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- Reciprocal (algebraic) method of cost allocation

The allocation of service department costs is incomplete if the method used for cost allocation ignores or does not give full recognition to interdepartmental services. Interdepartmental services are services that two or more service departments provide to each other. For example, consider a case where service department A provides service to service department B, and in turn, department B provides service to department A.

If you have already studied direct method and step method of cost allocation you may have noticed that the direct method completely ignores the interdepartmental services and step method gives them only a partial recognition because it allocates costs forward – never backward. To overcome this problem, a method known as reciprocal method is used which fully recognizes interdepartmental services and provides greater exactness in allocating the cost of a service departments to other departments. The reciprocal method uses the simultaneous equations technique and is therefore also referred to as simultaneous equations method and algebraic method of departmental cost allocation.

A company has two service departments and two producing departments. The two service departments provide service not only to two producing departments but also one another. The costs of four departments and relationship among them is shown below:

Required: Allocate the cost of service departments to producing departments using reciprocal/algebraic method.

Y = $7,260 + 0.3Z —— Eq.1 Z = $4,000 + 0.2Y —— Eq.2

Substituting the value of Z in equation 1:

Y = $7,260 + 0.3($4,000 + 0.2Y) Y = $7,260 + $1,200 + 0.06Y Y – 0.06Y = $7,260 + $1,200 0.94Y = $8,460 Y = $8,460/0.94 Y = $9,000

Substituting the value of Y in equation 2:

Z = $4,000 + 0.2(9,000) Z = $4,000 + $1,800 Z = $5,800

Distribution summary:

## Advantages and disadvantages of reciprocal or algebraic method

- Difference between service and operating departments
- Direct method of cost allocation
- Step down method of cost allocation
- Difference between cost center and profit center

I am happy for the explanation thank more lwill see..next

The work on advantage and disadvantage in good but too brief

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## Appendix: Service Department Allocation

Reciprocal method of allocation.

Step 1: Determine allocation bases

We will work with the administration cost formula in (b) first:

Total Administration cost = $ 4,000 administration department cost + (2/6 x total maintenance cost)

Using algebra, we can assign Total Administration Cost a variable of A giving the formula:

A = 4,000 + [ 2/6 x ($8,000 + 0.20)A]

A = 4,000 + (2/6 x 8,000) + (2/6 x 0.20A)

A = 4,000 + 2,666.67 + 0.067A — rounded

A or total administration cost = $7,145 rounded

** difference due to rounding in calculations.

## What Are the Three Methods of Cost Allocation? (Explain and Example)

## Direct Method

## The Way it Works

Pros and cons of the direct method.

## Step Method of Cost Allocation

## Limitations of the Step Allocation Method

Advantages of step allocation method, reciprocal method of cost allocation.

## Use of Reciprocal Approach of Cost Allocation

Benefits of reciprocal cost allocation method.

## Importance of Cost Allocation

## Which Method to Use?

## Accounting Details

Reciprocal method of cost allocation – service department costing, definition:.

## Explanation:

## Use of Reciprocal Method:

## You may also be interested interested in other articles from “service department costing” chapter:

- Selecting Allocation Bases
- Direct Method of Cost Allocation in Service department costing
- Step Method of Cost Allocation in Service Department Costing
- Reciprocal Method of Cost Allocation-Service Department Costing

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## How to Calculate Reciprocal Method Costing

Total Cost = Direct Cost + Allocated Cost.

Substitute the data from the example into the equation. Thus ...

DP = $250000 + 0.1HR and HR = $160000 + 0.2DP.

Solve the above mentioned simultaneous equations. Hence,

DP = $250000 + 0.1HR DP = $250000 + 0.1 ($214286) DP = $250000 + $21429 DP = $271429

The method is rarely used, as the math and computation can become complex.

## AccountingTools

Accounting CPE Courses & Books

## Cost allocation methods

## How to Allocate Costs

## Cost Allocation Based on Direct Labor

## Cost Allocation Based on Machine Time

## Cost Allocation Based on Square Footage

## Allocation of Corporate Costs

## Cost Allocation Based on Sales

## Cost Allocation Based on Profits

## Cost Allocation Based on Headcount

## The Reciprocal Method of Cost Accounting

## Reciprocal Method

## Determining a Cost Allocation Base

## Using the Cost Allocation Base

## Calculating Fully Reciprocated Costs

## Allocating Fully Reciprocated Costs to Production Departments

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## Using reciprocal allocation of service department costs for decision making

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The reciprocal method uses the simultaneous equations technique and is therefore also referred to as simultaneous equations method and algebraic method of departmental cost allocation. Example A company has two service departments and two producing departments.

Total maintenance cost can be calculated as $8,000 department cost + $1,429 (7,145 x 20%) allocated from administration for a total of $9,429. Step 3: Show cost allocations Now that you have the TOTAL Cost of Maintenance and Personnel, it is time to allocate it using the Total Cost amounts from Step 2 and the percents from Step 1.

The reciprocal method of cost allocation uses algebra to capture and allocate 100% of service center (interdepartmental) costs. The mathematical tool required to perform the reciprocal...

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Reciprocal method is a method of allocating service department costs to other departments that gives full recognition to interdepartmental services. Explanation: The reciprocal method gives full recognition to interdepartmental services. Under the step method, only partial recognition of interdepartmental services is possible.

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This video shows how to use the Reciprocal Method allocate the costs of multiple support departments when the support departments provide services to each other. A shortcut for determining...

A or total administration cost = $7,145 rounded Total maintenance cost can be calculated as $8,000 department cost + $1,429 (7,145 x 20%) allocated from administration for a total of $9,429. Step 3: Show cost allocations

Various cost allocation methods are used to allocate factory overhead costs to units of production. Allocations are performed in order to create financial statements that are in compliance with the applicable accounting framework. The most common allocation methods are noted in the following bullet points, along with commentary about their ...

14.4: Reciprocal Method of Allocation. The final method, is the reciprocal method. Although it is the most accurate, it is also the most complicated. In the reciprocal method, the relationship between the service departments is recognized. This means service department costs are allocated to and from the other service departments.

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This video shows how to use the Reciprocal Method to allocate the costs of multiple support departments when the support departments provide services to each...

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Using the number of units produced as the allocation method, they can calculate overhead costs using this formula: $4,000 / 5,000 = $0.80 per notebook When added to Polly's direct costs, the cost to produce each notebook is $5.80, calculated as follows: Direct materials: $3 per notebook Direct labor: $2 per notebook Overhead: $0.80 per notebook

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