Allocation of costs to other departments

Everyone is accountable for the costs incurred in our day-to-day business operations. I have a myth-busting topic today to find out if we are doing it the right way. We usually learnt about cost allocation  methods like: Simultaneous Equation method, Reciprocal- Redistribution of costs, and finally Trial and Err methods of cost allocation to different departments a.k.a., Cost apportionment.

Lets understand the simple question first:

From the below, you are simply reallocating costs to various Production departments and Services departments within eg., X allocated its costs to A,B,C,Y and Y allocated its costs to A,B,C,X. 

Let us start with the Simultaneous Equation Method of allocation using two alternative means for equating this problem 

Equating Method 1:

We can conform all expressions are leading to the same answer where X= 2,500 $ and Y= 1,250 $. However, the allocation of actual costs from Y to other departments is 1,000 $ only and unfortunately we have 250$ INFLATED allocation. 

Now, lets take a look at Reciprocal/ Redistribution of cost allocation method below.

The outcome is the same- INFLATED due to repeat distribution. Whilst, all of the above techniques can lead to havoc, Trian & Err method proves the same. This is my observation that, traditional Direct Cost allocation is giving 100% accurate accounting thereby avoiding Tax consequences.

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Will be back with more myth-busting!!