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What factors affect our choice of method to treat overallocated or underallocated manufacturing overhead?

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Not sure if I understood the question correctly, but based on my understanding and assuming this is fixed manufacturing overhead, there normally would be a predetermined over rate that's based on a variable component such as direct labor hours or machine hours. Then, the actual manufacturing OH cost is then applied to the budgeted manufacturing OH based on the predetermined rate to figure whether or not actual cost is over or under applied. Please note that there is a difference between over or under applied rate and over or under allocated rate. Allocation would be a slightly different concept where cost is allocated based on a relevant factor such as usage in the case where different departments in a factory are allocated electricity cost based on their usage.