The weighted-average process-costing method calculates the equivalent units by

The weighted average method is used to assign all costs in a process-costing system to the products produced. 

In a process costing system, cost per equivalent unit is the term used to describe the average unit cost for each product. 

The concept of cost per equivalent unit used to assign costs to (1) completed units transferred out and (2) units still in work-in-process (WIP) inventory at the end of the period?

Costs are assigned to completed units transferred out and units in ending WIP inventory using a four-step process. 

We list the four steps in the following and then explain them in detail. 

Step 1. Summarize the physical flow of units and compute the equivalent units for direct materials, direct labor, and overhead.

Step 2. Summarize the costs to be accounted for (separated into direct materials, direct labor, and overhead).

Step 3. Calculate the cost per equivalent unit.

Step 4. Use the cost per equivalent unit to assign costs to (1) completed units transferred out and (2) units in ending WIP inventory.

What are Equivalent Units?

The process of accounting for the flow of costs through accounts used in a process costing system is fairly straight forward. 

In a process costing system, cost per equivalent unit is the term used to describe the average unit cost for each product. 

The concept of cost per equivalent unit is used to assign costs to (1) completed units transferred out and (2) units still in work-in-process (WIP) inventory at the end of the period?

The challenge is determining the unit cost of products being transferred out of each departmental work-in-process inventory account. 

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. The ending work-in-process inventory to be converted to the equivalent completed units (called equivalent units). 

Equivalent units 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:

Equivalent units = Number of physical units × 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.

Calculating Equivalent Units

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 article, we keep direct labor and manufacturing overhead separate.) 

Step 1. Summarize the physical flow of units and compute the equivalent units for direct materials, direct labor, and overhead.

This step uses the basic cost flow equation presented in to identify the physical flow of units (the basic cost flow equation applies to costs and to units):

Beginning balance + Transfers in (BB) + (TI) Units to be accounted for ==  Transfers out + Ending balance (TO) + (EB) Units accounted for 

What are the two categories used to summarized the physical flow of units?

The first category, units to be accounted for, includes the beginning balance (BB) and transfers in (TI). 

The second category, units accounted for, includes the ending balance (EB) and transfers out (TO). As you can see from the previous equation, units to be accounted for must equal units accounted for. 

The units accounted for (# transferred out and # in ending WIP inventory) must be converted into equivalent units for direct materials, direct labor, and overhead.

The # units transferred out are 100 percent complete for direct materials, direct labor, and overhead (otherwise, they would not be transferred out), which results in equivalent units matching the physical units. 

However, the # units in ending WIP inventory are at varying levels of completion for direct materials, direct labor, and overhead, and must be converted into equivalent units using the following formula (as described earlier in the chapter):

Equivalent units = Number of physical units × Percentage of completion

Later in step 3, we will use equivalent unit information for the Assembly department to calculate the cost per equivalent unit.

Step 2. Summarize the costs to be accounted for (separated into direct materials, direct labor, and overhead).

How do we summarize the costs that are used to calculate the cost per equivalent unit?

The total costs to be accounted for include the costs in beginning WIP inventory and the costs incurred during the period. shows these costs for the Assembly department. 

The costs are separated into direct materials, direct labor, and overhead.

Shows that costs totaling $ must be assigned to (1) completed units transferred out and (2) units in ending WIP inventory.

Step 3. Calculate the cost per equivalent unit.

We now have the costs () and equivalent units () needed to determine the cost per equivalent unit for direct materials, direct labor, and overhead.

The formula to calculate the cost per equivalent unit using the weighted average method is as follows:

In summary, the same formula is as follows:

Cost per equivalent unit = Costs in beginning WIP + Current period costs Equivalent units completed and transferred out + Equivalent units in ending WIP Cost per equivalent unit = Total costs to be accounted for

The cost per equivalent unit is calculated for direct materials, direct labor, and overhead. 

Simply divide total costs to be accounted for by total equivalent units accounted for. 

It is important to note that the information shown in allows managers to carefully assess the unit cost information in the Assembly department for direct materials, direct labor, and overhead. 

Recall our primary goal of assigning costs to completed units transferred out and to units in ending WIP inventory. How do we accomplish this goal?

Costs are assigned by multiplying the cost per equivalent unit by the number of equivalent units for direct materials, direct labor, and overhead. shows how this is done.

 Step 4. Use the cost per equivalent unit to assign costs to (1) completed units transferred out and (2) units in ending WIP inventory.

The total cost assigned to units transferred out equals the cost per equivalent unit times the number of equivalent units. 

For example, the cost assigned to direct materials of $120,000 = 4,000 equivalents units × $30 per equivalent unit.

The total cost assigned to units in ending inventory equals the cost per equivalent unit times the number of equivalent units. 

For example, the cost assigned to direct materials of $90,000 = 3,000 equivalent units× $30 per equivalent unit.

This must match total costs to be accounted for. Although not an issue in this example, rounding the cost per equivalent unit may cause minor differences between the two amounts.

On completion of step 4, it is important to reconcile the total costs to be accounted for with the total costs accounted for.  

The two balances must match (note that small discrepancies may exist due to rounding the cost per equivalent unit). 

This reconciliation relates back to the basic cost flow equation as follows:

 Beginning balance + Transfers in (BB) + (TI) Costs to be accounted for  == Transfers out + Ending balance (TO) + (EB) Costs accounted for 

Although the examples in this chapter have been created in a way that minimizes rounding errors, always round the cost per equivalent unit calculations in step 3 to the nearest thousandth (e.g., if the cost per equivalent unit is $2.3739, round this to $2.374 rather than to $2). 

Although rounding differences still may occur, this will minimize the size of rounding errors when attempting to reconcile costs to be accounted for (step 2) with costs accounted for (step 4).

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