How many equivalent units for materials would there be using the FIFO method?

In manufacturing facilities, equivalent units of production are calculated to determine the value of a department’s work-in-process inventory at the end of an accounting period. EUPs represent the number of completed goods that could have been produced using the direct materials, direct labor and manufacturing overhead inputs actually consumed during the period. The methods of calculating EUP are slightly different between weighted average costing and first-in, first-out costing.

Accounting for Direct Materials and Conversion Costs

1. In both costing methods, direct materials and conversion costs -- direct labor and manufacturing overhead required to convert direct materials into completed units -- are calculated separately when determining EUP. Direct materials may all be added at the beginning of the manufacturing process or consumed evenly throughout the process. Conversion costs are generally assumed to be incurred evenly throughout the production process. In order to calculate EUP, it is important to know the percentage of completeness for beginning WIP inventory and ending WIP with respect to direct materials and conversion costs using a separate percentage for each type of cost.

Weighted Average EUP Calculation for Direct Materials

1. Under the weighted average costing method, beginning WIP is considered to be started and completed during the current period, regardless of when the units were actually started. Therefore, all units transferred out (completed) during the current period are multiplied by 100 percent when calculating EUP. Ending WIP units are multiplied by the percentage they are considered complete. These two products are added to get the weighted average EUP for direct materials.

FIFO Costing EUP Calculation for Direct Materials

1. Under FIFO costing, beginning WIP units for EUP are calculated by multiplying beginning WIP units by the percentage remaining to be completed at the beginning of the period because the percentage completed was included in the prior period calculation. If direct materials are added at the beginning of the process, the number of beginning WIP units would be multiplied by zero percent because all of the direct materials were consumed in the prior period. The units started and completed during the current period -- equal to units transferred out minus beginning WIP units -- are multiplied by 100 percent in calculating EUP. Ending WIP units are multiplied by the percentage they are considered complete. These three products are added to get the weighted average EUP for direct materials.

Weighted Average EUP Calculation for Conversion Costs

1. As with direct materials, under FIFO costing, beginning WIP units for EUP are calculated by multiplying beginning WIP units by the percentage remaining to be completed at the beginning of the period with respect to conversion costs. The units started and completed during the current period -- equal to units transferred out minus beginning WIP units -- are multiplied by 100 percent in calculating EUP. Ending WIP units are multiplied by the percentage they are considered complete. These three products are added to get the weighted average EUP for conversion costs. Be sure to use the percentage remaining to be completed when calculating EUP for beginning WIP, and use percentage completed when calculating EUP for ending WIP for both conversion costs and direct materials under FIFO costing.

   Equivalent units FIFO method is used by a manufacturer to express partially completed units of product in terms of finished units.

   The objective of using equivalent units is to be able to apportion the costs of production to completed units and partially completed units held in work in process.

   Equivalent Units Formula

   Equivalent units are calculated by multiply the number of physical units in work in process by the estimated percentage of completion of the units.

   The equivalent units formula can be stated as follows:

   

   How to Calculate Equivalent?

   As a simple example, suppose a business has 300 units of a product in work in process and they are estimated to be 40% complete. Using the equivalent units of production formula we get:

   Equivalent units of production = Units × Percentage of completion
   Equivalent units of production = 300 × 40%
   Equivalent units of production = 120
   

   What this example shows is that although there are 300 physical units of product in work in process, as they are only 40% complete it is equivalent to having 120 units of finished, fully completed product.

   Estimating the Percentage of Completion

   In the example above we simply stated that the estimated percentage of completion was 40%. In practice the percentage of completion needs to be based on each factor of production such as direct materials, direct labor, and manufacturing overheads. For example the work in process units might be 50% complete in terms of direct materials, 40% complete in terms of direct labor, and 10% complete in terms of manufacturing overhead.

   If we have 300 units in work in process, then the equivalent units are calculated as follows:

   Materials = 300 x 50% = 150
   Labor = 300 x 40% = 120
   Overheads = 300 x 10% = 30
   

   Equivalent Units FIFO Method Example

   The following example is used to demonstrate how the equivalent units FIFO method is used to allocate production costs between completed and partially completed units.

   At the start of an accounting period a business has 2,000 units in beginning work in process. During the accounting period a further 8,000 units are added to the production process and 6,000 units are completed and transferred out, leaving an ending balance of 4,000 units in work in process.

   Physical Units

   The table below summarizes the movement of physical units during the accounting period.

   Physical units movementUnitsBeginning2,000Added8,000Completed-6,000Ending4,000

   During the period costs are incurred in the production process to complete the 2,000 beginning WIP units, to start and complete an additional 4,000 units, giving a total of 6,000 units transferred out of the process, and to partially complete the 4,000 units remaining in work in process, a total of 10,000 units are in production.

   Physical units in productionUnitsBeginning WIP2,000Started and completed4,000Ending WIP4,000Total10,000

   Equivalent Units FIFO Method

   The next step is to convert the physical units in production shown above (10,000) into equivalent units.

   The treatment of the beginning WIP units will depend on which costing method, usually weighted average or FIFO, the business is using.

   If the equivalent units FIFO method is used then only the percentage of beginning WIP units completed during the accounting period and the production costs incurred in completing those units, are included in the calculation of the cost per equivalent unit – see below.

   If an alternative weighted average method is used then the beginning WIP units are treated as started and completed (100%) during the accounting period. The treatment using this method is discussed in our equivalent units of production- weighted average method tutorial.

   In this example the FIFO method is used and the beginning WIP units are partially completed at the start of the accounting period. The production costs incurred during the accounting period are therefore spent on the uncompleted part of the beginning WIP units.

   Obviously the units started and completed during the period are 100% complete and the equivalent units are the same as the physical units. The beginning WIP units are already partially complete at the start of the period and are further completed during the period and need to be converted to equivalent units. Likewise, the ending work in process units are only partially complete at the end of the period and again, need to be converted to equivalent units.

   If we assume that the state of completion of the beginning WIP units is material 90%, labor 55%, and overheads 30%, and the state of completion of the ending WIP units is material 85%, labor 65%, and overheads 35%, then the equivalent units are calculated as follows:

   Beginning WIP
   Materials = 2,000 x (100% - 90%) = 200
   Labor = 2,000 x (100% - 55%) = 900
   Overheads = 2,000 x (100% - 30%) = 1,400
   Notice that the production costs are spent on the uncompleted part of the beginning WIP.
   Ending WIP
   Materials = 4,000 x 80% = 3,200
   Labor = 4,000 x 65% = 2,600
   Overheads = 4,000 x 35% = 1,400
   The production costs are spent on the completed part of the ending WIP.
   

   The physical units can now be represented as equivalent units for each production factor.

   Equivalent units FIFO methodMaterialLaborOverheadBeginning WIP2009001,400Started and completed4,0004,0004,000Ending WIP3,2002,6001,400Total7,4007,5006,800

   Cost per Equivalent Unit Formula

   The cost per equivalent unit formula is as follows:

   Cost per equivalent unit = Production cost / Equivalent units

   As mentioned above, the variables used in the cost per equivalent unit formula depend on which costing method the business is using. In this example we will use the equivalent units FIFO method in which case the two variables used in the formula are defined as follows:

   1. Production cost = Costs added during the period
   2. Equivalent units = Beginning WIP units (% to complete) + Started and completed units (100%) + Ending WIP units (% to completed)

   Cost per Equivalent Unit Calculation

   Suppose the production cost data for the manufacturing process shows that the brought forward beginning WIP costs are materials 23,000, labor 5,500, and overhead 1,700, a total of 30,200. During the period the production costs added are materials 69,000, labor 28,900, and overhead 9,400, giving a total of 107,300

   The total production costs to allocate are 137,500 comprising, materials 92,000, labor 34,400 and overhead 11,100. Using the formula above, the cost per equivalent units for each production factor are calculated as follows:

   Materials = 69,000 / (200 + 4,000 + 3,200) = 9.324
   Labor = 28,900 / (900 + 4,000 + 2,600) = 3.853
   Overheads = 9,400 / (1,400 + 4,000 + 1,400) = 1.382
   Total = 9.324 + 3.853 + 1.382 = 14.560
   

   In the example, the cost per equivalent unit for direct materials is 9.324, cost per equivalent unit for direct labor is 3.853, and the cost per equivalent unit for manufacturing overhead is 1.382. This gives a total cost per equivalent unit of 14.560.

   Allocating the Cost of Production

   To allocate the cost of production to completed units and work in process we now simply multiply each equivalent unit by its respective cost per equivalent unit as follows:

   Beginning Work in Process

   Materials = 200 x 9.324 = 1,865
   Labor = 900 x 3,583 = 3,468
   Overheads = 1,400 x 1.382 = 1,935
   Total = 7,268
   

   Started and completed

   Materials = 4,000 x 9.324 = 37,297
   Labor = 4,000 x 3,583 = 15,413
   Overheads = 4,000 x 1.382 = 5,529
   Total = 58,240

   Ending Work in Process

   Materials = 3,200 x 9.324 = 29,838
   Labor = 2,600 x 3,583 = 10,019
   Overheads = 1,400 x 1.382 = 1,935
   Total = 11,100

   The allocation of production costs is summarized in the table below:

   Allocation of production costsMaterialLaborOverheadTotalBeginning WIP (Actual)23,0005,5001,70030,200Beginning WIP completion1,8653,4681,9357,268Started and completed37,29715,4135,52958,240Completed62,16224,3819,16595,708Ending WIP29,83810,0191,93541,792Total92,00034,40011,100137,500

   The production costs for the period have now been allocated between the completed units and the partially completed units held in work in process. The production process account can now be completed as follows:

   Production process accountUnitsCostsBeginning (Actual)2,00030,200Added (Actual)8,000107,300Completed (Allocated)-6,000-95,708Ending (Allocated)4,00041,792

   By using the equivalent units of production weighted average method the business has taken actual production costs of 137,500 and allocated 95,708 to the 6,000 completed units, and 41,792 to the 4,000 partially completed units held in work in process.

   Last modified November 26th, 2019 by Michael Brown

   About the Author

   Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a degree from Loughborough University.

   What are equivalent units of production for material assuming FIFO?

   Equivalent units under FIFO method of process costing are the number of finished units that could have been prepared in a process during a period had there been no unfinished units, either in opening WIP or closing WIP.

   What is the total number of equivalent units for direct materials?

   To calculate the amount transferred to the next department, we see that there are 1,500 direct materials equivalent units at a cost of $1.25 per unit, giving us a cost of $1,875. ... Separate Equivalent Units for Direct Materials and Conversion Costs..

   What is FIFO method?

   First In, First Out, commonly known as FIFO, is an asset-management and valuation method in which assets produced or acquired first are sold, used, or disposed of first. For tax purposes, FIFO assumes that assets with the oldest costs are included in the income statement's cost of goods sold (COGS).