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This answer results partially from allocating the Systems Department's costs first. The question says to begin with the Maintenance Department. However, another mistake is allocating the Maintenance Department's costs to the Machining Department using the budgeted usage for the Systems Department, instead of the budgeted usage for the Maintenance Department.
This is the total overhead for the Machining Department to allocate to its products using the direct method. The question says to use the step-down method, beginning with the Systems Department's costs.
In the step-down method, the costs of one of the service departments are allocated first, and those costs are allocated to the other service department(s) and the production departments. When the second service department’s costs are allocated, the second service department's costs to be allocated include its own costs incurred plus the costs allocated to it from the first service department. Those costs are allocated to the other service departments except for the first service department and to the production departments. Any service department whose costs have already been allocated does not receive an allocation from any other service department. This answer results from allocating 45% of the System's Department's budgeted overhead costs of $95,000, or $42,750, to the Machining Department. This is incorrect for two reasons. One, the Systems Department's costs to be allocated should include not only its own budgeted overhead of $95,000 but also the costs allocated to it from Maintenance, which are $36,000, for a total of $131,000 to be allocated by the Systems Department. Second, remember that in allocating the Systems costs, we do not allocate any cost to the Maintenance Department, even though Maintenance is budgeted to use 5% of the Systems Department's services. That leaves only the Machining and the Fabrication departments to receive the Systems Department’s cost allocations; and the amounts allocated to those two departments need to total to 100%, not 95%, of the total Systems costs of $131,000. The Machining Department is budgeted to receive 45% of the Systems Department’s services, and the Fabrication Department is budgeted to receive 50%. But instead of multiplying the total to be allocated ($131,000) by 45% to get the amount of Systems cost to allocate to Machining, we need to remember that the users’ usage totals only 95% because nothing is to be allocated to Maintenance. Therefore, the factor to use in allocating the Systems Department’s costs to Machining is .45/.95, which equals .473684. The Systems Department’s cost allocated to Machining will be $131,000 × .473684, which equals $62,053.
In the step-down method, the costs of one of the service departments are allocated first, and those costs are allocated to the other service department(s) and the production departments. When the second service department’s costs are allocated, the second service department's costs to be allocated include its own costs incurred plus the costs allocated to it from the first service department. Those costs are allocated to the other service departments except for the first service department and to the production departments. Any service department whose costs have already been allocated does not receive an allocation from any other service department. Beginning with the Maintenance Department, the first amount to be allocated is $360,000 in budgeted overhead for Maintenance. That is allocated 10% or $36,000 to Systems, the other service department; 50% or $180,000 to Machining, and 40% or $144,000 to Fabrication. The next department’s costs to be allocated is Systems. The Systems costs to be allocated include the Systems Department’s budgeted overhead of $95,000 plus the amount allocated to Systems from Maintenance, which is $36,000, for a total of $131,000 to be allocated. In allocating the Systems costs, we do not allocate any cost to the Maintenance Department, which is budgeted to use 5% of the Systems Department’s services. That leaves the Machining and the Fabrication departments to receive the Systems Department’s cost allocations. The Machining Department is budgeted to receive 45% of the Systems Department’s services, and the Fabrication Department is budgeted to receive 50%. But instead of multiplying the total to be allocated ($131,000) by 45% to get the amount of Systems cost to allocate to Machining, we need to remember that the users’ usage totals only 95% because nothing is to be allocated to Maintenance. Therefore, the factor to use in allocating the Systems Department’s costs to Machining is .45/.95, which equals .473684. The Systems Department’s cost allocated to Machining will be $131,000 × .473684, which equals $62,053. In addition to the Systems Department’s allocated costs of $62,053, the Machining Department will be allocated the $180,000 from Maintenance, and it will have budgeted overhead in its own department of $200,000. Thus, the total overhead for the Machining Department to allocate to its products is $200,000 of its own overhead + $180,000 from Maintenance + $62,053 from Systems, which equals $442,053.