Setup, order handling and inspection are paid once per order; the minimum quantity is how many units it takes to carry them.
The minimum order quantity that covers a setup is the cost of starting one batch divided by what each unit leaves after its own costs. For an illustrative bracket selling at 95.00, a batch costing 1,450 to set up, schedule and inspect needs 60 units to break even on full cost, 34 just to cover the batch costs that are actually avoidable, and 142 to earn a 15 per cent margin. The customer's average order is 25.
Worked in full in Cost Accounting by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A unit cost printed in a standard cost file assumes a batch size. Most never say which one. When the real orders are a fraction of that size, the setup, the order paperwork and the first-off inspection are spread over far fewer units than the standard assumed, and a part that shows a healthy margin loses money on every order. The minimum order quantity, worked from batch-level cost, is the number that tells the sales desk where the floor is.
| Input | Value |
|---|---|
| Selling price per unit | 95.00 |
| Material per unit | 38.00 |
| Direct labour per unit | 14.00 |
| Machine running cost per unit | 6.50 |
| Facility overhead absorbed per unit | 12.00 |
| Setup and changeover, per batch | 950.00 |
| Order handling and scheduling, per batch | 280.00 |
| First-off inspection, 2 at 110.00, per batch | 220.00 |
| Avoidable share: setup, order handling, inspection | 90% / 70% / 80% |
| Target margin on price | 15% |
| Customer's average order, units | 25 |
Two kinds of cost sit in this list. Unit-level costs, 58.50 of material, labour and machine running, are incurred once per bracket. Batch-level costs, 1,450 in all, are incurred once per order whether it is for 10 brackets or 500. The facility overhead of 12.00 is neither: it is a share of rent and management that does not move with this order at all.
Step 1: what each unit leaves. Contribution per unit is 95.00 − 58.50 = 36.50. Over full cost, including the facility share, the margin per unit is 95.00 − 70.50 = 24.50.
Step 2: the batch cost, full and avoidable. Full batch cost is 950 + 280 + 220 = 1,450. If the order is refused, 90 per cent of setup, 70 per cent of order handling and 80 per cent of inspection would not be spent: 855.00 + 196.00 + 176.00 = 1,227.
Step 3: three minimum quantities, three questions.
=ROUNDUP(Batch/(Price*(1-Target)-UnitCost),0), with Target set to zero for break-evenThe cash floor answers whether one order next week, taken into idle capacity, puts money in the bank. The full-cost figure answers whether a year of orders of this size is sustainable. The target-margin figure is the one to print on the quotation.
At the customer's average of 25 units, each bracket carries 58.00 of batch cost, its full cost is 128.50 against a price of 95.00, and the order loses 837.50 on full cost, a margin of −35.3 per cent. It fails the cash test too: 25 × 36.50 = 912.50 of contribution does not cover the 1,227 of avoidable batch cost, so each order of 25 takes 314.50 out of the bank even with the factory half empty.
There are three ways out, and each has a number. Raise the order quantity to 60. Charge a setup fee of 837.50 an order, or 1,404.41 for a 15 per cent margin on the whole invoice. Or quote a small-batch price of 128.50 to break even, 151.18 to earn 15 per cent.
| Units per order | Batch cost per unit | Full cost per unit | Margin | Profit per order | Cash after avoidable |
|---|---|---|---|---|---|
| 10 | 145.00 | 215.50 | −126.8% | −1,205.00 | −862.00 |
| 25 | 58.00 | 128.50 | −35.3% | −837.50 | −314.50 |
| 34 | 42.65 | 113.15 | −19.1% | −617.00 | 14.00 |
| 60 | 24.17 | 94.67 | 0.4% | 20.00 | 963.00 |
| 100 | 14.50 | 85.00 | 10.5% | 1,000.00 | 2,423.00 |
| 142 | 10.21 | 80.71 | 15.0% | 2,029.00 | 3,956.00 |
| 250 | 5.80 | 76.30 | 19.7% | 4,675.00 | 7,898.00 |
| 500 | 2.90 | 73.40 | 22.7% | 10,800.00 | 17,023.00 |
The curve is steep below 60 and flat above 250. Beyond a few hundred units the batch cost barely matters and the unit cost tends to 70.50; below a few dozen it is the whole story. That shape is why a single standard cost can be right for the long runs and badly wrong for the short ones.
The minimum order quantity here is the seller's floor for one order. It is not the economic order quantity, which balances a buyer's ordering cost against holding cost. A customer optimising its own stock may rationally order 25; the price of that convenience is what the setup fee recovers.
The common mistake is to cost every order at the standard batch. Suppose the standard file was built on a batch of 200: setup cost per unit is then 7.25, the standard cost 77.75, and the bracket shows an 18.2 per cent margin. Actual orders of 25 cost 128.50. Over a year of 80 orders, 2,000 units, the factory spends 116,000 on batch costs and the standard recovers 14,500 of it. The other 101,500 appears as an overhead variance that nobody connects to the bracket, and the sales team keeps quoting 95.00 because the standard says it makes money.
The fix is to hold batch-level cost as a separate line, per order, and add it to the quote after the order quantity is known, rather than baking it into the unit cost at an assumed run length.
The book prices batches from the setups, orders and inspections that actually drive them, and the free workbook for this case on the Cost Accounting companion page reconciles one order's cost back to the annual pools. The rates behind the batch costs are built in how to calculate activity-based costing per unit, and the step from cost to quoted price in how to calculate a cost-plus price for a target margin.
Take the batch cost and subtract what the order's units contribute towards it. A 25-unit order of a bracket with 1,450 of batch cost and 24.50 a unit over full cost covers 612.50, so it needs a setup charge of 837.50 to break even, or 1,404.41 for a 15 per cent margin on the whole invoice. Charging it separately keeps the unit price comparable across order sizes.
Only if it covers its avoidable batch cost and the capacity would otherwise sit idle. Here that cash floor is 34 units: 1,227 of avoidable batch cost over 36.50 of contribution. An order of 25 fails even that test and loses 314.50 in cash, so it should be refused or carry a setup fee.
The minimum order quantity is the seller's floor: the smallest batch whose margin covers its setup, 60 units here on full cost. The economic order quantity is the buyer's choice, balancing the cost of placing orders against the cost of holding stock. The two are unrelated, which is why a buyer's sensible order can still be below a seller's break-even.
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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