# 4.3: Determining Equivalent Units

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Skills to Develop

• Understand the concept of an equivalent unit.

Question: The beginning of this chapter describes process costing and the flow of costs through accounts used in a process costing system. The challenge is determining the unit cost of products being transferred out of each departmental work-in-process inventory account. We start the process of determining unit cost information with an important concept, the concept of equivalent units. What are equivalent units, and how are equivalent units calculated?

Units of product in work-in-process inventory are assumed to be partially completed; otherwise, the units would not be in work-in-process inventory. Process costing requires partially completed units in ending work-in-process inventory to be converted to the equivalent completed units (called equivalent units). Equivalent units4 are calculated by multiplying the number of physical (or actual) units on hand by the percentage of completion of the units. If the physical units are 100 percent complete, equivalent units will be the same as the physical units. However, if the physical units are not 100 percent complete, the equivalent units will be less than the physical units.

For example, if four physical units of product are 50 percent complete at the end of the period, an equivalent of two units has been completed (2 equivalent units = 4 physical units × 50 percent). The formula used to calculate equivalent units is as follows:

$$\text{Equivalent units} = \text{Number of physical units} \times \text{Percentage of completion}$$

Figure 4.3 provides an example of the equivalent unit concept in which four desks, 50 percent complete, are the equivalent of two completed desks.

Figure 4.3 - Concept of Equivalent Units, © Thinkstock

Question: With the concept of equivalent units now in hand, we can calculate equivalent units for the three product costs—direct materials, direct labor, and manufacturing overhead. Why do we calculate equivalent units separately for direct materials, direct labor, and manufacturing overhead?

Equivalent units in work in process are often different for direct materials, direct labor, and manufacturing overhead because these three components of production may enter the process at varying stages. For example, in the Assembly department at Desk Products, Inc., direct materials enter production early in the process while direct labor and overhead are used throughout the process. (Imagine asking workers to assemble desks without materials!) Thus equivalent units must be calculated for each of the three production costs. (Note that direct labor and manufacturing overhead are sometimes combined in a category called conversion costs, which assumes both are added to the process at the same time. In this text, we keep direct labor and manufacturing overhead separate.) The next section presents how we use the equivalent unit concept for product costing purposes. Be sure you understand the concept of equivalent units before moving on.

###### Calculating Full-Time Equivalent Students

The concept of an equivalent unit can be applied to determine the number of full-time equivalent students (FTES) at a school. Colleges use FTES data to plan and make decisions about course offerings, staffing, and facility needs. Although having information about the number of students enrolled (the headcount) is helpful, headcount data do not provide an indication of whether the students are full time or part time. Clearly, full-time students take more classes each term and generally use more resources than part-time students. Thus administrators often prefer to convert enrollment data to FTES.

Using a simple example to explain this concept, assume 30 students attend school and each takes half a full load of classes. The headcount is 30. However, this is the equivalent of 15 full-time students, or 15 FTES.

To apply this to the real world, let’s look at the enrollment data for Sierra College, a community college located near Sacramento, California. During a recent semester, the student headcount in a specific department at Sierra College was 8,190. Because a large number of students in the department were part time, the full-time equivalent number of students totaled 3,240.

Source: Based on enrollment data from Sierra College.

KEY TAKEAWAYS

• When units of work-in-process (WIP) inventory exist at the end of the reporting period, process costing requires that these partially completed units be converted to the equivalent completed units (called equivalent units). The equation used to calculate equivalent completed units is as follows:$$\text{Equivalent units} = \text{Number of physical units} \times \text{Percentage of completion}$$
• Because direct materials, direct labor, and manufacturing overhead typically enter the production process at different stages, equivalent units must be calculated separately for each of these production costs.

REVIEW PROBLEM 4.3

Soap Production Company’s Mixing department shows the following information for the 1,000 units of product remaining in work in process at the end of the period. Assume there was no beginning inventory.

 Direct materials 90 percent complete Direct labor 30 percent complete Overhead 60 percent complete

Calculate the equivalent units for each of the three product costs—direct materials, direct labor, and overhead.

The formula used to calculate equivalent units is as follows: $$\text{Equivalent units} = \text{Number of partially completed units} \times \text{Percentage of completion}$$
 Materials $$\text{900 equivalent units} = \text{1,000 partially completed units} \times \text{90 percent}$$ Labor $$\text{300 equivalent units} = \text{1,000 partially completed units} \times \text{30 percent}$$ Overhead $$\text{600 equivalent units} = \text{1,000 partially completed units} \times \text{60 percent}$$