the cost of unused capacity.
Dividing by clock hours. 93,200 over 4,160 hours gives a rate of 28.68, 14.9 per cent too low. Since the machine can only ever run 3,400 productive hours, that rate recovers at most 76,173 of the 93,200, and 17,027 a year is never charged to any product. Every quote built on it is underpriced before the salesperson offers a discount.
Putting the operator in twice. If operators are charged to jobs as direct labour, their wages must stay out of the machine rate. Adding an operator costing 41,600 a year to the pool lifts the rate by 12.24 to 45.92, and every job then pays for its operator once on the timesheet and once on the machine. Where an operator is permanently tied to one machine and not timesheeted, the opposite applies: put the wage in the rate and keep it out of direct labour.
Counting setup hours as productive. Put the 600 setup hours in the denominator while jobs are still charged only for running time and the rate falls to 29.57 on 4,000 hours, leaving 13,980 a year unrecovered. Setup hours belong in the denominator only if each batch is also charged for its own setup hours. That is the better design where batch sizes vary widely, because a rate spread over running hours makes a run of 2,000 parts carry the same changeover cost per hour as a run of 12.
The book's case runs a whole machining factory's overhead on five drivers, machine hours among them, and the free workbook for this case on the Cost Accounting companion page computes each rate from its pool and its driver count. How the same pool behaves on a single labour-hour base is worked in how to calculate the predetermined overhead rate.
The costs of owning the machine, depreciation, maintenance contract, floor space, insurance and a share of supervision, plus the costs of running it, power and tooling per hour. In the worked case the fixed costs total 93,200 a year and running costs 6.27 an hour. Operator wages go in only if operators are not already charged to jobs as direct labour.
Practical capacity. The machine here has 3,400 productive hours, giving 33.68 an hour; the budget of 3,000 hours gives 37.34. Striking the rate on the budget loads the cost of idle hours onto the parts that were made and raises prices in exactly the years demand is weak. Report the 10,965 of idle cost separately instead.
When machines, not people, consume the overhead: depreciation, power, maintenance and space follow running time. A job of 40 parts taking 10.0 machine hours carries 336.84 at 33.68 an hour. On a plant-wide labour-hour rate it would carry whatever its operator hours happen to be, which bears no fixed relation to machine time.
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 1340 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.