The cost that is allocated and apportioned to service cost centers is reapportioned to production cost centers on a suitable basis. This process is called reapportionment of overheads.

It is the third step of absorption costing in which we absorb the production overheads into the cost of product.

Before we explain what reapportionment is, let us understand what the terms **production cost center** and **service cost center**.

### Production Cost Center

A production cost center is a location or department in a business where the production takes place. Examples of production cost centers would be assembly, finishing, painting, etc.

### Service Cost Center

A service cost center is a location or department in a business where the production doesnâ€™t take place rather it provides services to production departments. Some examples of production cost centers would be a canteen, maintenance department, stores etc.

**Reapportionment of overheads explained**

In this step, the cost that is allocated and apportioned to service cost centers is reapportioned to production cost centers on a suitable basis. There are three methods of reapportionment depending on whether the service cost centers provide services to each other too. These are:

- Direct Method
- Step-Down Method
- Reciprocal Method

Let us consider each method in detail.

**Direct method for reapportionment of overheads**

In this method, the service cost centers only work for production cost centers. Therefore, the order of reapportionment does not matter. Overheads charged to service cost centers can be reapportioned to production cost centers in either order. Let us take the example of Audi AG, an automobile manufacturing company. The management of Audi has estimated the overheads for two production centers Assembly and Finishing, and two service centers, Canteen and Stores. The accountant has already allocated and apportioned the costs to the respective departments as follows:

**Note: **We only took the number of employees and material requisitions relating to assembly and finishing because we do not need to reapportion the overheads cost of service cost centers between themselves as no service cost center does work for the other.

**Step-down method for reapportionment of overheads**

In this method, the order of reapportionment is relevant because one of the service cost centers does work for the other service cost center along with production cost centers. Thus, the overheads relating to the service cost center that works for the other service cost center as well are first reapportioned between production cost centers and the other service cost center. Afterwards, the overheads of the second service cost center, which now has a share of the first service cost center as well, are reapportioned between the production cost centers.

Let us take the same example as above, but assume the canteen works for the store department as well. Now, first, we need to reapportion the overheads cost of the canteen between assembly, finishing and stores. Then, we will reapportion the overheads cost of the store between assembly and finishing. This is demonstrated below:

**Reciprocal method for reapportionment of overheads**

In this method, both of the service cost centers perform work for each other along with the production cost centers. So, we need to reapportion the overheads cost of service cost centers to each other and production cost centers turn by turn. The order of reapportionment does not matter. There are two ways in which the reciprocal method can be carried out.

- Repeated Distribution Technique
- Using Simultaneous Equations

Both methods are simple, and you can choose the one that suits you. Let us consider both methods turn by turn.

## Repeated Distribution

In this method, the cost of each service cost center is apportioned between the production cost centers and each service cost center one by one. This process is carried on until all of the overheads of both service cost centers are apportioned to production cost centers.

Let us take the same example as above but assume both service cost centers work for each other too.

The reapportionment can be carried out as follows:

## Simultaneous Equations

In this method, simultaneous equations are drawn up and solved for the reapportionment of service cost center overheads. Taking the same example as above, we can draw simultaneous equations as follows:

It is often helpful to find percentages of work done by each service cost center for others as follows:

Since the Store Department has $30,000 already apportioned to it and 50% of employees are in stores so we can say:

Stores = $30,000 + 50% C *(C= Short for Canteen)*

In the same way, Canteen has $20,000 already allocated and apportioned to it and the number of material requisitions from the canteen is 17% of the total requisitions, so:

Canteen = $20,000 + 17% S *(S = Short for Stores)*

Now we can solve these simultaneous to reapportion the overheads cost of service cost centers as follows:

S = $30,000 + 50%C —- (i) |

C = $20,000 + 17%S —- (ii) |

Substituting the value of C in equation (i) |

S = $30,000 +50% ($20,000 + 17%S) |

S = $30,000 +$10,000 +0.085S) |

S – 0.085S = $40,000 |

0.915S = $40,000 |

S = $40,000 / 0.915 |

S = $43,715.85 |

Substituting the Value of S in equation (ii) |

C = $20,000 + 17% ($43,715.85) |

C = $20,000 + $7,431.69 |

C = $27,431.69 |

Since the Assembly department has $12,000 already apportioned to it and constitutes 30% of employees and 33% of material requisitions, So: |

Assembly = $12,000 +30% C +33% S |

Putting Values of C and S in the above equation, we get |

Assembly = $12,000 +30% ($27,431.69) +33% ($43,715.85) |

Assembly = $34,656 |

Similarly, the Finishing department has $18,000 already apportioned to it and constitutes 20% of employees and 50% of material requisitions, So: |

Finishing = $18,000 +20% C +50% S |

Putting Values of C and S in the above equation, we get |

Finishing = $18,000 +20% ($27,431.69) +50% ($43,715.85) |

Finishing = $45,344 |

Therefore, the total overheads reapportioned to assembly and finishing are:

Assembly | Finishing | Total | |

$ | $ | $ | |

Total Overheads Allocated, Apportioned and Reapportioned | 34,656 | 45,344 | 80,000 |