Answer
A traceable cost of a segment is a cost that is incurred because of the existence of a particular business segment, and that would be eliminated if the segment were eliminated.
A common cost is a cost that supports more than one segment, but is not traceable in whole or in part to any one of the segments. If the departments of a company are treated as segments, then examples of the traceable costs of a department would include the salary of the department's supervisor, depreciation of machines used exclusively by the department, and the costs of supplies used by the department.
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