## Reciprocal Method

The Reciprocal Method, also known as the Algebraic Method, is an approach used in cost accounting to allocate service department costs to other service departments and production departments. This method recognizes the mutual services provided among service departments, hence the name “reciprocal.”

The Reciprocal Method is the most accurate and comprehensive of the service department cost allocation methods, but it’s also the most complex. The basic premise is to account for the interaction between service departments and not simply ignore the services they provide to each other.

Here’s how it works:

**Formulate Equations**: For each service department, set up an equation to represent its costs. The equation should account for its own direct costs plus a portion of costs from other service departments.**Solve Simultaneously**: If there are two service departments, you’ll have two equations to solve simultaneously. The number of equations will match the number of service departments.**Allocate Costs**: Once the service department costs have been determined, these costs can be allocated to the production departments based on a chosen allocation base like direct labor hours, machine hours, etc.

## Example of the Reciprocal Method

Let’s dive deeper into a hypothetical example to understand the Reciprocal Method’s application:

**Scenario**:

A manufacturing company named “TechGears” has two service departments: Information Technology (IT) and Human Resources (HR). Both of these departments provide services to each other and to two production departments: Assembly (A) and Quality Control (QC).

**Given Costs**:

- Direct costs for IT: $60,000
- Direct costs for HR: $30,000

**Given Services**:

- IT uses 15% of the HR services.
- HR uses 25% of the IT services.

**Objective**: Allocate the service department costs to each other and the two production departments.

**Step 1: Set up the equations**:

For IT:

IT’s Total Cost = Direct cost of IT + 25% of HR’s cost

IT = $60,000 + 0.25HR

For HR:

HR’s Total Cost = Direct cost of HR + 15% of IT’s cost

HR = $30,000 + 0.15IT

**Step 2: Solve the equations simultaneously**:

Using the first equation from IT, substituting the value of HR from the second equation:

IT = $60,000 + 0.25($30,000 + 0.15IT)

Solving this gives:

IT = $67,500 HR = $40,125

**Step 3: Allocate costs to the production departments**:

Let’s assume the following allocation basis:

- IT costs are allocated based on the number of computer systems.
- HR costs are allocated based on the number of employees.

Given:

- Assembly (A) has 30 computer systems and 50 employees.
- Quality Control (QC) has 20 computer systems and 30 employees.

Total systems = 50; Total employees = 80.

Allocation to A:

IT costs: (30/50) x $67,500 = $40,500

HR costs: (50/80) x $40,125 = $25,078.13

Allocation to QC:

IT costs: (20/50) x $67,500 = $27,000

HR costs: (30/80) x $40,125 = $15,046.88

So, for Assembly (A): Total allocated service costs = $40,500 + $25,078.13 = $65,578.13

For Quality Control (QC): Total allocated service costs = $27,000 + $15,046.88 = $42,046.88

This example showcases how the Reciprocal Method takes into account the mutual services between the IT and HR departments while also allocating costs to the production departments based on relevant allocation bases.