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    Reciprocal Method of Cost Accounting with a Matrix Algebra equation

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    Warren Ltd. has two production departments, Building A and Building B, and two service departments, Maintenance
    and Cafeteria. Direct costs for each department and the proportion of service costs used by the various departments
    for the month of June follow:
    Proportion of Services Used by

    Department Direct Costs Maintenance Cafeteria Building A Building B
      Building A $ 505,000
      Building B 315,000
      Maintenance 217,000 â?" 0.2 0.6 0.2
      Cafeteria 165,000 0.7 â?" 0.1 0.2

    Use the reciprocal method to allocate the service costs. (Matrix algebra is not required.) (Note: Due to rounding, the
    cost allocations to the various departments may not add up to the total service department costs being allocated.)

    Cost Allocated To:
    From: Maintenance Cafeteria Building A Building B
    Service Dept 217,000 165,000 0 0

    Set up the equations:
    Total service = Direct costs of the + Cost allocated
    department costs service department to the service
       S1 (Maintenance) = $217,000 + 0.70 S2
       S2 (Cafeteria) = 165,000 + 0.20 S1

    Substituting, the first equation into the second yields,

    S2 = $165,000 + 0.20 ($217,000 + 0.70 S2)
    S2 = $165,000 + $43,400 + 0.14 S2
    .86S2 = $208,400
    S2 = $242,326

    I do not understand how S2 has been determined to be .86, can someone please explain it to me?

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    Solution Summary

    The following posting helps with a problem involving the reciprocal method for cost allocations.