Case 2: Process Costing With Zero Beginning and Some Ending Work-in-Process Inventory

Learning Objective 3 Describe the five steps in process costing and calculate equivalent units

• to assign total costs to units completed and to units in work in process
• output units adjusted for incomplete units

In February 2020, Pacific Electronics places another 400 units of SG-40 into production. Recall there is no beginning inventory of partially completed units in the assembly department on February 1. Of the 400 units started in February, only 175 units are completed and transferred to the testing department. Data for the assembly department for February 2020 follow:

The 225 partially assembled units as of February 29 2020, are fully processed for direct materials because all direct materials in the assembly department are added at the beginning of the assembly process. Conversion costs, however, are added evenly during assembly. An assembly department supervisor estimates that the partially assembled units are, on average, 60% complete with respect to conversion costs.

The accuracy of the completion estimate depends on the care, skill, and experience of the estimator and the nature of the conversion process. Estimating degree of completion is usually easier for direct materials costs than for conversion costs because the quantity of direct materials needed for a completed unit and the quantity of direct materials in a partially completed unit can be measured more accurately. In contrast, the conversion sequence usually consists of a number of operations, each for a specified period of time, at various steps in the production process.^* The degree of completion for conversion costs depends on the proportion of total conversion costs needed to complete one unit (or a batch of production) that has already been incurred on units still in process.

Department supervisors and line managers often estimate completion rates for conversion costs because they are most familiar with the conversion process. However, in some industries, such as semiconductor manufacturing, no exact estimate is possible because manufacturing occurs inside sealed environments that can only be opened when the process is complete. In other industries, such as textiles, vast quantities of unfinished products, such as shirts and pants, make the task of estimation too costly. In these cases, to calculate conversion costs, managers assume that all work in process in a department is complete to some preset degree (for example, one-third, one-half, or two-thirds).

Because some units are fully assembled and some are only partially assembled, a common metric, called equivalent units, is needed to compare the work that’s been done on them and, more importantly, obtain a total measure of the work done. We will explain this concept in greater detail next as part of the set of five steps required to calculate (1) the cost of fully assembled units in February 2020 and (2) the cost of partially assembled units still in process at the end of that month, for Pacific Electronics. The five steps of process costing are shown below:

1. Step 1: Summarize the flow of physical units of output.
2. Step 2: Compute output in terms of equivalent units.
3. Step 3: Summarize total costs to account for.
4. Step 4: Compute cost per equivalent unit.
5. Step 5: Assign total costs to units completed and to units in ending work-in-process inventory.

Summarizing the Physical Units and Equivalent Units (Steps 1 and 2)

In Step 1, managers track the physical units of output. Physical units are the number of output units, whether complete or incomplete. The physical-units column of Exhibit 18-1 tracks where the physical units came from (0 units from beginning inventory and 400 units started) and where they went (175 units completed and transferred out and 225 units in ending inventory).

In Step 2, managers compute output in equivalent units, not in physical units. Equivalent units are a derived measure of output calculated by (1) taking the quantity of each input (factor of production) in units completed and in incomplete units of work in process and (2) converting the quantity of input into the amount of completed output units that could be produced with that quantity of input. To see what is meant by equivalent units, suppose that during a month, 50 physical units were started but not completed. These 50 units in ending inventory are 70% complete for conversion costs. Suppose all conversion costs represented in these units were used to make fully completed units instead. How many completed units could be made? The answer: 35 units. Why? Because conversion costs incurred to produce 50 units that are each 70% complete could have instead produced 35 $(0.70\times 50)$ units that are 100% complete. The 35 units are called equivalent units of output. That is, in terms of the work done on them, the 50 partially completed units are considered equivalent to 35 completed units. Note that equivalent units of output are calculated separately for each input (such as direct materials and conversion costs). Moreover, every completed unit, by definition, is composed of one equivalent unit of each input required to make it.

When calculating equivalent units in Step 2, focus on quantities. Disregard dollar amounts until after equivalent units are computed. In the Pacific Electronics example, all 400 physical units—the 175 fully assembled units and the 225 partially assembled units—are 100% complete with respect to direct materials because all direct materials are added at the start of the process. Therefore, Exhibit 18-1 shows 400 equivalent units of output for direct materials: 175 equivalent units for the 175 physical units assembled and transferred out and 225 equivalent units for the 225 physical units in ending work-in-process inventory.

The 175 fully assembled units have incurred 100% of conversion costs. The 225 partially assembled units in ending work in process are 60% complete (on average). Therefore, their conversion costs are equivalent to conversion costs incurred by 135 fully assembled units $(225\times 60\%=135)$. Hence, Exhibit 18-1 shows $310\hspace{0.17em}(175+135)$ equivalent units of output for conversion costs: 175 equivalent units for the 175 physical units assembled and transferred out and 135 equivalent units for the 225 physical units in ending work-in-process inventory.

This chapter focuses on manufacturing settings, but equivalent-unit calculations are also used in nonmanufacturing settings. For example, universities convert part-time student enrolments into “full-time student equivalents” to get a better measure of faculty–student ratios over time. Part-time students take fewer academic courses and do not need the same number of instructors as full-time students. Without this adjustment, an increase in part-time students would give a misleading picture of a lower faculty–student ratio.