What are the equivalent units of production for materials during the period?

Another acceptable method for determining unit cost under process costing is the first-in, first-out (FIFO) cost method.  Under the FIFO method, we assume any units that were not completed last period (beginning work in process) are finished before anything else is started.  The following table shows the differences between the weighted average method and the FIFO cost method:

Weighted AverageFIFOUnits Completed and transferred out:Total units completed this periodTotal units finished from beginning work in process + units started and completed this periodEquivalent Units based on:Units completed this period + Units in Ending Work in ProcessUnits from Beg. Work in Process completed + units started and completed + units in Ending Work in ProcessCost per Equivalent Unit based on:Beg. Work in Process Costs + Costs added this periodCosts added this period onlyAssign costs using:Equivalent Units x Cost per Equivalent Units for Units completed and units in ending Work in ProcessBeg. Work in Process Costs + Equivalent Units x cost per equivalent unit for units finished from Beg. Work In Process, Units started and completed and units in End. Work In Process

We will look at each item individually as we discuss the steps of process costing.  Under either method, weighted average or FIFO, process costing consists of 5 steps:

1.  Physical Flow of Units
2.  Equivalent Units
3.  Cost per Equivalent Unit
4.  Assign Costs to Units Completed and Ending Work in Process Inventory
5.  Reconcile Costs

Physical Flow of Units

The physical flow of units is as follows under the weighted average method:

Units in Beg. WIPUnits Completed and Transferred+ Units Started this period+ Units in End. WIP= Total Units = Total Units

This is altered just slightly under the FIFO method as we must separate the items in units completed into Units Completed from beginning work in process and Units started and completed this period since under FIFO, we must finish anything from beginning work in process before we start something new.  Under the FIFO, we the physical flow of units would be documented as:

Units in Beg. WIPUnits Completed and Transferred:+ Units Started this period     Beg. Work in Process Units Completed= Total Units     + Units started and Completed this period= Units completed and transferred+ Units in End. WIP = Total Units

Just as in the weighted average method, the 2 Total Units figures must agree!

Equivalent Units of Production

Under the FIFO method, we will calculate equivalent units for 3 things:  Units completed from beginning work in process, units started and completed this period and units remaining in ending work in process.  This video will discuss the differences between the Weighted Average and FIFO methods for equivalent units (if you are comfortable with the weighted average method, skip to minute 4:06 to begin the discussion on the FIFO method).

Equivalent units for the period will be calculated as follows under FIFO (keep in mind, you may have different percent complete for materials, labor and overhead):

1.  Units from beginning work in process:  you want to complete this units, so how much MORE effort will be needed to finish these units.  You will calculate this as beginning work in process units x (100% – given % complete) to calculate the amount of additional work necessary to make the unit 100% complete.
2. Units started and completed this period:  take the units x 100% complete since they were started and completed they have received all of their materials, labor and overhead and will not receive any more since they are finished.
3. Units in Ending work in process:  just like with the weighted average method, we will take the ending work in process units x a given % complete.

To illustrate the computation of equivalent units under the FIFO method, assume the following facts (for simplicity we are using just one percent complete for materials, labor and overhead):

Beginning work in process inventory3,000 units, 40% completeUnits started this period10,000 unitsEnding work in process inventory5,000 units, 20% complete

The physical flow of units would be (calculate units started and completed as units started 10,000 – units in ending work in process 5,000):

Units in Beg. WIP3,000Units Completed and Transferred:Units Started this period10,000   Units from Beg. WIP3,000Total Units13,000   Units started and completed5,000(10,000 – 5,000)Total Units completed and txfr8,000Units in End. WIP5,000Total Units 13,000

The equivalent production for the period would be:

Units from beginning WIP   [3,000 units x (100% – 40% complete)]   1,800Units started and completed   5,000 units x 100% complete    5,000Units in ending WIP   5,000 units x 20% complete   1,000     Total Equivalent Units     7,800

Cost per Equivalent Unit

Under the weighted average method, we use beginning work in process costs AND costs added this period.  Under the FIFO method, we will only use the costs added this period.  This video will explain the differences between the two approaches.

The formula we will use for calculating cost per equivalent unit under the FIFO Method is:

Current Costs added this period÷ Total Equivalent Units= Cost per Equivalent Units

Assign Costs

When we assign costs to units completed and transferred and units remaining in ending work in process under the FIFO method, we need the following items:

1.  Costs from beginning work in process:  these were the costs we started the period with or the unfinished items from the previous period (no calculation required — just bring over the costs from beginning work in process).  Remember, under FIFO, these are finished first so their costs must be passed along to completed units.
2.  Costs to complete beginning work in process:  you will take the Equivalent units calculated for completing beginning work in process x the cost per equivalent unit.  You will do this for materials, labor and overhead (or for conversion costs which is the both direct labor and overhead).
3. Costs of units started and completed:  you will take the equivalent units calculated for units started and completed x the cost per equivalent unit for materials, labor and overhead (or conversion).
4. The sum of these 3 will be the cost of units completed and transferred which is also known as cost of goods manufactured.  This amount is transferred to the next department or to finished goods and out of work in process for the units completed this period.
5. Cost of units remaining in ending work in process:  you will take the ending work in process equivalent units x the cost per equivalent unit for materials, labor and overhead (or conversion) just as we did under the weighed average method.  This amount rolls over to be the next period’s beginning work in process inventory.

This video will provide a demonstration of cost assignment under the FIFO method.

Reconcile Costs

Finally, something is the same under FIFO and Weighted Average.

We want to make sure that we have assigned all the costs from beginning work in process and costs incurred or added this period to units completed and transferred and ending work in process inventory.

First, we need to know our total costs for the period (or total costs to account for) by adding beginning work in process costs to the costs incurred or added this period.  Then, we compare the total to the cost assignment in step 4 for units completed and transferred and ending work in process to get total units accounted for.  Both totals should agree.

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