# Equivalent units of production

Written by True Tamplin, BSc, CEPF®
Updated on June 22, 2021

## Definition of Equivalent units of production

A department’s output is always stated in terms of equivalent units of production. Equivalent units can be defined as the number of units that could have produced given the total amount of manufacturing effort expended for the period under consideration.

## Explanation

The problem of work-in-progress in process industries is very important. In continuous processes, there must be some work-in-progress at the beginning and at the end of a period and the degree of completion of closing work-in-progress. Work-in-Progress can be valued on the basis of actual cost, i.e., an attempt may be made to find out how much materials have been used on the incomplete units and how much amount of labor and expenses have been spent on them.
But the problem of work-in-progress can also be solved calculating what is known as ‘Equivalent Unit of Production’ or ‘Effective Production’. Equivalent or effective units of production represent the production of a process expressed in terms of completed units.

## Formula to Compute Equivalent Units of Production

Equivalent Units of Production = Actual Number of units in process of manufacture X Percentage of Work Completed
The closing stock of 200 units in a process, 60% complete in respect of material, wages and overhead, is equivalent to 120 units (i.e., 200 x 60%) which are 100% complete.

### Why we compute the equivalent units of production?

The answer is very simple because completed units alone will not accurately measure output in a
department since part of the department’s efforts during a period have been expended on units that are only partially complete. To accurately measure output, these partially completed units must also be considered in the output computation. This is done by mathematically converting the partially completed units into fully completed units and then adjusting the output figure accordingly.

### Computation of equivalent units of production

The computation of units of equivalent production shall be made with the help of the following steps:
(i). At the first place, the equivalent production of opening work-in-progress will be ascertained by taking into account the degree of work to be done on it during the current period. For example, if the opening work-in-progress is 500 units, 40% complete in all respects, then the degree of work required to be performed on it during the current period is 60%. As such, the equivalent production for opening work-in-progress during the period will be 300 units (i.e. 500 x60%).
(ii). At the second place, the number of units introduced and completed during the current period will be computed. It can be done by deducting the closing work-in-progress from the introduced in the process during the current period.
(iii). At the third place, the equivalent units of production for the closing work-in-progress will be ascertained by taking into account the number of units of closing Work in progress and the degree of work completed on them. If the closing work in progress is 800 units, 70% complete in all respect, the equivalent units of production of closing work-in-progress will be 560 units (i.e., 800 x 70%).
(iv). At the end, the equivalent units of production calculated under the above mentioned three steps will be aggregated to ascertain total output in terms of equivalent units or equivalent production.
A unit would not be transferred out unless it is completed. Thus every transferred out unit is an equivalent unit. Units remaining in, ending work in process inventory, however, are not complete. So to convert the work in process inventory into equivalent units you must have to keep the percentage of completion in the calculation.

### Example

Assume that department A of a company had the following data for January 2019.

Required:
What is the output in January for department A?
Solution:
The solution is to calculate the equivalent units of production:

## Evaluation of Equivalent Units of Production

The evaluation of equivalent production is usually made by preparing the following three statements.
(i). Statement of Equivalent Production: This statement shows the number of equivalent completed units.
(ii). Statement of Cost per Equivalent Unit: This statement is prepared to compute the element-wise cost per equivalent unit. For this purpose, the cost of each element (i.e., material, labor and overhead) is divided by the equivalent units of production of that element.
(iii). Statement showing the Apportionment of Costs or Statement of Evaluation: The statement shows the apportionment of the total process cost to the finished output and work-in-progress of the process.