Is this a duplication of costs since they are billed indirectly and then billed again directly to a specific project? What is the best way to show these expenses?
IF the same expense / cost is billed or charged to a project in part or in its entirety and then that same expense / cost is included in an indirect cost allocation and billed to one or more projects, this would appear to be a double billing or as you have put it a “duplication of costs.”
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Proper charging of expenses / costs to projects is improved by consistently applying consistent cost accounting policies. More specifically, it may be very helpful in reaching this goal of consistency for the organization to have established cost accounting policies and practices that define what costs / expenses are allocated to projects directly and what costs /expenses are allocated to projects indirectly. Your question does not indicate what if any regulatory accounting rules might be applicable. If regulation is applicable, it should be followed. Even when not invoked by your situation, the cost accounting related rules of the Federal Acquisition Regulation (FAR) and the Cost Accounting Standards Board (CAS) may provide a solid basis upon which to build such consistent cost accounting policy and practice. With respect to charging costs direct or indirect, costs incurred for the same purpose, in like circumstances, must be either direct costs only or indirect costs only with respect to projects. (e.g., see CAS 48 CFR 9904.402 and FAR 31.202).