# Equivalent Units FIFO method

Equivalent units FIFO method is 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 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 formula can be stated as follows: ## How to Calculate Equivalent?

As a simple example, suppose a business has 300 units of a product in work in process and they are estimated to be 40% complete. Using the equivalent units of production formula we get:

```Equivalent units of production = Units × Percentage of completion
Equivalent units of production = 300 × 40%
Equivalent units of production = 120
```

What this example shows is that although there are 300 physical units of product in work in process, as they are only 40% complete it is equivalent to having 120 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 40%. 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 50% complete in terms of direct materials, 40% complete in terms of direct labor, and 10% complete in terms of manufacturing overhead.

If we have 300 units in work in process, then the equivalent units are calculated as follows:

```Materials = 300 x 50% = 150
Labor = 300 x 40% = 120
Overheads = 300 x 10% = 30
```

## Equivalent Units FIFO Method Example

The following example is used to demonstrate how the equivalent units FIFO method is 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
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 FIFO Method

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 equivalent units FIFO method is used then only the percentage of beginning WIP units completed during the accounting period and the production costs incurred in completing those units, are included in the calculation of the cost per equivalent unit – see below.

If an alternative weighted average method is used then the beginning WIP units are treated as started and completed (100%) during the accounting period. The treatment using this method is discussed in our equivalent units of production- weighted average method tutorial.

In this example the FIFO method is used and the beginning WIP units are partially completed at the start of the accounting period. The production costs incurred during the accounting period are therefore spent on the uncompleted part of the beginning WIP units.

Obviously the units started and completed during the period are 100% complete and the equivalent units are the same as the physical units. The beginning WIP units are already partially complete at the start of the period and are further completed during the period and need to be converted to equivalent units. Likewise, the ending work in process units are only partially complete at the end of the period and again, need to be converted to equivalent units.

If we assume that the state of completion of the beginning WIP units is material 90%, labor 55%, and overheads 30%, and 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:

```Beginning WIP
Materials = 2,000 x (100% - 90%) = 200
Labor = 2,000 x (100% - 55%) = 900
Overheads = 2,000 x (100% - 30%) = 1,400

Notice that the production costs are spent on the uncompleted part of the beginning WIP.

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

The production costs are spent on the completed part of the ending WIP.
```

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

Equivalent units FIFO method
Beginning WIP 200 900 1,400
Started and completed 4,000 4,000 4,000
Ending WIP 3,200 2,600 1,400
Total 7,400 7,500 6,800

### 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 equivalent units FIFO method in which case the two variables used in the formula are defined as follows:

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

### 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. Using the formula above, the cost per equivalent units for each production factor are calculated as follows:

```Materials = 69,000 / (200 + 4,000 + 3,200) = 9.324
Labor = 28,900 / (900 + 4,000 + 2,600) = 3.853
Overheads = 9,400 / (1,400 + 4,000 + 1,400) = 1.382
Total = 9.324 + 3.853 + 1.382 = 14.560
```

In the example, the cost per equivalent unit for direct materials is 9.324, cost per equivalent unit for direct labor is 3.853, and the cost per equivalent unit for manufacturing overhead is 1.382. This gives a total cost per equivalent unit of 14.560.

## 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 = 200 x 9.324 = 1,865
Labor = 900 x 3,583 = 3,468
Overheads = 1,400 x 1.382 = 1,935
Total = 7,268
```

### Started and completed

```Materials = 4,000 x 9.324 = 37,297
Labor = 4,000 x 3,583 = 15,413
Overheads = 4,000 x 1.382 = 5,529
Total = 58,240```

### Ending Work in Process

```Materials = 3,200 x 9.324 = 29,838
Labor = 2,600 x 3,583 = 10,019
Overheads = 1,400 x 1.382 = 1,935
Total = 11,100```

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

Allocation of production costs
Beginning WIP (Actual) 23,000 5,500 1,700 30,200
Beginning WIP completion 1,865 3,468 1,935 7,268
Started and completed 37,297 15,413 5,529 58,240
Completed 62,162 24,381 9,165 95,708
Ending WIP 29,838 10,019 1,935 41,792
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