# What Are the Three Methods of Cost Allocation

What Are the Three Methods of Cost Allocation: Service departments are those departments that provide support to production departments but do not engage directly in the production of the products e.g. the accounting department, maintenance department, and the legal department. Service departments provide services to each other and at the same time to the production department. The methods of allocating service costs include

1. Direct Allocation Method
2. Step-wise Method
3. Reciprocal Method

## What Are the Three Methods of Cost Allocation?

### (i) Direct Method

The service costs are only allocated to the production department according to the usage of the services provided. For example, maintenance services offered to the  mixing department will be charged to the mixing department directly.

### (ii) Step-wise Method

It is also referred to as elimination method. Some of the costs of the reciprocal services will be recognized although only to some extent. The steps followed include:

Choose one of the service departments and allocate its costs to all the other departments

including the other service departments. Normally, the basis of choosing that service

department to start with is the service department that provides services to the greatest

number of other departments or the greatest percentage of the service costs incurred

in that department is attributed to service offered to other departments.

Another service department is chosen and its total costs allocated the remaining

departments excluding the first service departments.

Repeat the process until all the service department costs have been allocated to the

production departments.

### (iii) Reciprocal Method

This method fully considers all reciprocal services. It is the most precise in technically

finished method.

## Cost Allocation Example

Assume the following data:

User Dept           Units of services provided          Costs Prior to Service Department

S1           S2           S3                           \$

S1                           0             2,000     4,500                     92,400

S2                           1,000     0             0                             184,800

S3                           2,000     4,000     0                             138,600

P1                           4,000     10,000 1,500                     400,000

P2                           3,000     4,000     9,000                     500,000

Totals                    10,000 20,000 15,000                 1,315,800

### (i) Direct Method allocation to production departments;

S1           S2           S3           P1                    P2

Cost Prior to Allocation                 92,400 184,800 138,600 400,000 500,000

Allocate S1(4:3)                                (92,400)                               52800            39,600

Allocate S2 (5:2)                                               (184,800)             132000          52,800

Allocate S3(1 :6)                                                               (138,600) 19800      118,800

### ii) Step wise method (Elimination Method)

S1           S2           S3           P1               P2              Total

Cost Prior to Allocation                 92,400 184,800 138,600  400,000  500,000   1,315,800

Allocate S1(1:2:4:3)                                         9,240     18,480 36,960       27,720

194,040 157,080  436,960  527,720

Allocate S2 (2:5:2)                                            (194,040) 38,808  97,020      58,212

195,888  533,980   585,932

Allocate S3(1 :6)                                                                (195,888) 27,984    167,904

561,964  753,836     1,315,800

### (iii) Reciprocal Method

Let Sa be the total costs of service dept 1

Let Sb be the total costs of service dept 2

Let Sc be the total costs of service dept 3

Each of the coefficients in the expressions hereunder (used to get cost after recognition)are percentages based on proportional service received by a department from the departments

Sa=92400+0.1Sb+ 0.30Sc Equation (i)

Sb=184,800 +0.1Sa            Equation (ii)

Sc=138,600 +0.2Sa+0.2b  Equation (iii)

Substituting Equation (ii) into Equation (i) and solving, we get;

Sa=92400+0.1(184,800 +0.1Sa+ 0.0sc)+ 0.30Sc………Equation (i)c

Sa=92400+(18,480 +0.01Sa)+ 0.30Sc

Sa=110,880 +0.1Sa+ 0.30Sc

0.99Sa=110,880+ 0.30Sc

Substituting Equation (ii) into Equation (iii) and solving, we get,

Sc=138,600 +0.2Sa+0.2(184,400+0.1Sa)     Equation (iii)

Sc=138,600 +0.2Sa+36,880+0.02Sa

Sc=175,480 +0.2Sa+0.02Sa

0.98Sc=175,480+ 0.2Sa                                              Equation (iv)

Substituting (v) into Equation (iv) and solving we get,

0.99Sa=110,880+ 0.30Sc

0.99Sa=110,880+ 0.30(175,480+ 0.2Sa)

0.99Sa=110,880+ 52,644+ 0.06Sa

0.99Sa=163524+ 0.06Sa

0.93Sa=163524

Sa=163524

0.93

Sa=175,832

Therefore

Sb=184,400 0.1(175,832) = 201,983

Sc= 138,600+ 0.2(175,832) +0.2(201,983)= 214,163

Cost Prior to                       S1            S2           S3           P1           P2               Total

Allocation

92,400  184,800  138,600  400,000  500,000      1,315,800

Cost after

recognition                         175,832    201,983  214,163

Allocate S1(1:2:4:3)                            9,240     18,480     36,960     27,720

194,040    157,080    436,960     527,720

Allocate S2 (2:5:2)                            (194,040)  38,808       97,020        58,212

195,888       533,980       585,932

Allocate S3(1 :6)                                                     (195,888)       27,984      167,904

561,964     753,836   1,315,800

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