## Equivalent Units

### Learning Outcomes

• Understand and calculate equivalent units of production

The formula for equivalent units is:

Number of actual units in process * % complete

In other words, a unit that is 25% done is the equivalent of ¼ of a completed unit.

Let’s put this into context using a plywood mill. In this example, direct materials (logs) are 100% complete because they are added at the beginning of the process. Let’s assume for the sake of simplicity that it takes about 50 days to process logs into sheets of plywood that are then ready to move on to the finishing department where they are sanded and the edges are trimmed. The mill starts up the machines at the beginning of the month, putting in enough logs to make 1,000 sheets of plywood. At the end of the month, the process is about 60% complete.

Therefore, in terms of direct materials, the 1,000 sheets of plywood are 100% complete because all the logs came in at the beginning of the process.

In terms of conversion costs, however, the 1,000 sheets of plywood are only 60% complete, so they are the equivalent of 600 completed sheets in terms of accumulating costs.

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Let’s now look at a slightly more involved example.

Dad’s Perfect Pies actually only makes pie crusts. In January, the company put into production enough raw materials (butter and flour) to make 3,000 crusts in four batches, as follows:

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The first three batches were finished and transferred over to the baking department.

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Units transferred in, completed, and then transferred out are 100% complete, and the Equivalent Units and Actual Units will always be the same for those items.

The last batch was started on the 28th and was only halfway done at the end of the month; therefore, it stayed in the mixing department as work-in-process:

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Notice that since the materials are added first, those 750 pie shells are 100% complete as to direct materials and so the equivalent units are 750, but for conversion costs, the pie shells are only halfway done, so we convert them from 750 half-units to 375 equivalent whole units in order to allocate costs.

Here is another way to look at the same data:

Physical Units Material EUs Conversion EUs
Units accounted for:
Completed and transferred out                 2,250                 2,250                 2,250
Ending work-in-process                     750                     750                     375
Equivalent Units of Production                 3,000                 3,000                 2,625

The formula is simple, but the application can be a bit confusing. The trick is to make sure you completely understand how to calculate Equivalent Units and to take the allocation of costs base on EUs step-by-step, which is what we will do in the next section.

Here is a brief video explanation of this concept:

There is an exception to the basic concept of EUs as # of physical units times % complete, but we’ll address that when we get to the FIFO production cost report.

Before we apply the concept of equivalent units to process costing, check your understanding of how equivalent units are calculated.