Repeated and Simultaneous Equation method

Cost Apportionment is a crucial part of cost accounting, ensuring that overheads are fairly distributed among various departments. Two commonly used methods for allocating service department costs to production departments are the Repeated Distribution Method and the Simultaneous Equation Method.

Repeated Distribution Method

Repeated Distribution Method is an iterative approach used to allocate service department costs to production departments. This method repeatedly distributes the service department costs among other departments, including other service departments, until all costs are completely assigned to production departments.

Process of Repeated Distribution Method:

1. Identify Costs: Determine the total overheads of each service department.

2. Select an Allocation Base: Choose an appropriate basis for distribution, such as labor hours or machine usage.

3. Allocate Service Department Costs: Start with the service department with the highest cost and distribute its overhead to production and other service departments.

4. Repeat the Process: The newly allocated costs to other service departments are further distributed until all costs are fully transferred to production departments.

Example of Repeated Distribution Method:

Consider two service departments, Maintenance and Canteen, serving two production departments, Cutting and Assembly. The cost allocations are based on predefined percentages. The process is repeated until the remaining balance in the service departments is negligible.

Advantages of Repeated Distribution Method:

• Logical Approach: Allocates costs fairly based on usage.

• More Accurate than Direct Methods: Takes inter-service department allocations into account.

• Easy to Implement in Small Firms: Suitable for companies with simple cost structures.

Disadvantages of Repeated Distribution Method:

• Time-Consuming: Requires multiple steps to allocate costs.

• Less Precise for Large Organizations: Complex and may not fully capture reciprocal services.

Simultaneous Equation Method

Simultaneous Equation Method provides a mathematical approach to allocate service department costs by solving linear equations. This method is highly accurate as it fully recognizes the reciprocal services between service departments before allocating costs to production departments.

Process of Simultaneous Equation Method:

1. Define the Equations: Create cost equations for service departments, incorporating the percentage of services provided to each department.

2. Solve the Equations: Use algebraic methods to determine the exact cost of each service department.

3. Allocate Costs: Once service department costs are calculated, allocate them to production departments.

Example of Simultaneous Equation Method:

Assume two service departments, Maintenance (M) and Canteen (C), serve two production departments, Cutting and Assembly. Given cost allocations, the cost equations are:

M = Initial Cost of M + (Percentage of C’s Cost Used by M) × C

$$C=\text{Initial Cost of C }+(Percentage\; ofM’sCostUsedbyC)\times M$$

By solving these equations, we determine the accurate cost of each service department before allocating them to production departments.

Advantages of Simultaneous Equation Method:

• Highly Accurate: Fully considers inter-service department costs.

• Mathematical Precision: Eliminates errors from iterative methods.

• Effective for Large Organizations: Suitable for complex costing structures.

Disadvantages of Simultaneous Equation Method:

• Complex Calculations: Requires algebraic skills and sometimes software tools.

• Time-Intensive: Solving equations manually can be difficult.

Comparison of Repeated Distribution and Simultaneous Equation Methods