Equivalent Units of Production

Equivalent Units of Production:

Definition and Explanation of Equivalent Units of Production:

After materials, labor and overhead costs have been accumulated in a department, the department's output must be determined so that unit cost can be computed. A department usually has some partially completed units in its ending inventory. It does not seem reasonable to count these partially completed units as equivalent to fully completed units when counting the department's output. These partially converted units are mathematically converted into an equivalent number of fully completed units. In process costing this is done by using the following formula:

Equivalent Units = Number of partially Completed Units × Percentage of Completion

Equivalent units of production for a period can be calculated in two different ways

1. Weighted Average method
2. First in First Out (FIFO) method

Equivalent Units―Weighted Average Method:

Weighted Average method blends together units and costs from the current period with units and costs from the prior period. In a weighted average method the equivalent units of production for a department are the number of units transferred to the next department of finished goods plus the equivalent units in the department's ending work in process inventory.

Example:

Following is the data from Shaping and Milling department, one of the departments at Norton Company

Shaping and Milling Department	Percent Complete
	Units	Materials	Conversion
Work in process, May 1 Units started in production during May Units completed in May and transferred to the next department Work in Process, May31	200 5,000 4,800 400	55% 100%* 40%	30% 100%* 25%

*It is always assumed that units transferred out of a department are 100% complete with respect to the processing done in that department.

Note that the May1 beginning Work in Process is 55% complete with respect to materials costs, and 30% complete with respect to conversion costs. This means that 55% of the materials costs required to complete the units in the department has already been incurred. Likewise, 30% of the conversion cost required to complete the units has already been incurred.

Since Norton's work in process inventories are at different stages of completion in terms of amounts of materials cost and conversion cost that have been added in the department, two equivalent unit figure must be completed. The equivalent units computations are shown below.

Shaping and Milling Department	Materials	Conversion
Units transferred to the next department Work in Process, May 31 400 units × 40% 400 units × 25% Equivalent units of production	4,800    160    --------  4,960   =====	4,800   100   -------- 4,900   =====

Note from above computations that units in the beginning work in process inventory are ignored. The weighted average method is concerned only with the fact that there are 4,900 equivalent units for conversion cost in ending inventories and in units transferred to the next department―the method is not concerned with the additional fact that some of this work was accomplished in the prior periods. This is a key point in the weighted average method that is easy to overlook

Equivalent Units―First-in-First-Out (FIFO) Method:

The computation of equivalent units under FIFO method differs from weighted average method in two ways. First the units transferred out figure is divided into two parts. One part consists of the units from beginning inventory that were completed and transferred out, and the other part consists of the units that were both started and completed during the current period. Second full consideration is given to the amount of work expended during the current period on units in the beginning work in process inventory as well as units in the ending inventory. Thus, under the FIFO method, it is necessary to convert both beginning and ending inventories to an equivalent unit basis. For the beginning inventory, the equivalent units represent the work done to complete the units; for the ending inventory, the equivalent units represent the work done to bring the units to a stage of partial completion at the end of the period (the same as with the weighted average method). The formula for computing equivalent units of production is more complex under FIFO method than under weighted average method.

Formula for Calculating Equivalent Units―FIFO method:

Equivalent Units of Production = Equivalent units to complete beginning inventory* + Units started and completed during the period + Equivalent units in ending work in process inventory

*Equivalent units to complete beginning inventory = Units in beginning inventory × (100% − Percentage completion of beginning inventory)

Or, the equivalent units of production can also be determined as follows:

Equivalent Units of Production = Units transferred out + Equivalent units in ending work in process inventory − Equivalent units in beginning inventory.

Example:

To illustrate the FIFO method, Refer again the data of shaping and milling department of Norton Company.

Shaping and Milling Department	Materials	Conversion
Work in Process May 1: 200 units × (100% − 55%)* 200 units × (100% − 30%)* Units started and completed in MayWork in process, May 31: 400 units × 40% 400 units × 25% Equivalent Units of Production	90 **4,600 160 -------- 4,850 =====	140 **4,600 100 -------- 4,840 =====

*This is the work needed to complete the units in the beginning inventory.
**(5,000 units started) − (400 units in the ending work in process) = 4,600 units started and completed. The FIFO method assumes that the units in the beginning inventory are finished first.