Absorption of Overheads: Solution to Reapportionment of service costs question

This is a solution to the question found here
First we will use the repeated distribution method to redistribute service costs
Lastly we will use the algebraic method to reapportion costs
We have already looked at why we need to reapportion service costs among production departments here

As shown the technique is simple you need to pick one service department and reapportion all its overheads to the other three departments in our case we first picked stores
Then you pick the other department (in this case maintenance) and reapportion all its overheads to the other three departments
The second step means there are now overheads costs in the stores department due to its share of the maintenance costs
This cost has to be reapportioned again
This process is repeated until there are immaterial costs in all service departments which can be reapportioned among the two production departments without the need to reapportion a share into the service departments
In our case there remains $2 in the end which we split equally among the two departments (a result of rounding off $0.6
We could have continued with the reapportioning but the benefits from continuing would not have been much
You will have to use your discretion to determine when to stop reapportioning but its something you can do when amounts reach single digits

The Algebraic Method

This involves the use of simultaneous equations to solve the problem of having to reapportion costs
From our question we know that the total overheads in the stores department ought to be $20 000 plus 15% of the maintenance costs
However we don’t know what the actual final for total overheads will be since they will also have to include a 20% share of stores cost which have already said ought to include a share of the maintenance costs
From the above we have two unkowns i.e. the actual maintenance costs m and the actual stores costs s
We can thus formulate two equations:
$s=20000+0.15m$
$m=15000+02s$
Now there a number of ways to solve simultaneous equations but here we will use the substitution method
Replace M in equation 1 to get:
$s=20000+2250+0.03s$
This becomes:
$0.97s=22250$
Which after we divide both sides by 0.97 gives:
$\text{s=\$22 938}$
Now that we know the value of s things get a little easier all you have to do is substitute the value of s into the second equation above:
$m=15000+0.2(22938)$
Solving this gives:
$\text{m=\$19 588}$
What all this means is that the total stores overheads including a share of maintenance overheads is $19 588
It also means the total maintenance overheads including the share of stores overheads is $22 938
Now we can reapportion these costs easily as shown below:

Despite all appearances the algebraic is much faster and accurate that the repeated reapportionment method
Wherever possible always use the algebraic method unless otherwise directed by the exam question

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