Accounting: The Language of Business - Vol. 1 (Part 115)

"I will go to the lovely Sur Rivers / And dip my arms in them up to the shoulders. / I will find my accounting where the alder leaf quivers / In the ocean wind over the river boulders." - Robinson Jeffers 

Process Cost System (Part B)

by

Charles Lamson

The First-In, First-Out (Fifo) Method

In a process cost system, the accountant determines the cost transferred out and thus the amount remaining in inventory for each department. To determine this cost, the accountant must make a cost flow assumption. Like merchandise inventory, costs can be assumed to flow through the manufacturing process using the first in, first out (fifo) or average cost methods. Because the first-in, first-out (fifo) method is often the same as the physical flow of units, we use the fifo method in the next several posts.

Most process manufacturers have more than one department. In the illustrations that follow, McDermott Steel Inc. has two departments, Melting and Casting. McDermott melts scrap metal and then pours the molten metal into an ingot casting.

To illustrate the first in, first out method, we will simplify by using only the Melting Department of McDermott Steel Inc. The following data for the Melting Department are for July 2023: 

We assume that all materials used in the department are added at the beginning of the process, and conversion costs (direct labor and factory overhead) are incurred evenly throughout the melting process. The objective is to determine the cost of goods completed and the ending inventory valuation, which are represented by the question marks. We determine these amounts by using the following four steps:

1. Determine the units to be assigned costs.

2. Calculate equivalent units of production.

3. Determine the cost per equivalent unit.

4. Allocate costs to transfer data and partially completed units.

Step 1: Determine the Units to Be Assigned Costs

The first step in our illustration is to determine the units to be assigned costs. A unit can be any measure of completed production such as tons, gallons, pounds, barrels, or cases. We use tons as the definition for units in McDermott Steel.

McDermott Steel had 1,500 tons of direct materials charged to production in the Melting Department for July, as shown below.

There are three categories of units to be assigned costs for an accounting period: (A) units in beginning in-process inventory, (B) units started and completed during the period, and (C) units in ending in-process inventory. Exhibit 4 illustrates these categories in the Melting Department for July. The 500-ton beginning inventory (A) was completed and transferred to the Casting Department. McDermott Steel started another 1,000 tons of material into the process during July. Of the 1,000 tons introduced in July, 400 tons were left incomplete at the end of the month (C). Thus, only 600 of the 1,000 tons were actually started and completed in July (B).

EXHIBIT 4 July Units to Be Costed---Melting Department

The total units (tons) to be assigned costs for McDermott Steel can be summarized as shown below.

Note that the total tons to be assigned costs equals the total tons accounted for by the department. The 3 unit categories (A, B, and C) are used in the remaining steps to determine the cost transferred to the Casting Department and the cost remaining in work in process inventory at the end of the period.

Step 2: Calculate Equivalent Units of Production

Process manufacturers often have some partially processed materials remaining in production at the end of the period. In these cases, the costs of production must be allocated between the units that have been completed and transferred to the next process (or finished goods) and those that are only partially completed and remain within the department. This allocation can be determined by using the equivalent units of production.

The equivalent units of production are the number of units that could have been completed within a given accounting period. In contrast, whole units are the number of units in production during a period, whether or not completed. For example, assume that 400 whole units are in work in process at the end of a period. If the units are 25% complete, the number of equivalent units in process is 100 (400 * 25%).

Equivalent units for materials and conversion costs are usually determined separately because they are often introduced at different times or in different rates in the production process. In contrast, direct labor and factory overhead are combined together as conversion costs because they are often incurred in production at the same time and rate.

Materials Equivalent Units

To allocate materials costs between the completed and partially completed units, it is necessary to determine how materials are added during the manufacturing process. In the case of McDermott Steel, the materials are added at the beginning of the melting process. In other words, the melting process cannot begin without the scrap metal. The equivalent unit computation for materials in July is as follows:

The whole units from Step 1 are multiplied by the percentage of materials that are added in July for the in-process inventories and units started and completed. The equivalent units for direct materials are Illustrated in Exhibit 5.

EXHIBIT 5 Direct Materials Equivalent Units

The direct materials for the 500 tons of July 1 in process inventories were introduced in June. Thus, no materials units were added in July for the inventory in process on July 1. All of the 600 tons started and completed in July were 100% complete with respect to materials. Thus, 600 equivalent units of materials were added in July. All the materials for the July 31 in-process inventory were introduced at the beginning of the process. Thus, 400 equivalent units of material for the July 31 in-process inventory were added in July. 

Conversion Equivalent Units

The conversion costs are usually incurred evenly throughout a process. For example, direct labor, utilities, and machine depreciation are usually used uniformly during processing. Thus, the conversion equivalent units are added in July in direct relation to the percentage of processing completed in July. The computations for July are as follows:

The whole units from Step 1 are multiplied by the percentage of conversion completed in July for the in-process inventories and units started and completed. The equivalent units for conversion are Illustrated in Exhibit 6.

The conversion equivalent units of the July 1 in-process inventory are 30% of the five hundred tons, or 150 equivalent units. Since 70% of the conversion had been completed on July 1, only 30% of the conversion effort for these tons was incurred in July. All the units started and completed used converting effort in July. Plus, conversion equivalent units are 100% of these tons. The equivalent units for the July 31 in process inventory are 25% of the 400 tons because only 25% of the converting has been completed with respect to these tons in July.

Step 3: Determine the Cost per Equivalent Unit

In Step 3, we calculate the cost per equivalent unit. The July equivalent unit totals for McDermott Steel's Melting Department are reproduced from Step 2 as follows:

The cost per equivalent unit is determined by dividing the direct materials and conversion costs incurred in July by the respective total equivalent units for direct materials and conversion costs. The direct materials and conversion costs were given at the beginning of this illustration. These calculations are as follows:

We will use these rates in Step 4 to allocate the direct materials in the conversion cost to the completed and partially completed units.

Step 4: Allocate Costs to Transferred and Partially Completed Units

In Step 4, we multiply the equivalent unit rates by their respective equivalent units of production in order to determine the cost of transferred and partially completed units. The cost of the July 1 in-process inventory, completed and transferred out to the Casting Department, is determined as follows:

The July 1 in-process inventory cost of $28,150 is carried over from June and will be transferred to Casting. The cost required to finish the July 1 in-process inventory is $1,710, which consists of conversion costs required to complete the remaining 30% of the processing. This total does not include direct materials costs, since these costs were added at the beginning of the process in June. The conversion costs required to complete the beginning inventory are added to the balance carried over from the previous month to yield a total cost of the completed July 1 in-process inventory of $29,860.

The 600 units started and completed in July receive 100% of their direct materials and conversion costs in July. The costs associated with the units started and completed are determined by multiplying the equivalent units in Step 2 by the unit costs in Step 3, as follows:

The total cost transferred to the Casting Department is the sum of the beginning inventory cost from the previous period ($28,150), the additional costs incurred in July to complete the beginning inventory ($1,710), and the costs incurred for the units started and completed in July ($36,840). Thus, the total cost transferred to Casting is $66,700.

The units of ending inventory have not been transferred, so they must be valued at July 31. The costs associated with the partially completed units in the ending inventory are determined by multiplying the equivalent units in Step 2 by the unit costs in Step 3, as follows:

The units in the ending inventory have received 100% of their materials in July. Thus, the materials cost incurred in July for the ending inventory is $20,000, or 400 equal amount units of materials multiplied by $50. The conversion costs incurred in July for the ending inventory is $1,140 which is 100 equivalent units of the conversion (400 units, 25% complete) for the ending inventory multiplied by $11.40. Summing the conversion and materials costs, the total ending inventory cost is $21,140. 

*WARREN, REEVE, & FESS, 2005, ACCOUNTING, 21ST ED., PP. 788-793*

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