6.2 Overhead Allocation, Apportionment & Reciprocal Reapportionment

Overhead Allocation, Apportionment & Reciprocal Reapportionment

Core Principle: Overheads represent indirect costs that cannot be directly or economically traced to a specific cost unit. To comply with International Accounting Standard IAS 2 (Inventories) and establish realistic full-cost prices, businesses must systematically channel indirect production expenses into product unit costs through the classic three-stage absorption costing framework: Allocation, Apportionment, and Service Cost Centre Reapportionment.

---

1. The Nature and Definition of Overheads

Direct vs. Indirect Expenses

In cost accounting, expenses divide into direct and indirect categories:

• Direct Expenses: Expenses incurred specifically and exclusively for a single cost unit, job, or contract (e.g., patent royalties payable per unit produced, software license fees dedicated to a single client contract, or the hire of a specialised crane for a custom construction job). Direct expenses form part of Prime Cost.
• Indirect Expenses (Overheads): All other operational expenses that cannot be economically traced to a single unit. Overheads represent the shared infrastructure and operational support necessary to sustain commercial activity.

$\text{Total Cost} = \text{Prime Cost (Direct Materials + Direct Labour + Direct Expenses)} + \text{Overheads}$

Classification of Overheads by Function

1. Production (Manufacturing) Overheads: All indirect costs incurred within the factory gates from receipt of raw materials to delivery of the finished item to the warehouse (e.g., factory rent, machine depreciation, heating, lighting, supervisors' wages, maintenance supplies).
2. Administration Overheads: Costs incurred in directing, managing, and administering the enterprise (e.g., executive salaries, corporate headquarters rent, internal audit, legal fees).
3. Selling & Distribution Overheads: Costs incurred in marketing, securing sales orders, and physically delivering products to customers (e.g., advertising, sales commissions, showroom lease, delivery vehicle depreciation, logistics fuel).

Why Production Overheads Must Be Absorbed: IAS 2 Compliance

Under IAS 2 (Inventories), inventory valuation on the Statement of Financial Position must include not only prime costs but also a systematic allocation of fixed and variable production overheads incurred in converting materials into finished goods. Non-production overheads (administration, selling, distribution) are excluded from inventory valuation and treated as period expenses written off to the Statement of Profit or Loss.

---

2. The Three-Stage Absorption Costing Framework

To establish an accurate overhead absorption rate for products, cost accountants process overheads through three sequential stages:

Stage 1: ALLOCATION
Charge whole, identifiable overhead items directly to specific cost centres.
                         │
                         ▼
Stage 2: APPORTIONMENT
Share general overhead costs between production and service cost centres using equitable bases.
                         │
                         ▼
Stage 3: REAPPORTIONMENT
Transfer all service cost centre costs into production cost centres (Direct, Step-Down, or Reciprocal).
                         │
                         ▼
Result: Total Overhead Assigned Exclusively to Production Cost Centres
(Ready for calculating Overhead Absorption Rates)

Stage 1: Allocation

Allocation is the process of charging an entire, discrete overhead cost item directly to a single cost centre without any division or apportionment. Allocation occurs when an expenditure can be uniquely identified with a specific department.

• Examples: The salary of the supervisor of the Machining Department is allocated 100% to Machining; specific repair parts for a machine in the Finishing Department are allocated 100% to Finishing; catering supplies for the canteen are allocated 100% to the Canteen Cost Centre.

Stage 2: Apportionment

Apportionment is the process of sharing joint or general overhead costs between two or more cost centres (both production and service centres) on an equitable, fair, and logical basis that reflects the benefit received or the cause-and-effect cost driver.

Standard Apportionment Bases

Selecting an equitable apportionment base is a central topic in the ACCA exam:

[!TIP] Apportionment Calculation Rule: To apportion an overhead to Cost Centre $i$: $\text{Apportioned Cost}_i = \text{Total Overhead} \times \left(\frac{\text{Base Amount}_i}{\text{Total Base Across All Centres}}\right)$

---

3. Stage 3: Reapportionment of Service Cost Centres

Why Service Cost Centres Must Be Emptied

In a factory, departments divide into two functional types:

1. Production Cost Centres (PCCs): Departments directly engaged in manufacturing saleable goods (e.g., Machining, Fabrication, Assembly, Finishing). Products physically pass through these centres.
2. Service Cost Centres (SCCs): Departments that do not make goods, but provide essential support services to production departments (e.g., Maintenance, Canteen, Stores, Boiler House, Tool Room).

Because saleable products never physically pass through the Canteen or Boiler House, service departments have no direct output units over which to absorb their costs. Therefore, all service cost centre costs must be completely transferred (reapportioned) into the production cost centres so they can ultimately be absorbed into product unit costs.

Methods of Reapportionment

Depending on the operational interaction between service departments, three methods are available:

1. Direct Method:

   • Applicability: Used when service departments provide services only to production departments, with zero inter-service departmental support (e.g., Maintenance does not use the Canteen, and Canteen requires no Maintenance).
   • Procedure: Service centre costs are reapportioned directly to production departments in proportion to their relative usage shares.

2. Step-Down (Sequential) Method:

   • Applicability: Used when service departments provide support to other service departments in a one-way (non-reciprocal) hierarchy (e.g., Canteen feeds Maintenance staff, but Maintenance does not service Canteen equipment).
   • Procedure: The service department providing service to the greatest number of other service departments is closed first. Its costs are apportioned to all other departments (including other service centres). Once a service department is closed, it receives no subsequent charges from departments closed later in the sequence.

3. Reciprocal Reapportionment Methods:

   • Applicability: Used when service departments provide mutual, reciprocal support to one another (e.g., Canteen feeds Maintenance staff, while Maintenance repairs Canteen kitchen equipment).
   • Techniques: Solved using either Simultaneous Equations (Algebraic Method) or the Repeated Distribution Method.

---

4. Reciprocal Reapportionment: The Simultaneous Equations Method

The simultaneous equations method provides an exact, non-iterative mathematical solution by expressing the total cost of each service department as a linear algebraic equation.

Formulating the Equations

Let $M$ = Total overhead of Service Centre 1 (Maintenance) after including its share of Service Centre 2. Let $C$ = Total overhead of Service Centre 2 (Canteen) after including its share of Service Centre 1.

$M = \text{Initial Overhead of } M + (\text{\% of } C \text{ used by } M) \times C$ $C = \text{Initial Overhead of } C + (\text{\% of } M \text{ used by } C) \times M$

Once $M$ and $C$ are solved simultaneously, their gross totals are apportioned to the production departments based on their initial percentage shares.

Comprehensive Worked Example: The Simultaneous Equations Method

Scenario: Sterling Precision Ltd has two production departments (Machining $P_1$, Assembly $P_2$) and two service departments (Maintenance $S_1$, Canteen $S_2$).

Primary distribution (Stage 1 allocation + Stage 2 apportionment) produced the following initial overheads:

• Machining ($P_1$): $161,000
• Assembly ($P_2$): $82,000
• Maintenance ($S_1$): $53,000
• Canteen ($S_2$): $34,000
• Total Overhead: $330,000

Operational studies show the service proportions provided by each service centre:

Step 1: Formulate the Simultaneous Equations Let $M$ = Total cost of Maintenance. Let $C$ = Total cost of Canteen.

$M = 53,000 + 0.20 C \quad \text{--- (Equation 1)}$ $C = 34,000 + 0.10 M \quad \text{--- (Equation 2)}$

Step 2: Solve for $M$ and $C$ by Substitution Substitute Equation 2 into Equation 1: $M = 53,000 + 0.20 (34,000 + 0.10 M)$ $M = 53,000 + 6,800 + 0.02 M$ $M = 59,800 + 0.02 M$ $0.98 M = 59,800$ $M = \frac{59,800}{0.98} = \mathbf{61,020.41}$

Now substitute $M$ back into Equation 2 to find $C$: $C = 34,000 + 0.10 (61,020.41)$ $C = 34,000 + 6,102.04 = \mathbf{40,102.04}$

Step 3: Reapportion to Production Departments Now reapportion the gross solved amounts to Machining ($P_1$) and Assembly ($P_2$) using their respective percentage shares:

• Machining ($P_1$):

  • From Maintenance ($S_1$): 50% of $M$ = $0.50 \times 61,020.41 = 30,510.20$
  • From Canteen ($S_2$): 40% of $C$ = $0.40 \times 40,102.04 = 16,040.82$
  • Total Reapportioned to $P_1$ = $30,510.20 + 16,040.82 = \mathbf{46,551.02}$

• Assembly ($P_2$):

  • From Maintenance ($S_1$): 40% of $M$ = $0.40 \times 61,020.41 = 24,408.16$
  • From Canteen ($S_2$): 40% of $C$ = $0.40 \times 40,102.04 = 16,040.82$
  • Total Reapportioned to $P_2$ = $24,408.16 + 16,040.82 = \mathbf{40,448.98}$

Step 4: Mathematical Verification & Final Production Centre Overheads Check total reapportioned: $46,551.02 + 40,448.98 = \mathbf{87,000.00}$ Notice that $53,000 + $34,000 = $87,000.00. Exactly 100% of the service centre costs have been transferred into the production cost centres without a penny of rounding loss!

Final Total Overheads in Production Cost Centres:

• Machining ($P_1$): $161,000 + 46,551.02 = \mathbf{207,551.02}$
• Assembly ($P_2$): $82,000 + 40,448.98 = \mathbf{122,448.98}$
• Check Grand Total: $207,551.02 + 122,448.98 = \mathbf{330,000.00}$

---

5. Reciprocal Reapportionment: The Repeated Distribution Method

The repeated distribution method (continuous distribution) achieves the same outcome by iteratively reapportioning service department balances back and forth in successive rounds until the remaining balance dwindles to an immaterial sum (e.g., less than $10), which is then distributed directly to production departments.

Repeated Distribution Schedule

Using the same figures from Sterling Precision Ltd:

Notice: The final totals ($207,551 for Machining and $122,449 for Assembly) match the simultaneous equations solution down to the nearest dollar. In computer-based ACCA exams, the simultaneous equations method is significantly faster and avoids rounding errors.

---

6. ACCA Exam Traps & Common Pitfalls

[!WARNING] Exam Trap 1: Apportioning Depreciation on Machine Hours: Students often incorrectly apportion plant depreciation on machine hours. Depreciation is a fixed capital cost related to asset ownership; it must be apportioned based on machine carrying value (cost or NBV), not machine runtime hours.

[!WARNING] Exam Trap 2: Direct Reapportionment Proportions: When using the direct method to reapportion a service department (e.g., Stores) across production departments, students often divide by 100% rather than recalculating the relative percentages. If Stores serves Machining 60% and Assembly 20% (with 20% to Canteen ignored), the direct reapportionment to Machining is 60 / (60 + 20) = 60 / 80 = 75%, and Assembly is 20 / 80 = 25%.

[!WARNING] Exam Trap 3: Reapportioning to Closed Service Centres in Step-Down: In step-down reapportionment, once a service centre is closed, it never receives a share from subsequent service departments. If Department A is closed first and charged to B, C, and D, when Department B is closed next, its costs are apportioned ONLY across C and D (and never back to A).