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The equivalent units of production for conversion costs using the first-in, first-out (FIFO) method are: Conversion Costs Completion of BWIP 2,500 Started & Completed 80,000 Starting of EWIP 4,800 Total EUP - FIFO 87,300 When FIFO is being used, the units in beginning work-in-process inventory are not included in the total equivalent units used to allocate the added costs between units completed and units in ending work-in-process inventory. That is because the costs in beginning work-in-process inventory are allocated 100% to completed units. Only the costs added during the period are allocated between completed units and EWIP according to equivalent units during the period. The 10,000 units in BWIP were 75% complete as to conversion costs, so 25% of the work or 2,500 EUP remained to be done in the current period. The number of units started and completed is equal to the number of units completed (90,000, given in the problem) minus the number of physical units in BWIP (10,000, also given in the problem), or 80,000 EUP. The number of EUP in EWIP is 60% of the 8,000 units in EWIP, or 4,800 EUP. Therefore, total equivalent units of production under FIFO are 2,500 + 80,000 + 4,800 = 87,300.
This is the number of units started and completed plus the number of physical units in ending work-in-process inventory. It is also the total number of units started during the month. The number of equivalent units of production for conversion costs is the number of equivalent units in BWIP that were completed during the month, plus the number started and completed, plus the number of equivalent units in ending work-in-process inventory. The number of equivalent units of production in beginning work-in-process inventory that were completed during the month is 25% of the number of physical units, since those units were 75% complete for conversion costs at the beginning of the month. The number of equivalent units in ending work-in-process inventory is 60% of the number of physical units in ending work-in-process inventory, since those units were 60% complete for conversion costs at the end of the month.
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This is the number of equivalent units for conversion costs in BWIP at the beginning of the month, plus the number started and completed, plus the number of equivalent units in ending work-in-process inventory at month end. The number of equivalent units in BWIP is not included in the total equivalent units when FIFO is used; however, the number of equivalent units in BWIP that were completed during the month is included. That number was 25% of the number of physical units, since the units in beginning work-in-process inventory were 75% complete for conversion costs at the beginning of the month.