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The major difference between allocation and apportionment methods are that allocation is used when the overhead can be directly related to one department and cost center, and apportionment is used when the overhead arises from a number of departments.
Allocation: Overhead Costs which are directly identifiable to a cost center are directly allocated to that cost centre.
Apportionment: Overheads which are not directly identifiable are first charged to general overhead and then those general overheads are apportioned on appropriate bases i.e. area, machine hour etc, then service department apportioned cost are apportioned among production department and finally the production overhead both allocated and apportioned are absorbed using absorbing rate.
Overheads apportionment is a traditional method of absorbing overhead. Activity based costing is a modern method of costing.