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This answer results from calculating the cost allocations by dividing each individual department's usage of the allocation base by the total usage by all the departments (9,300 computer usage hours or 11,600 square feet occupied). The proration of the costs should be based not on the total usage by all departments but on the total usage by only the departments to which the costs are being allocated.
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This answer results from beginning the allocations with the Facilities Department and also from not allocating any costs of the Facilities Department to the Systems Department, as would be appropriate if the allocation began with Facilities. But the question says to begin with the Systems Department, not with the Facilities Department.
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, those costs are allocated to any service department(s) other than the first service department allocated 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 Systems Department, its overhead cost of $200,000 is allocated to the Facilities, Machining, Assembly and Finishing departments on the basis of their computer usage hours. The usage of those four departments totals 900 + 3,600 + 1,800 + 2,700 = 9,000 hours. The usage of the Facilities Department is 900 hours, or 10% of that. Thus, the Facilities Department is allocated 10% of the Systems Department’s overhead cost of $200,000, or $20,000. The Facilities Department has overhead cost to allocate of $100,000 plus the $20,000 allocated to it from Systems, for a total of $120,000. Facilities costs are allocated on the basis of square feet occupied by the Machining, Assembly and Finishing departments. The square feet occupied by those three departments totals 2,000 + 3,000 + 5,000 = 10,000 square feet. The square feet occupied by the Machining Department is 2,000 square feet, or 20% of that. Thus, the Machining Department is allocated 20% of the Facilities Department’s overhead cost of $120,000, or $24,000.