Equivalent units of production is a term applied to the work-in-process inventory at the end of an accounting period. It is the number of completed units of an item that a company could theoretically have produced, given the amount of direct materials, direct labor, and manufacturing overhead costs incurred during that period for the items not yet completed. In short, if 100 units are in process but you have only expended 40% of the processing costs on them, then you are considered to have 40 equivalent units of production. Equivalent units is a cost accounting concept that is used in process costing for cost calculations. It has no relevance from an operational perspective, nor is it useful for any other type of cost derivation other than process costing. Equivalent units of production are usually stated separately for direct materials and all other manufacturing expenses, because direct materials are typically added at the beginning of the production process, while all other costs are incurred as the materials gradually work their way through the production process. Thus, the equivalent units for direct materials are generally higher than for other manufacturing expenses. When assigning a cost to equivalent units of production, you typically assign either the weighted average cost of the beginning inventory plus new purchases to the direct materials, or the cost of the oldest inventory in stock (known as the first in, first out, or FIFO, method). The simpler of the two methods is the weighted average method. The FIFO method is more accurate, but the additional calculations do not represent a good cost-benefit trade off. Only consider using the FIFO method when costs vary substantially from period to period, so that management can see the trends in costs. Example of Equivalent Units of ProductionABC International has a manufacturing line that produces large amounts of green widgets. At the end of the most recent accounting period, ABC had 1,000 green widgets still under construction. The manufacturing process for a green widget requires that all materials be sent to the shop floor at the start of the process, and then a variety of processing steps are added before the widgets are considered complete. At the end of the period, ABC had incurred 35% of the labor and manufacturing overhead costs required to complete the 1,000 green widgets. Consequently, there were 1,000 equivalent units for materials and 350 equivalent units for direct labor and manufacturing overhead.
Knowing how to calculate equivalent units of production is an important tool for those in the business and accounting world. When thinking about how goods are manufactured and sent in a finished form to their destination, there are a lot of steps. There are costs involved at each step, from starting production to mid-production to finished production. Tip
Knowing how to calculate equivalent units of production is an important tool in the business and accounting world. There are two ways to calculate this metric, known as the weighted average method or the first-in, first-out method. Accountants use the term equivalent units to explain how costs are segmented between items that are still in production versus items that are in completed form. Many items are in continuous production, so without some way to calculate equivalent units, it would be difficult to determine how much money was tied up in production costs. Incomplete work must be accounted for on a regular basis so that a value can be placed on the incomplete work. There is a simple formula that is used to calculate the equivalent units of production for those partially completed units. This formula not only applies to materials that are in continuous production, but also to labor costs and overhead costs. Let’s say a parts maker is supposed to make 1,000 parts. At the end of the first quarter, there are 500 completed parts and 300 parts that are still in process. The parts maker’s best estimate is that these additional 300 parts are 50 percent completed. These parts are only half done, so they can’t be counted as finished parts, but the costs involved in making them need to be accounted for. If a report was created, it would indicate that there are 1,150 equivalent units of production. Here’s the formula: The number of partially completed units x percentage of completion = equivalent units of production Plugging in the information that you have from the parts maker, there are 300 partially completed units. These 300 units are 50 percent completed. 300 x .5 = equivalent units of production equivalent units of production = 150 These equivalent units are added to the 500 parts that are already done, and the total units of production come to: 500 + 150 = 650 equivalent units of production The weighted average method to calculate equivalent units of production combines units and costs from the current period with units and costs from the prior period. The calculation is different for a weighted average. Here is the weighted average formula: Total equivalent units for a cost component = A + B × C WhereA = units transferred out to the next department/finished goodsB = units in closing work in process C = percentage of completion with respect to the relevant cost component Using the formula given in the first section (Number of partially completed units × percentage of completion = equivalent units), the equivalent units of production are transferred to the next department of finished goods plus the equivalent units in the department's ending work-in-process inventory. Total equivalent units = 650 equivalent units of production + 300 + .5 Total equivalent units = 800 Note that, in the weighted average method, beginning work-in-process inventory is ignored. When you use weighted averages, all work accomplished in prior periods is not factored into the equations. The second method of calculating equivalent units of production uses a FIFO method or First-in First-out. Businesses will first sell the finished inventory that they first receive, followed by any inventory they receive later, hence first in, first out. Use the following equation for FIFO: Equivalent Units of Production = equivalent units to complete beginning inventory + units started and completed during the period + equivalent units in ending work in process inventory. Equivalent units to complete beginning inventory = units in beginning inventory × (100 percent − percentage completion of beginning inventory). The entire equation can be further simplified to: Equivalent units of production = units transferred out + equivalent units in ending work in process inventory − equivalent units in beginning inventory. Calculate the units of production from both materials and conversion. Using FIFO, you'll have two percentages to determine for beginning and ending inventory. Equivalent units under FIFO method are calculated using more variables than the previous example: Equivalent units for each cost component = (100% − A) × B + C + D × E Where, E = units in closing work in process Here’s a walkthrough of the formula using our parts example if there are 1,000 parts in beginning production during the month of March. During that accounting period (March), let’s say that an additional 4,000 parts are added to production. During March, 3,000 parts are completed and moved out of production. Let’s say there were 2,000 parts completed at the end of the last accounting period and that the parts- in-process are 30 percent done. This leaves: A = 2,000B = 1,000C = 4,000 D = 30% 1,000 (beginning production)+ 4,000 (added to production) – 3,000 (parts completed) = 2,000 parts in production. E = 2,000 To use the FIFO method, only the percentage of beginning parts completed during the accounting period is used, along with the production costs incurred in completing those units. You can use the same method for calculating the overhead costs and materials if you know the percentage of completion of each pricing factor. Another acceptable method for determining unit cost under process costing is the first-in, first-out (FIFO) cost method. Under the FIFO method, we assume any units that were not completed last period (beginning work in process) are finished before anything else is started. The following table shows the differences between the weighted average method and the FIFO cost method:
We will look at each item individually as we discuss the steps of process costing. Under either method, weighted average or FIFO, process costing consists of 5 steps:
Physical Flow of Units The physical flow of units is as follows under the weighted average method:
This is altered just slightly under the FIFO method as we must separate the items in units completed into Units Completed from beginning work in process and Units started and completed this period since under FIFO, we must finish anything from beginning work in process before we start something new. Under the FIFO, we the physical flow of units would be documented as:
Just as in the weighted average method, the 2 Total Units figures must agree! Equivalent Units of Production Under the FIFO method, we will calculate equivalent units for 3 things: Units completed from beginning work in process, units started and completed this period and units remaining in ending work in process. This video will discuss the differences between the Weighted Average and FIFO methods for equivalent units (if you are comfortable with the weighted average method, skip to minute 4:06 to begin the discussion on the FIFO method).  A YouTube element has been excluded from this version of the text. You can view it online here: http://pb.libretexts.org/ma/?p=78 Equivalent units for the period will be calculated as follows under FIFO (keep in mind, you may have different percent complete for materials, labor and overhead):
To illustrate the computation of equivalent units under the FIFO method, assume the following facts (for simplicity we are using just one percent complete for materials, labor and overhead):
The physical flow of units would be (calculate units started and completed as units started 10,000 – units in ending work in process 5,000):
The equivalent production for the period would be:
Cost per Equivalent Unit Under the weighted average method, we use beginning work in process costs AND costs added this period. Under the FIFO method, we will only use the costs added this period. This video will explain the differences between the two approaches. A YouTube element has been excluded from this version of the text. You can view it online here: http://pb.libretexts.org/ma/?p=78 The formula we will use for calculating cost per equivalent unit under the FIFO Method is:
Assign Costs When we assign costs to units completed and transferred and units remaining in ending work in process under the FIFO method, we need the following items:
This video will provide a demonstration of cost assignment under the FIFO method. A YouTube element has been excluded from this version of the text. You can view it online here: http://pb.libretexts.org/ma/?p=78 Reconcile Costs Finally, something is the same under FIFO and Weighted Average. We want to make sure that we have assigned all the costs from beginning work in process and costs incurred or added this period to units completed and transferred and ending work in process inventory. First, we need to know our total costs for the period (or total costs to account for) by adding beginning work in process costs to the costs incurred or added this period. Then, we compare the total to the cost assignment in step 4 for units completed and transferred and ending work in process to get total units accounted for. Both totals should agree. The cost reconciliation would be:
In the next page, we will do a demonstration problem of the FIFO method for process costing.
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Under the first-in, first-out method, the cost of equivalent units of production is calculated by
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