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2. Equivalent Units

One feature of process costing scenarios is that inventory is usually produced in a continuous process. Production does not start and stop just because a calendar page is being flipped. It is very likely that goods will be in various stages of production within each department at the end of each accounting period. For example, at the end of each month, Navarro Steel may have vats of iron ore that are in the process of being melted, other pools of material may have been skimmed but not yet laced with the requisite alloys, and partially cooled material may be awaiting the extrusion process. How are the costs incurred to be allocated between work in process versus finished goods?

To deal with the aforementioned question, accountants have devised the concept of an equivalent unit. An equivalent unit is a physical unit expressed in terms of a finished unit. As a simple example, ten units in process that are 30% complete equates to three equivalent units of output. None of the ten units is complete; merely the equivalent amount of work necessary to complete three units is said to be performed. As you might suspect, this determination of equivalent units is a bit abstract.

2.1. Factors of Production

For starters, it is necessary to consider equivalent units relative to each of the factors of production. In other words, 80% of necessary direct material may be in process, but only 60% of the direct labor and factory overhead (i.e., conversion cost) has been incurred. Therefore, proper costing methodology for 100 units in process would require us to state that 80 equivalent units have been produced based on material, while 60 equivalent units based on conversion have been produced.

To assess the equivalent units of production requires careful reasoning about the amount of direct material injected into production for each department, relative to the total amount of direct material that will ultimately be needed to complete the process within that department. This type of assessment must be repeated for direct labor and overhead (i.e., conversion costs). If overhead is applied based on labor, the process is simplified because the "percent complete" would the same for labor and overhead. However, if overhead is applied on some other basis (like machine hours) then a separate determination of equivalency would be needed for labor and for overhead (note: the illustrations within this chapter will assume overhead is applied based on labor, and the equivalent units for labor and overhead are therefore shown to be the same - but be aware that such is not always the case).

2.2. An Illustration of Equivalent Units Calculations

To better understand equivalent units, let's focus on an example for Navarro Steel. To begin, one needs to identify the total units that are to be considered, no matter their stage of completion at the beginning and end of the month.

The first stage in Navarro's production process is the Melting Department. Navarro started the month of June with 300,000 tons of iron ore in process in the Melting Department. During June, an additional 600,000 tons were introduced into the melting vats. This means 900,000 total units must be "reconciled." The quantity schedule below provides this reconciliation. It shows that 650,000 units were transferred on to the Skim/Alloy Department, leaving 250,000 tons still in process. You should not proceed to try to calculate equivalent units until you have done this reconciliation.

An Illustration of Equivalent Units Calculations

In reconciling total units into production with the total units transferred out/still in process, it is not uncommon to come up short; many processes may involve scrap, waste, or spoilage (e.g., evaporation, spilling, etc.). Such units would be "identified" as the missing amount needed to balance the quantity schedule column. Advanced managerial accounting courses usually demonstrate the mechanics of handling the cost of spoilage within a process cost system. However, for now you should simply know that the cost of "normal" spoilage is allocated to the inventory of good units, while the cost of excessive waste is charged off as a loss on the income statement. The remaining details are left for subsequent courses.

Once the total units have been reconciled, the equivalent units are computed. The correct manipulation of the data will depend on the inventory method in use. In this illustration, Navarro is assumed to use the weighted-average costing method (first-in, first-out is illustrated later). This simplifies the process because the beginning inventory and current period production can be combined or "averaged" together; thus, the 650,000 units that were completed are counted as 650,000 equivalent units of output (a 1:1 correspondence for material, labor, and factory overhead) - no matter their origin from beginning inventory or otherwise. However, the units in ending work in process require more thoughtful consideration. Let's assume that the 250,000 tons in ending work in process are 50% complete with respect to material (i.e., 125,000 equivalent units) and 40% complete with respect to conversion (i.e., 100,000 equivalent units of direct labor and factory overhead). The right-hand side of the following schedule shows how the total units are translated into equivalent units:

2.3. Cost per Equivalent Unit

The equivalent units, as determined in the blue schedule above, are carried forward into the tan schedule below (see the small arrow on the right-hand edge). This "cost per equivalent unit" schedule shows how the combined costs from beginning work in process (assumed at $2,104,500 for Navarro, broken down between materials, labor, and overhead as shown) and current period production (assumed at $7,365,000, again broken down as shown) are divided by the equivalent units. The result is the weighted-average cost per equivalent unit for each factor of production: direct material, direct labor, and factory overhead. The individual cost factors can be combined to identify conversion cost per equivalent unit, and overall cost per equivalent unit. It can be very important to extend the decimals beyond the "cent" level (avoid rounding) because the per unit cost may ultimately be multiplied times millions of units!

Cost per Equivalent Unit

 
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