## Equivalent Unit Calculations

### Learning Outcomes

• Calculate equivalent units of production and cost per equivalent unit using the weighted average and FIFO methods

So the Ultimate Planner goes through three departments on its way to finished goods inventory. In each department raw materials, labor and overhead are being added to the planners. In order to calculate a product unit cost, those costs need to be accumulated, as the planner isn’t finished. Each department has an ending inventory of unfinished planners. How can we figure out the costs at each stage of production? The easiest way is to figure out what percentage of the planner is completed, as to the work in that department. We call this the equivalent units of production method of costing:

equivalent units = number of partially completed units × Percentage completed

At the end of process 1, our planners have their paper and ink ready to be printed. Let’s assume we figure the ending WIP inventory to be 35% complete as to the process. If we have 1000 units in the ending WIP inventory after process 1, this would equal 350, using the formula for equivalent units.  We could then add these equivalent units to the ending WIP inventory for process 1. Any units that have been moved into process 2, will be subtracted from the WIP inventory for process 1.

There are two ways we can calculate the equivalent units of production for a department or process: weighted-average or FIFO (first in, first out).

## Weighted Average

In this method we use the following equation:

$\begin{array}{rr}&\text{Units transferred to the next department or to finished goods}\\+&\text{Equivalent units in ending work in process inventory}\\&\hline\\&\text{Equivalent units of production}\end{array}$

One thing to keep in mind when using the weighted average method, we don’t need to compute the equivalent units for the ones transferred out. Those are considered 100% complete for the work done in that department, otherwise they wouldn’t be moving forward to the next process.

### Example

In the current period, we transferred 500 units to process 2, and have 350 equivalent units in our WIP inventory. So our equivalent units of production for the period would be 850 units.  Essentially saying, that process 1 completed 850 units to completion of process 1 in this period.

### Example

700 units were transferred from process 1 to process 2. We also have 1000 partially completed units that are 50% complete.

We would have 500 equivalent units in our WIP inventory. (1000 × 50%) + 700 units that were transferred out. Our equivalent units of production for the period is 1,200 units (700 + 500).

## FIFO

Equivalent units can also be calculated using the FIFO method. In this method, the units that have been moved to the next process are divided into two parts:

1. The units that were in beginning inventory and completed
2. The units that were both started and finished in the current period.

In this method, both the beginning and ending inventory is converted into equivalent units, so there is a bit more work to do. For those units that were in the beginning inventory, we need to figure out how much work was DONE on them in this period to get them to the point of being transferred to the next process. For those items in the ending inventory, it is the same as the weighted-average method, where we need to calculate how much work has been done to them already.

### Example

We have 500 units in our beginning inventory that needed 50% more done to them yet = 250 units

We also completed 500 units that were started and finished in this period = 500 units

And we have 1000 units that are 25% complete at the end of the period =  250 units

So how many units did we complete during the period? 250 + 500 +250 = 1000 units were completed through process 1 for the period.

In our next section, we will do a comparison and reconciliation of the same number of products through one process with each of the two methods.