# Trial and error overhead cost apportionment method

1.1 Introduction

Definition: Trial-and-error overhead cost apportionment method of reciprocal nature which is under secondary distribution which advocates use of hit and miss nature of approach of apportioning overheads (guesswork approach). It replaces the simultaneous equation method especially when the number of service departments are more than two.

1.2 Why is the Method Referred to as Trial-and-Error Method?

This is because the method involves setting of distribution percentages for every service department as thought best by the decision maker. For example, when dealing with apportionment of overheads of a certain service department, let us call it the donating department the recipient departments (i.e., the production and other service departments) on the other hand will be assigned a different or dissimilar distribution percentages as compared to the ones assigned to the same departments when the overheads of the second, third and the Nth service department are being apportioned. Then the final cumulative overhead cost is distributed to the respective production departments as per the set ratio or percentages assigned from the beginning.

Therefore, in a nutshell, the trial-and-error approach involves apportionment of the overhead cost of inter-service departments such that the overhead of one service department which serves another service department is distributed to that other reciprocal service department until no balances remain in this department. The same thing applies to the other counter-service department. Its overheads are again re-distributed to the other service department. This process continues until all the service departments have zero balances.

Let us assume that in a certain manufacturing company, there were THREE production departments and FOUR service departments as summarized in the table below;

Note that the above assignment of distribution percentages is on trial-and-error method. After that is done, the apportionment of the overhead costs is done also. For this exercise of apportioning the service overhead costs to the production department, this goal or objective is achieved by broadly dividing the process in to two steps;

i). Primary trial-and-error overhead apportionment step.

ii). Secondary trial-and-error overhead apportionment step.

## Steps under primary trial-and-error overhead apportionment

Primary trial-and-error overhead apportionment step is a stage of apportioning the service overhead costs amongst the reciprocal service departments until the process of distribution re-distributions ends up exhausting all the amounts. The following primary steps are used to achieve this objective;

### Step 1: Determine the total overhead costs for both the production and service department.

As a producer or if you are a student, check the data containing the total overhead cost for both production and service departments as per the primary apportionment (i.e., the commonly referred to as overhead allocation process).

### Step 2: Develop a primary trial-and-error percentage distribution matrix (i.e., table)

At this stage, the decision maker should assign distribution percentages to be used to apportion overhead costs to all the two department categories using trial-and-error method.

Note one, that; the major percentages set goes to the production departments while the minor percentages go to the service departments.

Note two, that; the sum of the major percentages and the minor percentages should add up to 100 percent. A distribution matrix can be as indicated below;

### Step 3: Distribution and re-distribution of the service overhead costs

Distribution and re-distribution of the service overhead costs amongst the service departments using the sum of the minor percentages.

In this step, use the individual minor percentages assigned to the respective service department to distribute the overhead cost one service department to the other reciprocal service departments. This process should be repeated in turns from one service department to the other. To achieve this, the first service department should be named the donor department like in Biology on issues of blood donation in human beings and the other service departments be named recipient departments. In the next turn the first donor department becomes a recipient and the second service department becomes the donor department. This distribution re-distribution continues until all service department have zero or negligible overhead cost to be distributed.

### Step 4: Sum up the cumulative overhead costs for each service department

Once step 3 above is over, add up all the cumulative overhead costs for each service departments. NB: This step 4 process marks the end of primary overhead apportionment process which only focuses on the service departments.

## Steps under secondary trial-and-error overhead apportionment

The secondary overhead cost distribution step only focuses on further distribution of the total cumulated overhead costs from the service departments to the production departments. So, the following steps are utilized in achieving this objective.

### Step 1: Post the production department overhead costs

Post the production department overhead costs to the respective columns of each aforementioned production departments as per the primary distribution which was done from the beginning.

### Step 2: Sum up all the corresponding major percentages associated with the production departments

Sum up all the corresponding major percentages associated with the production departments

as it was assigned by the decision maker using trial-and-error method.

In this step, you need to consider the total major percentage initially assigned to the respective production departments on trial-and-error basis and sum them up. For example if through trial-and-error method production department “A” had been assigned 30%; 25% and 20%  of  overhead cost of service departments 1, 2 and 3 in that order, then sum them up together. That is, 30%+ 25% +20% =85%

### Step 3: Compute or establish the equivalent amount of corresponding overhead cost from the respective service departments

Compute or establish the equivalent amount of corresponding overhead cost from the respective service departments using the summed-up major percentage determined in step 2 above. For example, in step 2 above we got 85%. Then, compute the corresponding amount of overhead cost from the respective service department. For example, if the total overhead cost of service department int the primary distribution step was \$60,000. Then 85% of 60,000 will be \$51,000.

### Step 4: Go back to your summed up major percentage figure and un pack it into its individual percentage components.

Go back to your summed up major percentage figure and un pack it into its individual percentage components. Then convert those individual percentages in to ratio expressions. For example, in step 2, you got a summation of 85% made up of 30%; 25% and 20%. This can be converted in to 30:25:20 which is further simplified in to a ratio expression of 6:5:4

### Step 5: Use the equivalent amount of overhead cost gotten in step 3 above is distributed amongst the respective production departments

Use the equivalent amount of overhead cost gotten in step 3 above is distributed amongst the respective production departments using the ratio established in step 4 above.

### Step 6: Add the total production overhead cost associated to the production department as allocated during primary distribution process

Add the total production overhead cost associated to the production department as allocated during primary distribution process plus the apportioned overhead cost from the respective service department as determined by use of the aforementioned ratio.

Example

High Level producers has THREE production departments and FOUR service departments. The total overheads of each as per the primary distribution are as follows;

Interpretation of the grand total amounts in the above table

Before I go a head and demonstrate to you how to compute the total overhead cost apportioned to the respective production departments, let me interpret for you what the grand total overhead cost in the table above means.

The figures, namely; 17,315;   17,850;22,903 and 21, 391.

In this case, am taking only two cases to represent the others. That is figure 17,315 and figure 22,903       of 1 and 3 service departments respectively.

One, figure 17,315 means the summation of overhead costs as per primary distribution done originally for service department 1 which was \$12,000 plus \$5,315 apportioned and re-apportioned from the other reciprocal departments, 2,3 and 4 due to the inter-services this department (department 1) received from those others.

Two, figure 22,903 means the summation of overhead costs as per primary distribution done originally for service department 3 which was \$20,000 plus \$2,903 apportioned and re-apportioned from the other reciprocal departments, 1, 2 and 4 due to the inter-services this department (department 1) received from those others.

Now let us go to secondary distribution. How do we handle this case? It’s simple;

1. More comprehensive and through

Trial-and-error method carry an in depth meaning of the apportionment approach of overhead costs and so it is reliable.

1. Trial-and-error method is objective

Trial-and-error method is a process that is lengthy but ensures elimination of all personal judgement for there is distribution and re-distribution of the overhead costs such that no biasness.

1. Trial-and-error method is more suitable where simultaneous method has failed to apply

Simultaneous method considers only two service departments. In case they are more than two, then the trial-and-error method applies for it considers more than two service departments.

1. Trial-and-error method ensures exhaustive distribution of inter-service overhead costs.

Trial-and-error method ensures all the service department overhead cost associated to another service department is fully transferred to it. Hence no pending overheads.