A factory’s overheads start out in a heap: rent, power, depreciation, insurance, supervision. Before any product can be charged with a fair share, that heap has to be divided between the departments that caused it, and the costs of the support departments, such as repairs and the canteen, have to be passed on to the departments that actually make the goods.
This is apportionment, and it produces the total overhead of each production department.
This is one of the most calculation-heavy topics in the paper. It covers choosing a basis for each shared cost, then reapportioning service department costs in three situations: when service departments serve only production, when one serves another, and when they serve each other. The last case is solved by repeated distribution or by simultaneous equations, and examiners expect both methods to give the same answer.
In 30 seconds
Primary apportionment shares general overheads between all cost centres using a fair basis for each cost (floor area for rent, kilowatt hours for power, cost of equipment for depreciation and equipment insurance). Secondary apportionment then shares each service department’s total between the production departments. If service departments do not use each other, apportion directly. If one uses another, apportion the one that is used by others first.
If they use each other (reciprocal), use repeated distribution or simultaneous equations. At the end, all overhead sits in production departments, and the total is unchanged.
Apportioning shared costs: choosing a basis
A cost that cannot be allocated wholly to one cost centre is apportioned: divided on a basis that is fair. The apportionment of production overhead usually has two stages. First, general costs are shared between production centres and service centres. Second, the costs of the service centres are shared between the production centres. The second stage is called secondary apportionment.
When both stages are done, the overhead of each production centre is made up of three parts: costs allocated directly to it, shared costs apportioned to it, and its share of the service departments’ costs.
| Cost | Usual basis | Reason |
|---|---|---|
| Rent, rates, building insurance, heating, lighting | Floor area (or volume) | A bigger department uses more of the building |
| Power for machines | Kilowatt hours, or machine hours | Departments that use more power cause more cost |
| Depreciation and insurance of equipment | Cost (or book value) of equipment | More valuable equipment loses more value and costs more to insure |
| Canteen, welfare, personnel | Number of employees | More staff use the service more |
| Stores and materials handling | Number or value of requisitions or materials issued | Measures how much each department uses the stores |
| Repairs and maintenance | Hours of work done for each department | Measures how much repair each uses |
For some costs there is an obvious basis, such as floor area for rent. Where there is none, the choice is a matter of judgement, but it should be fair and applied consistently. At the end, every overhead must have been allocated or apportioned to some cost centre.
Worked apportionment
A factory has two production departments (Cutting and Finishing) and two service departments (Maintenance and Canteen). Indirect labour has already been allocated. Shared costs are: rent ₦240,000; power ₦90,000; depreciation ₦120,000; equipment insurance ₦36,000.
| Cutting | Finishing | Maintenance | Canteen | Total | |
|---|---|---|---|---|---|
| Floor area (m²) | 600 | 300 | 60 | 40 | 1,000 |
| Power (000 kWh) | 70 | 15 | 10 | 5 | 100 |
| Cost of equipment (₦000) | 500 | 300 | 150 | 50 | 1,000 |
Rates: rent ₦240,000 ÷ 1,000 m² = ₦240 per m². Power ₦90,000 ÷ 100 = ₦900 per thousand kWh. Depreciation ₦120,000 ÷ ₦1,000,000 = 12% of equipment cost. Insurance ₦36,000 ÷ ₦1,000,000 = 3.6% of equipment cost.
| ₦ | Cutting | Finishing | Maintenance | Canteen | Total |
|---|---|---|---|---|---|
| Indirect labour (allocated) | 60,000 | 45,000 | 30,000 | 25,000 | 160,000 |
| Rent | 144,000 | 72,000 | 14,400 | 9,600 | 240,000 |
| Power | 63,000 | 13,500 | 9,000 | 4,500 | 90,000 |
| Depreciation | 60,000 | 36,000 | 18,000 | 6,000 | 120,000 |
| Equipment insurance | 18,000 | 10,800 | 5,400 | 1,800 | 36,000 |
| Total | 345,000 | 177,300 | 76,800 | 46,900 | 646,000 |
Check: the total of the five cost lines is ₦160,000 + ₦240,000 + ₦90,000 + ₦120,000 + ₦36,000 = ₦646,000, which equals the total of the department totals.
Secondary apportionment of service department costs
A service department makes no product. Its costs must be passed to the production departments, because only production departments have units to which an absorption rate can be applied. How this is done depends on who uses whose service.
Case 1: service departments serve production only
Each service department’s total is simply shared between the production departments in proportion to the service they use.
Example. Production departments P1 and P2 have overheads of ₦120,000 and ₦180,000. Service department S1 (₦90,000) serves P1 and P2 equally, and S2 (₦60,000) serves P1 70% and P2 30%. Neither uses the other.
| ₦ | P1 | P2 | S1 | S2 |
|---|---|---|---|---|
| Overhead before reapportionment | 120,000 | 180,000 | 90,000 | 60,000 |
| S1 (50:50) | 45,000 | 45,000 | (90,000) | |
| S2 (70:30) | 42,000 | 18,000 | (60,000) | |
| Total | 207,000 | 243,000 | nil | nil |
Total = ₦207,000 + ₦243,000 = ₦450,000, which equals the original ₦120,000 + ₦180,000 + ₦90,000 + ₦60,000. ✓
Case 2: one service department uses another (step method)
If one service department serves the other, but not the reverse, work in two stages. Apportion the department that is used by the other first, including a share to the other service department. Then apportion the second department’s new, larger total to the production departments.
Example (using the factory above). The Canteen serves Cutting, Finishing and Maintenance in the ratio of employees, 40:20:10. Maintenance does not serve the Canteen in return, and shares its cost between Cutting (60%) and Finishing (40%).
| ₦ | Cutting | Finishing | Maintenance | Canteen |
|---|---|---|---|---|
| Totals after first apportionment | 345,000 | 177,300 | 76,800 | 46,900 |
| Canteen (4:2:1) | 26,800 | 13,400 | 6,700 | (46,900) |
| Subtotal | 83,500 | |||
| Maintenance (60:40) | 50,100 | 33,400 | (83,500) | |
| Total | 421,900 | 224,100 | nil | nil |
Check: ₦421,900 + ₦224,100 = ₦646,000. ✓ If Maintenance were apportioned first, the share that the Canteen later sends to Maintenance would have nowhere to go, because Maintenance would already have been cleared. Always start with the service department that serves the other one but is not served by it.
Case 3: service departments serve each other (reciprocal method)
When both service departments serve each other as well as production, neither can be cleared first without leaving something behind in the other. The reciprocal method deals with this. There are two ways, which give the same final answer.
Example. Production departments P and Q have overheads of ₦80,000 and ₦60,000. Service department S1 has ₦20,000 and S2 has ₦30,000. S1 serves P 50%, Q 30% and S2 20%. S2 serves P 40%, Q 40% and S1 20%.
Method A: simultaneous equations
- Let X be the total cost to be apportioned from S1 and Y the total to be apportioned from S2. Each total is the department’s own overhead plus its share of the other’s.
- X = 20,000 + 0.2Y and Y = 30,000 + 0.2X.
- Substitute.
X = 20,000 + 0.2(30,000 + 0.2X) = 20,000 + 6,000 + 0.04X, so 0.96X = 26,000 and X = ₦27,083. - Then Y.
30,000 + 0.2 × 27,083 = 30,000 + 5,417 = ₦35,417. - Apportion X: P 50% = ₦13,542; Q 30% = ₦8,125; S2 20% = ₦5,417. Apportion Y: P 40% = ₦14,167; Q 40% = ₦14,167; S1 20% = ₦7,083.
- Final totals.
P = 80,000 + 13,542 + 14,167 = ₦107,708.
Q = 60,000 + 8,125 + 14,167 = ₦82,292.
Total = ₦190,000, which equals ₦80,000 + ₦60,000 + ₦20,000 + ₦30,000. ✓
(Small differences come from rounding.)
Method B: repeated distribution
Apportion each service department in turn, including a share to the other service department, and keep repeating until the amounts left in the service departments become negligible.
| ₦ | P | Q | S1 | S2 |
|---|---|---|---|---|
| Start | 80,000 | 60,000 | 20,000 | 30,000 |
| S1 (50:30:20) | 10,000 | 6,000 | (20,000) | 4,000 |
| S2 (40:40:20) on 34,000 | 13,600 | 13,600 | 6,800 | (34,000) |
| S1 on 6,800 | 3,400 | 2,040 | (6,800) | 1,360 |
| S2 on 1,360 | 544 | 544 | 272 | (1,360) |
| S1 on 272 | 136 | 82 | (272) | 54 |
| S2 on 54 | 22 | 22 | 11 | (54) |
| S1 on 11 | 5 | 3 | (11) | 3 |
| S2 on 3 and S1 on remainder | 1 | 1 | nil | nil |
| Total | 107,708 | 82,292 | nil | nil |
The repeated method reaches the same totals as the equations. In an exam, the simultaneous equation method is usually quicker and exact. Repeated distribution is easy to follow but longer.
Writing the equations
The rule is the same every time. For each service department, write: total to apportion = its own overhead + the percentage of the other service department’s total that it receives. With two service departments there are two equations. Solve them by substitution or by elimination. Then apply each department’s percentages to its total to find the share going to each production department.
The ideas in more depth
Why apportion service costs at all?
The aim is to calculate an absorption rate for each production department. Only production departments make goods. If the repairs department’s cost stayed in repairs, units would never carry it, and the full cost of the product would be understated. After secondary apportionment, all production overhead is in the production departments, ready for absorption.
Which method is more accurate?
The reciprocal method is the most accurate, because it reflects the fact that service departments use each other. The step method ignores some of the service one department gives the other and is only exact when the use is one-way. Direct apportionment ignores service between service departments completely.
For examination purposes, use the method the data requires: if the question gives percentages for service departments serving each other, use the reciprocal method.
The effect of the basis
The basis chosen changes the answer. If the Canteen cost were shared on the number of meals instead of the number of employees, the production departments would receive different amounts. This is why apportionment is said to involve judgement. The same total is always shared, but its distribution among departments, and so the unit costs of the products passing through them, depends on the basis.
Exam technique
- Set out a table with a column for each department and a row for each step. Show the original overhead, each apportionment (with the ratio in brackets) and the total.
- Cross-check that the total at the end equals the total at the start.
- Write the apportionment ratios as fractions or percentages of the whole service given, so that they add to 100%.
Worked example: a full reciprocal question
Scenario. Enugu Foods Ltd has two production departments, Mixing and Packing, and two service departments, Stores and Maintenance. Overheads allocated and apportioned so far are: Mixing ₦140,000; Packing ₦210,000; Stores ₦120,000; Maintenance ₦90,000. Stores serves Mixing 50%, Packing 30% and Maintenance 20%. Maintenance serves Mixing 40%, Packing 40% and Stores 20%. Apportion the service department costs using simultaneous equations.
- Equations.
S = 120,000 + 0.2M and M = 90,000 + 0.2S, where S and M are the total costs to be apportioned from Stores and from Maintenance. - Solve.
S = 120,000 + 0.2(90,000 + 0.2S) = 120,000 + 18,000 + 0.04S.
So 0.96S = 138,000 and S = ₦143,750.
M = 90,000 + 0.2 × 143,750 = 90,000 + 28,750 = ₦118,750. - Apportion Stores (₦143,750). Mixing 50% = ₦71,875. Packing 30% = ₦43,125. Maintenance 20% = ₦28,750.
- Apportion Maintenance (₦118,750). Mixing 40% = ₦47,500. Packing 40% = ₦47,500. Stores 20% = ₦23,750.
- Totals.
Mixing = 140,000 + 71,875 + 47,500 = ₦259,375.
Packing = 210,000 + 43,125 + 47,500 = ₦300,625. - Check.
₦259,375 + ₦300,625 = ₦560,000 = ₦140,000 + ₦210,000 + ₦120,000 + ₦90,000. ✓
Choosing between the three methods
| Method | When it applies | What it ignores | Accuracy |
|---|---|---|---|
| Direct apportionment | Service departments serve only production departments, or the question tells you to ignore service between them | Nothing, if there really is no service between service departments | Exact in that case |
| Step method | One service department serves another, but not the reverse | Nothing, if the use really is one-way | Exact in that case |
| Reciprocal method | Service departments serve each other | Nothing | The most accurate in every case |
If you apply direct apportionment to a situation where service departments serve each other, part of the service is left out. The production departments receive amounts that are slightly wrong. Real factories often use the simpler methods because the difference is small, but exams reward the method the data calls for.
From apportionment to the absorption rate
The final totals feed the absorption rate, which the next topic explains in full. Using the one-way example, Cutting ends with ₦421,900 and Finishing with ₦224,100. Suppose Cutting is expected to use 20,000 machine hours and Finishing 18,000 direct labour hours in the year. Then the rates are:
- Cutting.
₦421,900 ÷ 20,000 machine hours = ₦21.10 per machine hour. - Finishing.
₦224,100 ÷ 18,000 direct labour hours = ₦12.45 per direct labour hour.
A product that spends 3 machine hours in Cutting and 2 labour hours in Finishing then absorbs (3 × ₦21.10) + (2 × ₦12.45) = ₦63.30 + ₦24.90 = ₦88.20 of fixed production overhead. This shows why the apportionment bases and the reapportionment method matter: they move the totals on which each rate is built.
Apportioning when the data is given as usage
Questions rarely give the percentages ready made. They may give hours of service, number of requisitions or employees, and expect you to turn them into proportions. Suppose Maintenance spent 300 hours on Cutting, 150 hours on Finishing and 50 hours on the Canteen in the year. The total is 500 hours, so the proportions are 60%, 30% and 10%. If the Canteen did no work for Maintenance, this is a one-way case.
If it also spent 40 hours on Maintenance, the Canteen would be using Maintenance and Maintenance the Canteen, and you would use the reciprocal method. Always check the table of usage for service departments that appear on both sides.
Another common layout is to give the usage as a table of percentages with the service departments as rows and the receiving departments as columns, with a dash where there is no service. The dashes tell you where the one-way and reciprocal cases arise.
Administration and selling overheads
Absorption of production overhead is the main task of this chapter, but shared costs can also be apportioned between production centres and administration or selling and distribution centres. For example, the rent of a building shared by the factory, the head office and the sales department can be apportioned by floor area.
The overhead assigned to administration and selling centres is treated as a period cost and is not absorbed into the cost of units. Only the production part follows the route described here, through service departments into production departments and then into unit costs.
Common mistakes in the exam
- Using a basis that does not fit the cost, such as floor area for power in a department with heavy machines.
- Apportioning a service department’s own total only, when it has received a share from another service department first.
- In the equations, forgetting to include the department’s own overhead.
- Using percentages that do not add to 100% of the service given.
- Leaving some overhead stranded in a service department at the end.
- Not checking that the total overhead is unchanged by reapportionment.
- Mixing up the order of the step method. The department that is used by the other must go first.
Quick revision
- Apportion shared costs on a fair basis: area (rent, insurance of buildings), kWh (power), equipment cost (depreciation, equipment insurance), employees (canteen, welfare).
- Secondary apportionment moves service department costs to production departments.
- One-way service: apportion the department that serves the other first. Reciprocal service: simultaneous equations or repeated distribution.
- Equations: each total = own overhead + share of the other’s total.
- Total overhead before and after reapportionment must be equal.
Practice questions
These are original questions written in the style of the Institute of Chartered Accountants of Nigeria (ICAN) exam. Try each one before you open the answer.
Section A style: multiple choice
Question 1. Rent of ₦120,000 is apportioned by floor area. Department A has 400 m² and department B has 600 m². The rent charged to A is:
- ₦48,000
- ₦60,000
- ₦72,000
- ₦80,000
Show the answer
A. ₦120,000 × 400 ÷ 1,000 = ₦48,000.
Question 2. A service department’s costs of ₦60,000 are shared between P1 and P2 in the ratio 2:3. P1 receives:
- ₦24,000
- ₦30,000
- ₦36,000
- ₦40,000
Show the answer
A. ₦60,000 × 2 ÷ 5 = ₦24,000.
Question 3. Sharing the costs of service departments between production departments is called:
- Primary allocation
- Secondary apportionment
- Absorption
- Coding
Show the answer
B. It is also called reapportionment.
Question 4. Which basis is most suitable for apportioning depreciation of machinery?
- Floor area
- Number of employees
- Cost or value of machinery
- Kilowatt hours
Show the answer
C. Depreciation relates to the cost of the equipment.
Question 5. Canteen costs of ₦200,000 are shared between two departments with 10 and 30 employees. The department with 30 employees receives:
- ₦50,000
- ₦100,000
- ₦150,000
- ₦175,000
Show the answer
C. ₦200,000 × 30 ÷ 40 = ₦150,000.
Question 6. The two methods that can be used when service departments serve each other are:
- First in, first out (FIFO) and last in, first out (LIFO)
- Repeated distribution and simultaneous equations
- High-low and regression
- Marginal and absorption costing
Show the answer
B. Both give the same result.
Question 7. Service department A (own cost ₦10,000) receives 20% of the total cost of service department B. The equation for A’s total is:
- A = 10,000 + 0.2B
- A = 10,000 − 0.2B
- A = 0.2B
- A = 10,000 × 0.2B
Show the answer
A. Own overhead plus the share received from the other service department.
Question 8. After secondary apportionment is complete:
- All overhead is in production departments
- Service departments keep half the overhead
- Total overhead has increased
- Total overhead has decreased
Show the answer
A. The total is unchanged but all of it is now in production departments.
Question 9. The best basis for apportioning the electricity used by machines is:
- Kilowatt hours or machine hours
- Number of employees
- Floor area only
- Sales value
Show the answer
A. It measures how much power each department uses.
Question 10. In the step method, which service department is apportioned first?
- The one that receives service from the other
- The one that serves the other service department
- The one with the lowest cost
- Either, it does not matter
Show the answer
B. Start with the department that serves the other, so nothing is returned to it.
Section B style: written questions
Question 11 (10 marks). Explain the bases that may be used to apportion five overhead costs, and why the choice of basis matters.
Question 12 (20 marks). Yola Plastics Ltd has production departments P1 and P2 and service departments S1 and S2. Overheads so far are: P1 ₦140,000; P2 ₦210,000; S1 ₦120,000; S2 ₦90,000. S1 serves P1 50%, P2 30% and S2 20%. S2 serves P1 40%, P2 40% and S1 20%.
(a) Explain the difference between allocation, apportionment and absorption. (4 marks)
(b) Explain why service department costs are apportioned to production departments. (3 marks)
(c) Apportion the service department costs using the simultaneous equations method and state the total overhead of P1 and P2. (10 marks)
(d) State one advantage of the reciprocal method over ignoring service between service departments. (3 marks)
A further written question
Question 13 (10 marks). Production departments P1 and P2 have overheads of ₦90,000 and ₦110,000. Stores (₦60,000) serves P1 and P2 equally. The Canteen (₦40,000) serves P1 30%, P2 50% and Stores 20%. Stores does not serve the Canteen. (a) State the order in which the service departments should be apportioned and why. (2 marks) (b) Apportion the service department costs and find the total overhead of each production department. (8 marks)
Model answers
Show the model answer to Question 11
Shared overheads are apportioned on a basis that reflects how much each department uses or causes the cost. Rent and building insurance: floor area, because larger departments use more of the building. Power for machinery: kilowatt hours or machine hours, because departments that use more power cause more cost.
Depreciation and insurance of equipment: cost or book value of the equipment, because more valuable equipment loses more value and costs more to insure. Canteen and welfare costs: number of employees. Stores costs: number or value of requisitions or materials issued. Other suitable bases include hours of service for repairs.
The choice matters because the same total overhead is always shared, but the share going to each department depends on the basis. This affects each department’s absorption rate and so the unit cost of products passing through it, and therefore prices, profit by product and stock values.
Where no basis is obvious, the choice is a matter of judgement, but it should be fair, consistent and as close as possible to the way the cost is caused.
Show the model answer to Question 12
(a) Allocation charges a cost that belongs wholly to one cost centre directly to that centre. Apportionment divides a cost shared by several cost centres between them on a fair basis. Absorption charges the overhead of a production cost centre to the units made there by applying an absorption rate.
(b) Only production departments make the products, so only they have units to which an absorption rate can be applied. If service department costs stayed where they are, they would never be included in unit costs, and the full cost of products would be understated. Secondary apportionment moves all production overhead into the production departments so that rates can be calculated.
(c)
- Let S1 = total to be apportioned from S1 and S2 = total from S2.
- S1 = 120,000 + 0.2 S2 and S2 = 90,000 + 0.2 S1.
- Substituting.
S1 = 120,000 + 0.2(90,000 + 0.2 S1) = 138,000 + 0.04 S1, so 0.96 S1 = 138,000 and S1 = ₦143,750. - S2 = 90,000 + 0.2 × 143,750 = ₦118,750.
S1 (₦143,750): P1 50% = ₦71,875; P2 30% = ₦43,125; S2 20% = ₦28,750. S2 (₦118,750): P1 40% = ₦47,500; P2 40% = ₦47,500; S1 20% = ₦23,750.
Total overhead: P1 = 140,000 + 71,875 + 47,500 = ₦259,375. P2 = 210,000 + 43,125 + 47,500 = ₦300,625. Check: ₦259,375 + ₦300,625 = ₦560,000 = 140,000 + 210,000 + 120,000 + 90,000.
(d) It recognises that service departments use each other, so the cost of the services they exchange is properly traced to the production departments. Ignoring it, or using a one-way method, leaves out part of the service, so some departments receive too little overhead and others too much.
Show the model answer to Question 13
(a) The Canteen should be apportioned first, because it serves Stores but Stores does not serve the Canteen. Once the Canteen has passed a share to Stores, nothing returns to it. Stores, with its increased total, is then apportioned to the production departments.
(b)
- Canteen ₦40,000: P1 30% = ₦12,000
- P2 50% = ₦20,000
- Stores 20% = ₦8,000.
- Stores total.
₦60,000 + ₦8,000 = ₦68,000: P1 50% = ₦34,000 - P2 50% = ₦34,000.
- P1 = 90,000 + 12,000 + 34,000 = ₦136,000. P2 = 110,000 + 20,000 + 34,000 = ₦164,000. Check: ₦136,000 + ₦164,000 = ₦300,000 = 90,000 + 110,000 + 60,000 + 40,000.
Pathfinder on Overhead apportionment and service departments
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
Part (a) gives a soap factory with two production cost centres and a service cost centre and asks for the overhead to be apportioned and reapportioned to production.
Revise first: Secondary apportionment of service department costs
From the previous syllabus. An item asks about a common cost that is shared over cost centres, testing the meaning of apportionment.
Revise first: Apportioning shared costs: choosing a basis
Multiple-choice items often ask for the share of a cost under floor area or headcount, or which method handles services used by each other. Check Section A of every diet you practise.
Revise first: Secondary apportionment of service department costs
Source: ICAN Pathfinder, Management Accounting. Diets covered: November Diet, 2019 and November Diet, 2014 (previous syllabus). May Diet, 2025 and November Diet, 2024 are not covered here.
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