Simultaneous equation overhead apportionment method 

1.1 Introduction

Definition: Simultaneous equation overhead apportionment method is a type of reciprocal overhead apportionment method under secondary distribution which advocates use of simultaneous model in determination of the overhead cost associated to a particular service department. Once the exact overhead is established, it is distributed to the respective production departments using reliable apportionment percentages. This method was introduced to take care of the shortcoming of repeated distribution overhead apportionment method which repetitively keep on distributing the cumulative service department overhead to production department which is cumbersome and difficulty to compute.

Steps of simultaneous equation overhead absorption method

The following are the THREE helpful steps to guide you to compute the total overhead cost distributed to each production department where there are service department serving each other and at the same time serving the aforesaid production departments.

Step 1: Determine the total overhead cost for each service department putting in mind that the specific service department is made up of its original overhead cost plus other overhead cost re-distributed to it from other alternate service departments.

NB: To achieve the step 1 objective of determining the total overhead cost associated to each service department, a simultaneous equation is applied as shown herein; 


Assume that there are two service departments, X and Y and that;

Re-distribution of overhead cost from the sister service department is for X=0.2 and for Y is Y=0.1

Let service department X have overhead cost of $10,000

Let service department Y have overhead cost of $15,000

Then simultaneous equation will be set as;

Total overhead cost of X is X=10,000+ 0.1Y

Total overhead cost of Y is Y=15,000+ 0.2X

Step 2: Distribute straight away the total overhead cost for each service department as determined in step 1 above to the respective production department using the proportions given.

Step 3: Summation of the total overhead cost after the “one time” re-distribution of the service department overhead costs.


EXAMPLE (Extract from our article dealing with repeated distribution overhead apportionment method)

A food processing organization has THREE and TWO production departments and service departments respectively. The overhead costs for the three departments were assigned as follows


Show how the overheads are fully distributed to the three production departments using;

i). Simultaneous equation method.

ii). Compare the simultaneous equation method with that of repeated distribution method and make a conclusion



i). Simultaneous Equation Method

Given this information from the original question;

Service Department

NB1: It should be noted that originally, the service overhead re-distribution proportions were as follows

Originally, the production overhead costs were distributed as follows’

ii). Repeated distribution overhead apportionment method. 


Brief Explanation

This is the point, that the re-apportionment of the service department overhead cost is proportionately allocated to the production departments and the reciprocal service department (i.e., the other service department) in the first round or phase. Then in round two, the reciprocal service department’s overhead cost which is directly allocated overhead plus the apportionment from the other service department, is distributed to all the departments. This process continues up to the end until all the service departments have zero overhead costs.

So, as per this case, the total overhead cost for the three departments is 190,909+287,778+211,313=$690,000


The two methods, namely, the repeated distribution and simultaneous equation method are the same for you can see they both translate in to the same answer of $690,000.

Advantages of simultaneous equation overhead apportionment method

1). Inter service overhead apportionment.

Simultaneous equation overhead apportionment method creates a way for re-allocation or apportionment of the overhead costs which is commonly shared between two or more service departments.

2). Elaborative.

The stake holders are in a position to understand the in-depth logic used in overhead apportionment.

3). Accuracy.

Simultaneous equation overhead apportionment method uses a scientific method to estimate overhead. Hence it is more accurate.

4). Gives a comparative viewpoint.

Simultaneous equation overhead apportionment method is a method that allows one to compare results of apportionment for two or more periods for the results gotten in each period is reliable.

5). Objectivity is high.

Simultaneous equation overhead apportionment method is less bias for it is a scientific method used to determine the amount of overhead to be apportioned.

Disadvantages of simultaneous equation overhead apportionment method

1). Complicated.

It is not easy to use it for the approach is mathematical and many participants do not want use of the approach. So, it is less useful to many people.

2). Interpretation challenges.

Simultaneous equation overhead apportionment method results are not easy to read and relate the message to the applicability of the outcome.

About the Author - Dr Geoffrey Mbuva(PhD-Finance) is a lecturer of Finance and Accountancy at Kenyatta University, Kenya. He is an enthusiast of teaching and making accounting & research tutorials for his readers.