Three ways to push maintenance and stores costs into production departments, worked on the same factory, and why the step-down order can move cost more than the method does.
The reciprocal method is the only one of the three that recognises that service departments serve each other, so it is the right answer whenever they do; the direct and step-down methods are approximations of it. On an illustrative factory with 4,000,000 of maintenance and stores cost, the reciprocal method sends 2,650,435 to machining. The direct method sends 2,480,000, and step-down sends 2,928,000 or 2,144,000 depending only on which department goes first.
Worked in full in Cost Accounting by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Overhead rates are struck in production departments, the ones that touch the product. Maintenance, stores, quality and production engineering do not touch it, so their cost has to be pushed into machining and assembly before a machine hour or labour hour rate can be calculated. The complication is that service departments use each other: stores issues spares to maintenance, maintenance repairs the stores racking and forklifts. The three methods differ only in how much of that mutual service they admit.
| Department | Own cost | Maintenance used | Stores used | Rate base |
|---|---|---|---|---|
| Maintenance | 2,400,000 | 40% | ||
| Stores | 1,600,000 | 20% | ||
| Machining | 3,000,000 | 72% | 12% | 40,000 machine hours |
| Assembly | 1,000,000 | 8% | 48% | 60,000 labour hours |
| Total | 8,000,000 | 100% | 100% |
The sample part at the end uses 2 machine hours and 0.5 labour hours.
Ignore service between service departments and re-base each one's usage over the production departments only. Maintenance's 72 and 8 per cent become 0.9000 and 0.1000 of the 80 per cent used by production; stores' 12 and 48 per cent become 0.2000 and 0.8000 of 60 per cent.
Machining = 2,400,000 × 0.9000 + 1,600,000 × 0.2000 = 2,160,000 + 320,000 = 2,480,000
Assembly = 240,000 + 1,280,000 = 1,520,000
Allocate one service department in full, including to the other, then close the second over production only. The usual rule is to start with the department that gives the most service to other service departments: stores gives maintenance 40 per cent of 1,600,000, 640,000, and receives 480,000 back, so stores goes first.
Stores first: 640,000 to maintenance, 192,000 to machining, 768,000 to assembly.
Maintenance now holds 3,040,000; split 0.9000 / 0.1000: 2,736,000 and 304,000.
Machining = 192,000 + 2,736,000 = 2,928,000; assembly 1,072,000.
Reverse the order and maintenance goes first, sending 480,000 to stores, 1,728,000 to machining and 192,000 to assembly. Stores then closes 2,080,000 as 416,000 and 1,664,000, so machining receives 2,144,000. Same cost, same usage, 784,000 moved by a sequencing choice.
Write each service department's total cost, own cost plus what it receives from the other, and solve the two equations together.
M = 2,400,000 + 0.40 × S S = 1,600,000 + 0.20 × M
M = (2,400,000 + 0.40 × 1,600,000) ÷ (1 − 0.40 × 0.20) = 3,040,000 ÷ 0.920 = 3,304,348
S = 1,600,000 + 0.20 × 3,304,348 = 2,260,870
Machining = 0.72 × 3,304,348 + 0.12 × 2,260,870 = 2,650,435; assembly 1,349,565
Excel, any number of departments: =MMULT(MINVERSE(I-U),C), where U is the matrix of service shares between service departments and C their own costs.
The two totals sum to 5,565,217, more than the 4,000,000 actually spent, because they include service passed back and forth. Only the shares leaving to production matter, and those sum to exactly 4,000,000.
| Method | To machining | To assembly | Machine hour rate | Labour hour rate | Part overhead |
|---|---|---|---|---|---|
| Direct | 2,480,000 | 1,520,000 | 137.00 | 42.00 | 295.00 |
| Step-down, stores first | 2,928,000 | 1,072,000 | 148.20 | 34.53 | 313.67 |
| Step-down, maintenance first | 2,144,000 | 1,856,000 | 128.60 | 47.60 | 281.00 |
| Reciprocal | 2,650,435 | 1,349,565 | 141.26 | 39.16 | 302.10 |
Machining's rate is its own 3,000,000 plus the allocation, over 40,000 machine hours: 5,650,435 gives 141.26 on the reciprocal method. Against that, the sample part is 2.4 per cent under-costed on the direct method, 3.8 per cent over-costed on the textbook step-down order and 7.0 per cent under-costed on the other order. Every method allocates the same 4,000,000 in total. Each simply sends it to a different address, which is the theme of the free workbook for this case, where one overhead pool re-assigned on its real drivers moves money between four product families.
| Stores to maintenance / maintenance to stores | Direct | Step-down, stores first | Step-down, maintenance first | Reciprocal |
|---|---|---|---|---|
| 0% / 0% | 2,480,000 | 2,480,000 | 2,480,000 | 2,480,000 |
| 20% / 10% | 2,480,000 | 2,704,000 | 2,312,000 | 2,548,571 |
| 40% / 20% | 2,480,000 | 2,928,000 | 2,144,000 | 2,650,435 |
| 60% / 30% | 2,480,000 | 3,152,000 | 1,976,000 | 2,807,805 |
With no mutual service the methods agree. As it grows, the direct method stays put, because it ignores the mutual service entirely, while the two step-down orders fan out on either side of the reciprocal answer. At 60 and 30 per cent the step-down orders are 1,176,000 apart.
Choosing step-down because it is "more accurate than direct" and then picking the order by habit. In this case the wrong order is further from the reciprocal answer than the direct method is. The second mistake is allocating actual service costs, so that maintenance's overspend lands in the machining rate and machining's manager is charged for it. Allocate budgeted cost at budgeted rates and leave the spending variance where it arose. The rates the allocation feeds are the ones built in how to calculate a machine hour rate.
Conventionally the service department that provides the most service, in money, to other service departments. In the worked case Stores gives Maintenance 640,000 of service and receives only 480,000 back, so Stores goes first. That order lands within 3.8 per cent of the reciprocal answer on a sample part; the reverse order misses by 7.0 per cent.
Because each department's total includes the service it receives from the other. Maintenance's reciprocal cost is 3,304,348 and Stores' is 2,260,870, 5,565,217 together against 4,000,000 of actual cost. The excess is internal service passed back and forth; only the shares going to production leave the system, and they add back to exactly 4,000,000.
When service departments barely use each other. With no reciprocal use, the direct, step-down and reciprocal methods all give machining 2,480,000 in the illustrative case. The gap opens as mutual use grows: at 60 per cent and 30 per cent the step-down orders give 3,152,000 and 1,976,000 against 2,807,805 reciprocal.
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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