Articles

Should a factory buy a part quoted below its absorbed cost?

The absorbed cost says buy whenever a quote comes in under it. On the high-volume part it is the only one of three costs that says so, and it is wrong by 4,019,846 a year.

Julian R. Sterling · from Cost Accounting

Calderbrook Engineering’s standard bushing costs 6.53 in the reports, and an outside supplier quotes 5.90. On the reported cost, buying saves 0.63 a unit, which on 1,850,000 bushings a year is 1,162,407. Buy them and the factory is 2,857,439 a year worse off. The quote is below the cost the reports print and above the cost of every dollar of overhead the bushing actually consumes, and no assumption about what is avoidable changes that.

The make-or-buy test in most factories is one comparison: the supplier’s price against the standard cost. The standard cost is an absorbed cost, material and labour plus a share of the whole overhead pool spread on direct labour hours, and that share is the problem. Most of it does not leave when the part leaves, and on a high-volume, simple part it is not even the share the part consumes.

Three quotes, three costs

Three of Calderbrook’s four families have been quoted. Each quote can be set against three costs. The absorbed cost is what the reports show. The avoidable cost is what would actually stop being spent, pool by pool, if the family went: 90 per cent of setup and changeover, 70 per cent of order handling, 35 per cent of machine running, 10 per cent of engineering and 50 per cent of quality. The driver cost is the whole cost of the capacity the family occupies, on its five activity drivers.

The effect of buying is measured on the avoidable cost: (avoidable cost less the quote) times the annual volume. The_Decisions.xlsx, Make or Buy, rows 11 to 13.

Family	Quote	Absorbed	Avoidable	Driver	Absorbed says	Avoidable says	Effect of buying, a year
Standard bushings	5.90	6.53	4.36	4.87	buy	make	−2,857,439
Valve bodies	51.00	54.53	51.16	64.22	buy	buy	+18,414
Aerospace brackets	280.00	287.69	301.78	436.91	buy	buy	+424,633
Take all three							−2,414,392

The absorbed cost says buy on all three, and it says so for one reason: every quote came in under it. It is not the largest of the three costs. It is the largest only on the bushings. On the valve bodies the driver cost is higher, and on the brackets the absorbed cost is the lowest of the three, 287.69 against 301.78 avoidable and 436.91 on the drivers. On the valve bodies and the brackets the absorbed test happens to reach the answer the avoidable test also reaches. A rule that always says buy is right whenever buying is right.

Read the reports and the three purchases save 1,728,881 a year: 1,162,407 on the bushings, 416,568 on the valve bodies and 149,906 on the brackets. Measured on what actually stops being spent, the same three purchases cost 2,414,392. The whole of the difference in sign comes from one part.

Where the bushing’s 0.63 comes from

Open the bushing up. Material is 2.95 a unit and labour is 0.030 hours at 31.40, which is 0.942. That prime cost of 3.892 is the same in every column. Everything that separates the three costs is overhead.

The_Decisions.xlsx, Inputs, column C, rows 80 to 94.

A bushing	Absorbed	Driver	Avoidable
Direct material	2.950	2.950	2.950
Direct labour	0.942	0.942	0.942
Overhead	2.636	0.982	0.463
Unit cost	6.528	4.874	4.355
Against a quote of 5.90	buy	make	make
Overhead for the family, a year	4,877,207	1,816,015	857,361

The quote leaves 2.008 a unit above prime cost for the supplier to cover the overhead Calderbrook would have carried. The labour-hour rate of 87.88 charges the bushing 2.636, because the family works 55,500 of the factory’s 152,940 labour hours, 36.3 per cent of them, and so takes 36.3 per cent of the 13,440,000 pool. On the five drivers it consumes 1,816,015, which is 13.5 per cent. A bushing run yields 5,967.7 units from one setup; an aerospace bracket yields 11.5. Labour hours cannot see that contrast, so the highest-volume, simplest part in the building carries overhead that belongs to the complex end.

That is the whole mechanism. The absorbed cost overstates the bushing by more than the supplier’s discount, so a quote that is dearer than making the part looks cheaper than making it.

The verdict that needs no judgment

The five avoidable shares are the weakest numbers in the analysis. They are yellow cells in the workbook because they are somebody’s judgment, and nobody at Calderbrook has measured them. The calculator workbook moves all five together, from an overall share of 0.30 to 0.75 about the book’s pattern, and the result is uncomfortable.

Decisions in the order bushings / valve bodies / brackets. 0.50 reproduces the book’s five shares. Cost_Your_Own_Part.xlsx, Sensitivities, the judgments, rows 16 to 21.

Avoidable share	Avoidable cost, bushings	Avoidable cost, valve bodies	Avoidable cost, brackets	Decisions	Cost of taking all three quotes
0.30	4.17	44.25	242.01	make / make / make	4,738,289
0.40	4.26	47.70	271.89	make / make / make	3,576,340
0.50	4.36	51.16	301.78	make / buy / buy	2,414,392
0.60	4.44	53.89	325.42	make / buy / buy	1,481,403
0.75	4.53	56.39	347.11	make / buy / buy	590,717
Span					4,147,573

The cost of taking all three quotes moves across 4,147,573, more than the whole 4,053,091 cross-subsidy the book is built around, and two of the three decisions change sides inside the range. On the valve bodies the book’s shares make the case by sixteen cents a unit, 51.16 against 51.00, worth 18,414 a year; the cash case is marginal and the answer is whatever the avoidable shares turn out to be.

The bushing column does not move enough to matter. Its avoidable cost runs from 4.17 to 4.53, and the quote is 5.90. Push further than the table does: if every dollar of overhead the bushings consume left with them, a share of one on every pool, the avoidable cost would be the driver cost of 4.87, and buying would still cost 1,898,785 a year. The quote sits above the driver cost itself, so there is no avoidable share, measured or assumed, at which buying the bushing is right. The only cost in the building that says buy is the one built on labour hours.

The band the reports cannot see

Turn the question round and ask which quotes the reports would accept that the cash would refuse. On the bushing it is any price between the avoidable cost of 4.36 and the absorbed cost of 6.53. That band is 2.17 a unit wide, 4,019,846 a year at the family’s volume, and it is not a coincidence of these inputs. It is the absorbed overhead on the bushings, 4,877,207, less the 857,361 that would actually stop being spent. It is the overhead the reports assign to the part that does not leave with the part.

That money does not disappear when the bushings are bought. It stays in the pool and goes looking for hours. Buy the bushings alone and 12,582,639 of overhead is left over 97,440 labour hours, which takes the absorption rate from 87.88 to 129.13, and every remaining family’s reported cost rises with it. The workbook measures the same stranding on the driver basis as 958,654, the bushings’ driver overhead of 1,816,015 less the 857,361 avoidable; the two figures are the same fact on the two distributions of one pool.

Take all three quotes and the workbook follows the stranding to its end. 5,809,744 of overhead leaves with the three families and 7,630,256 stays. The 39,680 labour hours of the hydraulic fitting, the one family still made, absorb it at 192.29 an hour, 2.19 times today’s rate. The fitting, which earns 40.7 per cent on its driver cost and shows 34.1 per cent in the reports, prints at 6.5 per cent. It did not change. Three sourcing decisions that each looked sound on the absorbed number took the margin away from it.

The_Decisions.xlsx, Make or Buy, rows 21 to 30.

	Today	After all three quotes
Overhead pool	13,440,000	7,630,256
Direct labour hours	152,940	39,680
Absorption rate, an hour	87.88	192.29
Hydraulic fitting margin, as the reports show it	34.1%	6.5%

What it means for the next quote

A quote below the standard cost is not evidence that buying saves money. It is evidence that the quote is below the standard cost, and on a part that labour hours overcost that tells you almost nothing. Three things follow from these tables.

• Test every quote against the avoidable cost for the decision in front of you, and against the driver cost for whether the family belongs in the plan. Where the two agree, as on the bushing, the answer is settled. Where they disagree, as on the valve body, the horizon decides.
• Expect the absorbed test to fail on the high-volume, simple parts. They are the ones a labour-hour base overcosts, the ones a specialist supplier can quote keenly, and the ones where the band between avoidable and absorbed cost is widest in money.
• Spend the measurement effort where the verdict is fragile. The bushing needs no measurement of the avoidable shares at all. The valve body turns on sixteen cents, and taking a family out for a quarter and watching what actually stops being spent is the only way to settle it.

The last point runs against the usual instinct, which is to argue longest about the biggest number. The bushing is the biggest number here, 2,857,439 a year, and it is the one decision in the table that no reasonable assumption can reverse.

Reproducing it in the workbook

Everything above is in The_Decisions.xlsx. The three unit costs are on the Inputs sheet, rows 81, 89 and 92, with the family’s avoidable and stranded overhead in rows 90 and 94. The Make or Buy sheet sets them against the quotes in rows 11 to 13, with the annual effect of buying in column K, and follows the stranded pool to the surviving family in rows 21 to 30. Overtype the bushing quote in Inputs, cell C16, and the absorbed verdict flips at 6.53 while the avoidable one flips at 4.36. The avoidable-share table is in Cost_Your_Own_Part.xlsx, on the sheet Sensitivities, the judgments, rows 16 to 21, and it reads its five shares from the front sheet, so it re-runs on your own factory’s figures.

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