### Cambrige AS and A Level Accounting Notes (9706)/ ZIMSEC  Advanced Accounting Level Notes: Reapportionment of service costs where there is interwork

• 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

 Overheads Sewing Finishing Stores Maintenance Already allocated 70 000 30 000 20 000 15 000 Recharge stores 10 000 6 000 (20 000) 4 000 ----- 19 000 Recharge maintenance 8 550 7 600 2 850 (19 000) 2 850 ---- Recharge stores 1 425 855 (2 850) 570 ---- 570 Recharge maintenance 257 228 85 (570) 85 --- Recharge stores 43 25 (85) 17 ---- 17 Recharge stores 8 7 2 (17) 2 --- Recharge stores 1 1 (2) 90 284 44 716 ---- ----
• 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 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 things get a little easier all you have to do is substitute the value of 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:
 Overheads Sewing Finishing Stores Maintenance Already Allocated 70 000 30 000 20 000 15 000 Recharge stores 11 469 6 881 (22938) 4 588 Recharge maintenance 8 815 7 835 2 938 (19 588) Totals 90 284 44 716 ---- ----
• 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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