When units are equal units sold?

In cost accounting, equivalent units are the units in production multiplied by the percentage of those units that are complete (100 percent) or those that are in process. That covers everything.

If a unit is completed and transferred out, it’s 100 percent complete. Now, that may seem obvious, but it’s a point that gets lost when accountants start this analysis. Your approach to complex analysis should be to account for the easy stuff first. The completed and transferred out units are easier to address than work in process.

Say you’ve mixed enough sugar to make 600,000 units of candy. Assume that ending work in process is 25 percent complete for all components of production (material, labor, and overhead). The table below shows the computation of equivalent units.

Equivalent Units of ProductionUnitsCompleteEquivalent UnitsCompleted and transferred600,000100 percent600,000Work in process, ending600,00025 percent150,000Equivalent units750,000

Although 25 percent of the units are unfinished, in “equivalent unit talk” you can treat them as 150,000 completed units. Add them to the really completed units to get 750,000 units, which represents the number of equivalent whole units you have produced. It’s a lot easier to talk about a whole unit than some whole units and some partially completed units.

The next step is to compute the cost per equivalent unit. Take the total costs of $101,800, and divide by the number of units. Remember that the total costs are the sum of the beginning inventory cost ($48,000) and the costs added during production ($53,800):

Cost per equivalent unit = total costs ÷ number of units
Cost per equivalent unit = $101,800 ÷ 750,000
Cost per equivalent unit = $0.1357

The calculation goes to four decimal places, because when you’re making candy that sells for 20 cents per unit, and you’re producing hundreds of thousands of units, every tiny fraction of a dollar counts.

Now assign the cost per equivalent unit to the completed work and the WIP. The table below shows the calculation (costs are rounded).

Assignment of CostsUnitsCost/UnitCost AssignedCompleted and transferred600,000$0.1357$81,440Work in process, ending150,000$0.1357$20,360Equivalent units$101,800

You’ve assigned costs to both completed work and WIP. Congratulations! Maybe you should eat a pound or two of candy to celebrate.

For example, if we bring 1,000 units to a 40 % state of completion, this is equivalent to 400 units (1,000 x 40%) that are 100%  complete. Accountants base this concept on the supposition that a company must incur approximately the same amount of costs to bring 1,000 units to a 40% level of completion as it would to complete 400 units.

Here is a diagram of the concept of equivalent units. As you examine the diagram, think of the amount of water in the glasses as costs that the company has already incurred.

Now, watch the video for another example.

Units in Beg. Work in ProcessUnits Completed and Transferred+ Units Started this period+ Units in End. Work in Process= Total Units= Total Units

The total units in each column must agree with one another.  This formula explains how many units we had to work with (including units in beginning work in process + units started this period) and what happened to those units (units completed or units remain in work in process inventory since there are not complete).

Under the weighted average method, equivalent units are calculated based on 2 things:  units completed and transferred out and units in ending work in process inventory.

Units completed and transferred are finished units and will always be 100% complete for equivalent unit calculations for direct materials, direct labor and overhead.  For units in ending work in process, we would take the units unfinished x a percent complete.  The percent complete can be different for direct materials, direct labor or overhead.

Example – Jax Company

Assume that Jax Company manufactures and sells a chemical product used to clean kitchen counters and sinks. The company processes the product in two departments. Department A crushes powders and blends the basic materials. Department B packages the product and transfers it to finished goods.  We will look at equivalent units for Department B.  The June production data for Department B is:

 Department BBeginning work in process-0-Units started this period11,000Units completed and transferred9,000Ending work in process units2,000Direct materials$ 1,100Direct labor$ 2,880Applied overhead$ 8,880

The physical flow of units shows:

Units in Beg. WIP-0-Units Completed and Transferred9,000Units Started this period11,000Units in End. WIP2,000Total Units11,000 =Total Units11,000

The beginning step in computing Department B’s equivalent units for Jax Company is determining the stage of completion of the 2,000 unfinished units (remember units completed and transferred are always 100% complete).  In Department B, the ending units may be in different stages of completion regarding the materials, labor, and overhead costs. Assume that Department B adds all materials at the beginning of the production process. Then ending inventory would be 100% complete as to materials since we received all materials at the beginning of the process.

Accountants often assume that units are at the same stage of completion for both labor and overhead. Accountants call the combined labor and overhead costs conversion costs. Conversion costs are those costs incurred to convert raw materials into the final product (meaning, direct labor and overhead).

Let us assume that, on average, the 2,000 units in ending inventory are 40% complete as to conversion costs. This means that Department B transferred out 9,000 units fully completed and brought 2,000 units to a 40% completion state. Department B now has an equivalent of 800 fully completed units remaining in inventory (800 = 2,000 X 40 per cent).

The equivalent units for materials, labor and overhead would be calculated as:

MaterialsConversion CostsUnits Completed and Transferred9,0009,000(9,000 x 100% complete)Units in Ending WIP   Materials   (2,000 x 100% complete)2,000   Conversion Cost (2,000 x 40% complete)800Total Equivalent Units11,0009,800

Total equivalent units for each cost element (materials, conversion cost) is calculated as:

Equivalent units = Units completed + (Units in ending inventory X percent complete)

The key to equivalent units is determining the percent complete, especially for materials can be confusing.  Common terms you will see when determine ending work in process percent complete:

What is equivalent units in accounting?

What are equivalent units in process costing?

What are examples of equivalent units of production?

For which costing method is the concept of equivalent units relevant?