Cost allocation and apportion in Cost Accounting

In cost accounting, costing of products and services requires to allocate overheads to production cost centers from service departments using appropriate basesdepending on the nature of services rendered to production departments. The cost allocation is the traceable cost with each department. However, the indirect overhead cost are the costs apportined on a appropriate basis from service centres to production cost centeres. In cost accounting there are three methods to apportion overhead costs. These methods are as follows;

1. Direct method

2. step method

3. reciprocal method.

The direct method allocates service centre costs directly depending on the amount of services they use from each service department in one step. This is the easiest method. However this method is not accurate compared to step method. These two methods are applicable where the service cost centers do not use services within them. If services are used with service departments as well as production departments, reciprocal method is used. However, this method is complicated and it may need a computer to solve the eaquations.and the accuracy is not that high compared to step method. This the reason in practice step method is used by most firms in practice.

Cost of any product, cosist of direct material cost, direct labour cost and overhead costs. Overheads cannot be identified directly to goods and services. This is the reason in cost accounting one must have a basis of absorbinbg overheads in to goods and services. Before the cost absorbtion on a predetermied basis, the service center costs or overheads has to be apportined to production department. This has to be dome to accurately measure cost of goods and services of a firm.

Example of Direct method of cost apportionment

Say in a manufacturing organization it has two production sections and two service departments. The overhead of service section 1 is 350,000 as directly identifiable overhead cost. As well, the the overhead of section 2 is 250,000. The production cost department 1 is 500,000 and production department 2  is 400,000. The cost driver or the base of cost allocation for service department 1 is as follows:

service department 1 total employee hours is 40,000

employee hours in service department 1 - 5000

                       service     department 2 - 4000

                    production department 1   -  16000

                    productiondepartment  2  -    15,0000

Service department cost driver apportionment base is area is indirect material used by service department by service department 2.

Total indirect material used by the service department 2 is 125,000.

Indirect material used by service department 1 - 25000

                                    service department 2 - 15000

                                production department 1- 55000

                                production department 2- 30000

Apportion the service center cost to production department based on direct method.

Solution

Description                      P 1         P 2            S1              S2

Allocated costs              500000    400000    350000       250000

employee hours              16000     15000        5000           4000

Indirect material used      55000     30000      25000          15000

Apoortionment table

Description          P1             P2            S1              S2

Costs               500000       400000    350000     250000

                       180645       169355   (350000)

                       161765         88235                   (250000)   

Total                842410          657590    

One can see that, in this method the service deaprtment cost is allocated irrespective of the cost attributable to service departments and only based on the cost drivers of production departments. because of this omission, this method is the least accurate of cost apportionment method. This will lead to inaccurate product costs. This is the disadvantage of this method. However, it is a very simple method and takes little time compared to other methods. This is the reason this method is used frequently by many organizations in practice.

Example of step method

Take the above example again. In this method the highest overhead of the service department is first allocated to production and service department. Then the total allocated and apportioned cost of the highest cost service department cost is allocated directly ireespective of the cost attributable to other departments by the other service department. This method is more accurate as it recognize interdepartmental costs between service departments. However it is more time consuming and not simple compared to direct method and the accuracy achieved is not that great. However, it is most appropriate if the organization has interservice department between them and has more service departments. If this method is applied to the above example, the costs of production departments will be as follows:

Description                P1                P2              S1                S2

Costs                    500000        400000        350000       2500000

                            160000        150000       (350000)       400000

                            187647        102353                         (290000)

Total                      847647        652353

Percentage error of direct method compared to step method for departmetn 1 = 0.62%

                                                                                     for department 2 = -0.80%

One can see from the above calculations the the accuracy of direct method compared to step method is very negligible. However, if there are more service departments and they provide service between them the accuracy will become larger. This is the reason in practice wehn organizations have more service departments and they provide services between them they use step method insted of direct method if the accuracy achived is more beneficial than the cost of accuracy achieved.

Example of reciprocal method of cost apportionment

If there are more service department and they provide reciprocal services betwen them as well as production departments, then the reciprocal method is most accurate. However it is more complicated and have to use more complicated computer software and other resources to acieve this accuracy and there may be other uses of this resource which may be more valuable. In practice this method is least used because of its complexity and the accuracy achieved is not great compared to other simple methods and the resources required to acihive this accuracy. There is an opportunity costs for any activity if the resources can be used for alternative purposes. In this regared, reciprocal method is practically may not be feasible or not considred by managment in practice due to its complxity and the benefits compared its cost is justified.

Considering the above example, Service department 1 cost in percentage terms goes to service departmetn 2, itself and production department is as follows:

cost of service department 1 = 350000. Total employee hours = 40000

production department 1 as apercentage of total cost = 16000/40000*100 = 40%

production department 2 as percentage of total cost = 15000/40000 * 100 = 38%

Service department 1 as percentage of total cost = 5000/40000*100 = 12%

Service department 2 as percentage of total cost = 4000/40000*100 = 10%

Serive department 2 cost as a percentage to service department 1, itself and production department is as follows:

Productioin department 1 percentage of total cost service department 2= 55/125*100=  44%

production department 2  as a percentage  of total cost of service department 2  = 30/125*100 = 24%

Service department 1 as a percentage total cost of service department 2 = 25/125*100 = 20%

Servive department 2 as percentage of total cost of service department 2 itself = 15/125*100 = 12%

SC1 = 350000 + 0.12 SC1 + 0.20 SC 2

SC2 = 250000 + 0.12 SC 2 + 0.10 SC 1

That is 0.88 S C1 = 350000 + 0.20 S C 2

There fore S C 1 = 350000/0.88 + 0.20 S C2/0.88 = 397727 + 0.23 S C 2

S C 2 = 250000 + 0.12 S C 2 + 0.10* (397727 + 0.23 S C2 )

S C 2 = 250000 + 0.12 S C 2 + 39773 + 0.02 S C2

S C 2 ( 1 - 0.14 ) = 250000 + 39773

0.86 SC 2 = 289773

S C 2 = 289773/0.86 = 336945

S C 1 = 397727 + 0.23*336945 = 397727 + 77497 = 475224

Reciprocal cost apportionment table

Description                 P1            P2           S 1          S 2

original cost             500000    400000     350000    250000

                              190090    180585       57026     47522

                                                            (475224)

                              148256      80867        67389     40433

                                                                           (336945)

Total cost                 838246   661452

Conclusion

As demonstrated above, it is obvious the methods of allocation can arrive at different values for the overheads of production departments. The accuracy of the method is dependent on the sophistication of the allocationmethod. However, the more sophisticated method also becomes more complex and time consuming. As well the accuracy of the more sophisticated methods do not give altogether very different values. That is the error of the simpler methods do not vary considerably. The simp[ler methods are more than adequate for small number of production and service departments as well there is very little reciprocal services within the service departments. However, if there are large number of service departments and production departments, then the more sophisticated methods are wothwhile to explore and becomes more valuable as accuracy becomes important than time factors. I hope this makes easier for accounting students and others to understand cost allocation and apportionment and their strengths and weaknesses.