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

Repeated Distribution Method

• 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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