Abstract
In a manufacturing company, certain departments can be characterized as production departments and others as service departments. Examples of service departments are purchasing, computing services, repair and maintenance, security, food services, and so forth. The costs of such service departments must be allocated to the production departments, which in turn will allocate them to the product. It is known that one can view the cost allocation problem as an absorbing Markov process, with the production departments as the absorbing states and the service departments as the transient states. Using Markov analysis, we will show that this yields additional insight into the underlying concept of reciprocal service department cost allocation by proving that the “full service” department costs can be used to determine the price that should be paid to an external supplier of the same service currently supplied by the service department.
Highlights
The validity of the linear algebra model to solve the reciprocal service department cost allocation problem has been widely recognized since Kaplan’s seminal paper in The Accounting Review in 1973 [1]
It is known that viewing the cost allocation problem as an absorbing Markov process, with the production departments as the absorbing states and the service departments as the transient states, yields additional insight into the underlying concept of reciprocal service department cost allocation
The balancing of the journal entry for the production department cost debits and the service department cost credits will be seen to be a simple consequence of the fact that a Markov process, initially in a transient state, must eventually end in one of the absorbing states
Summary
We will show how this approach makes it transparent that the sum of the final costs allocated to all the production departments will always be equal to the sum of all traceable service department costs In this context, the balancing of the journal entry for the production department cost debits and the service department cost credits will be seen to be a simple consequence of the fact that a Markov process, initially in a transient state, must eventually end in one of the absorbing states. A dollar currently in one of the transient states is absorbed as collected or uncollectible with probabilities that can be determined by an understood algorithm. The same methodology can be used to allocate a portion of each service department cost to the respective production departments based on the absorption probabilities [2] The difference between this model and the accounts receivable model is that there generally are more than two absorbing states as each production department serves as an absorbing state
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