# Equivalent Units of Production

Equivalent units of production are used by a manufacturer to express partially completed units of product in terms of finished units.

The objective of using equivalent units is to be able to apportion the costs of production to completed units and partially completed units held in work in process.

## Equivalent Units of Production Formula

Equivalent units are calculated by multiply the number of physical units in work in process by the estimated percentage of completion of the units.

The equivalent units of production formula can be stated as follows:

Equivalent units = Units × Percentage of completion

## How to Calculate Equivalent Units?

As a simple example, suppose a business has 200 units of a product in work in process and they are estimated to be 25% complete. Using the equivalent units of production formula we get:

```Equivalent units of production = Units × Percentage of completion
Equivalent units of production = 200 × 25%
Equivalent units of production = 50
```

What this example shows is that although there are 200 physical units of product in work in process, as they are only 25% complete it is equivalent to having 50 units of finished, fully completed product.

## Estimating the Percentage of Completion

In the example above we simply stated that the estimated percentage of completion was 25%. In practice the percentage of completion needs to be based on each factor of production such as direct materials, direct labor, and manufacturing overheads. For example the work in process units might be 80% complete in terms of direct materials, 65% complete in terms of direct labor, and 35% complete in terms of manufacturing overhead.

If we have 200 units in work in process, then the equivalent units are calculated as follows:

```Materials = 200 x 80% = 160
Labor = 200 x 65% = 130
Overheads = 200 x 35% = 70
```

## Equivalent Units of Production Example

The following example is used to demonstrate how the equivalent units of production are used to allocate production costs between completed and partially completed units.

At the start of an accounting period a business has 2,000 units in beginning work in process. During the accounting period a further 8,000 units are added to the production process and 6,000 units are completed and transferred out, leaving an ending balance of 4,000 units in work in process.

## Physical Units

The table below summarizes the movement of physical units during the accounting period.

Physical units movement
Units
Beginning 2,000
Added 8,000
Completed -6,000
Ending 4,000

During the period costs are incurred in the production process to complete the 2,000 beginning WIP units, to start and complete an additional 4,000 units, giving a total of 6,000 units transferred out of the process, and to partially complete the 4,000 units remaining in work in process, a total of 10,000 units are in production.

Physical units in production
Units
Beginning WIP 2,000
Started and completed 4,000
Ending WIP 4,000
Total 10,000

## Equivalent Units

The next step is to convert the physical units in production shown above (10,000) into equivalent units.

The treatment of the beginning WIP units will depend on which costing method, usually weighted average or FIFO, the business is using.

If the weighted average method is used then the beginning WIP units are treated as started and completed (100%) during the accounting period, (likewise, the costs brought forward in beginning WIP are included in the calculation of the cost per equivalent unit – see below).

If an alternative method such as FIFO is used, then only the percentage of beginning WIP units completed during the accounting period are included, (in this case the costs brought forward in beginning WIP are excluded in the calculation of the cost per equivalent unit). This method is discussed in our equivalent units FIFO method tutorial.

In this example the weighted average cost method is used and the beginning WIP units are treated as being 100% completed during the period.

Obviously the completed units are 100% complete and the equivalent units are the same as the physical units. The ending work in process units however are only partially complete and need to be converted to equivalent units. If we assume that the state of completion of the ending WIP units is material 85%, labor 65%, and overheads 35%, then the equivalent units are calculated as follows:

```Materials = 4,000 x 80% = 3,200
Labor = 4,000 x 65% = 2,600
Overheads = 4,000 x 35% = 1,400
```

The physical units can now be represented as equivalent units for each production factor.

Equivalent units of production
Material Labor Overhead
Beginning WIP 2,000 2,000 2,000
Started and completed 4,000 4,000 4,000
Ending WIP 3,200 2,600 1,400
Total 9,200 8,600 7,400

### Cost per Equivalent Unit Formula

The cost per equivalent unit formula is as follows:

Cost per equivalent unit = Production cost / Equivalent units

As mentioned above, the variables used in the cost per equivalent unit formula depend on which costing method the business is using. In this example we will use the weighted average cost method in which case the two variables used in the formula are defined as follows:

1. Production cost = Beginning (brought forward) WIP costs + Costs added during the period
2. Equivalent units = Beginning WIP units (100%) + Started and completed units (100%) + Ending WIP units (% completed)

Notice that by including the costs brought forward, 100% of the cost of producing the units in beginning WIP are included.

### Cost per Equivalent Unit Calculation

Suppose the production cost data for the manufacturing process shows that the brought forward beginning WIP costs are materials 23,000, labor 5,500, and overhead 1,700, a total of 30,200. During the period the production costs added are materials 69,000, labor 28,900, and overhead 9,400, giving a total of 107,300

The total production costs to allocate are 137,500 comprising, materials 92,000, labor 34,400 and overhead 11,100. The cost per equivalent units for each production factor are calculated as follows:

```Materials = (23,000 + 69,000) / (2,000 + 4,000 + 3,200) = 10.00
Labor = (5,500 + 28,900) / (2,000 + 4,000 + 2,600) = 4.00
Overheads = (1,700 + 9,400) / (2,000 + 4,000 + 1,400) = 1.50
Total = 10.00 + 4.00 + 1.50 = 15.50
```

In the example, the cost per equivalent unit for direct materials is 10.00, cost per equivalent unit for direct labor is 4.00, and the cost per equivalent unit for manufacturing overhead is 1.50. This gives a total cost per equivalent unit of 15.50.

## Allocating the Cost of Production

To allocate the cost of production to completed units and work in process we now simply multiply each equivalent unit by its respective cost per equivalent unit as follows:

### Beginning Work in Process

```Materials = 2,000 x 10.00 = 20,000
Labor = 2,000 x 4.00 = 8,000
Overheads = 2,000 x 1.50 = 3,000
Total = 31,000
```

### Started and completed

```Materials = 4,000 x 10.00 = 40,000
Labor = 4,000 x 4.00 = 16,000
Overheads = 4,000 x 1.50 = 6,000
Total = 62,000
```

### Ending Work in Process

```Materials = 3,200 x 10.00 = 32,000
Labor = 2,600 x 4.00 = 10,400
Overheads = 1,400 x 1.50 = 2,100
Total = 44,500
```

The allocation of production costs is summarized in the table below:

Allocation of production costs
Material Labor Overhead Total
Beginning WIP 20,000 8,000 3,000 31,000
Started and completed 40,000 16,000 6,000 62,000
Completed 60,000 24,000 9,000 93,000
Ending WIP 32,000 10,400 2,100 44,500
Total 92,000 34,400 11,100 137,500

The production costs for the period have now been allocated between the completed units and the partially completed units held in work in process. The production process account can now be completed as follows:

Production process account
Units Costs
Beginning (Actual) 2,000 30,200
Added (Actual) 8,000 107,300
Completed (Allocated) -6,000 -93,000
Ending (Allocated) 4,000 44,500

By using the equivalent units of production weighted average method the business has taken actual production costs of 137,500 and allocated 93,000 to the 6,000 completed units, and 44,500 to the 4,000 partially completed units held in work in process.

Equivalent Units of Production November 6th, 2016

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