The cost-plus formula is one line of arithmetic; the cost it is applied to decides which orders a factory wins and which it loses.
A cost-plus price for a target margin is cost divided by (1 minus the margin), not cost times (1 plus the margin): a 28 per cent gross margin needs a markup of 38.9 per cent on cost. The formula is the easy half. On an illustrative machine shop, the same 28 per cent applied to a labour-hour standard cost quotes an aerospace bracket at 399.57, when the bracket's cost on its own activity drivers needs 606.81. Every bracket sold at the first quote loses 37.34.
Worked in full in Cost Accounting by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Cost-plus pricing is still how most job shops and component makers quote: build a standard cost, add the margin the board underwrites, send the price. It is only as good as the cost underneath it. When overhead is absorbed on a base that does not drive it, the quote is wrong in a predictable direction: too high on simple, high-volume parts, which the shop then loses, and too low on complex, low-volume parts, which it wins.
| Family | Units a year | List price | Cost, labour-hour absorption | Cost, activity drivers |
|---|---|---|---|---|
| Standard bushings | 1,850,000 | 9.20 | 6.53 | 4.87 |
| Hydraulic fittings | 640,000 | 23.50 | 15.50 | 13.95 |
| Valve bodies | 118,000 | 78.00 | 54.53 | 64.22 |
| Aerospace brackets | 19,500 | 348.00 | 287.69 | 436.91 |
Both costs carry the same material and the same direct labour at 31.40 an hour. They differ only in overhead. The labour-hour cost absorbs the whole 13,440,000 pool at 87.88 a direct labour hour. The driver cost assigns the same pool on setups, production orders, machine hours, engineering changes and inspections. On a bracket, overhead is 135.33 a unit on labour hours and 284.55 on drivers, because a bracket run of a dozen units carries a whole setup, an order and a share of the engineering changes. The target gross margin is 28.0 per cent of price.
Price for a target margin = cost ÷ (1 − margin)
Equivalent markup on cost = margin ÷ (1 − margin)
In Excel, with the unit cost in B2 and the target margin in B1: =B2/(1-B1). The markup that gives the same price is =B1/(1-B1), here 0.28 ÷ 0.72 = 38.89 per cent. Check the result by computing =(Price-B2)/Price, which must return the target margin.
Step 1, the bracket on its labour-hour cost: 287.69 ÷ 0.72 = 399.57. Step 2, the same bracket on its driver cost: 436.91 ÷ 0.72 = 606.81. Step 3, the bushing both ways: 6.53 ÷ 0.72 = 9.07, and 4.87 ÷ 0.72 = 6.77.
| Family | Price on labour-hour cost | Price on driver cost | Difference | Margin on driver cost at the labour-hour quote |
|---|---|---|---|---|
| Standard bushings | 9.07 | 6.77 | −2.30 | 46.2% |
| Hydraulic fittings | 21.52 | 19.37 | −2.15 | 35.2% |
| Valve bodies | 75.74 | 89.19 | 13.46 | 15.2% |
| Aerospace brackets | 399.57 | 606.81 | 207.25 | −9.3% |
The formula is applied correctly in both columns, and the two columns disagree by 51.9 per cent on the bracket. A shop quoting on labour-hour cost offers brackets at 399.57, believing it is earning 28.0 per cent. Against the driver cost of 436.91 it loses 37.34 a unit, a margin of minus 9.3 per cent. Across a year of 19,500 brackets that quote would lose 728,129 against the driver cost, and nothing in the quoting system would flag it, because the system checks the arithmetic, not the cost.
At the other end, the bushing is quoted at 9.07 when its driver cost supports 6.77. A competitor costing on drivers can quote 25.3 per cent lower and still make 28.0 per cent. The shop loses the high-volume work it is genuinely good at and wins the complex work it is underpricing. That is what a wrong standard cost does to the orders you win: the pricing formula sorts the order book in exactly the wrong direction. How the driver cost is built is shown in activity-based costing per unit. One refinement before quoting on it: the driver rates here spread the pool over actual activity, so they still carry the cost of idle capacity, and a target price built on them is slightly high. Stripping that charge out is worked in how to calculate the cost of unused capacity; it narrows the bracket's gap but does not close it.
| Target margin | Markup on cost | Bracket, labour-hour cost | Bracket, driver cost | Bushing, labour-hour cost | Bushing, driver cost | Margin if marked up by the margin % |
|---|---|---|---|---|---|---|
| 20.0% | 25.0% | 359.61 | 546.13 | 8.16 | 6.09 | 16.7% |
| 25.0% | 33.3% | 383.58 | 582.54 | 8.70 | 6.50 | 20.0% |
| 28.0% | 38.9% | 399.57 | 606.81 | 9.07 | 6.77 | 21.9% |
| 30.0% | 42.9% | 410.98 | 624.15 | 9.33 | 6.96 | 23.1% |
| 35.0% | 53.8% | 442.60 | 672.16 | 10.04 | 7.50 | 25.9% |
No plausible margin closes the bracket gap. Raising the target from 28.0 to 35.0 per cent on the labour-hour cost lifts the bracket quote to 442.60, still short of the 606.81 the driver cost needs at 28.0 per cent. The margin is not the lever; the cost is.
Before trusting any cost-plus quote, ask which base the overhead in it was absorbed on, and how much of the unit cost that overhead is. On the bracket it is 47.0 per cent of the labour-hour cost, which is why changing the base, and nothing else, raises the cost-plus price by 51.9 per cent.
Price = cost ÷ (1 − target margin), and the markup that gives it is margin ÷ (1 − margin): 38.9 per cent for a 28.0 per cent margin. Then test the cost, because the formula faithfully passes on whatever the allocation base puts into it: 399.57 or 606.81 for the same bracket. The free workbook for this case costs all four families both ways and works the price each would need to reach the board's margin.
Markup is profit as a percentage of cost; margin is profit as a percentage of price. A 28.0 per cent margin needs a markup of 0.28 divided by 0.72, or 38.9 per cent. Marking a 287.69 cost up by 28 per cent gives 368.24, which earns only 21.9 per cent margin, 31.33 a unit short of the 399.57 the target requires.
It is a sound floor test if the cost is right and a dangerous price if the cost is wrong. On the illustrative shop, cost-plus on a labour-hour standard cost quotes bushings 2.30 too high, at 9.07 instead of 6.77, and brackets 207.25 too low, at 399.57 instead of 606.81, so the shop loses the work it does well and wins the work it underprices.
Full cost with overhead assigned on what actually drives it, setups, orders, machine hours, engineering changes and inspections, rather than one labour-hour rate. For an aerospace bracket that moves overhead from 135.33 to 284.55 a unit and the 28.0 per cent price from 399.57 to 606.81. For a one-off order with idle capacity, compare the price with avoidable cost instead.
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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