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Cost Per Equivalent Unit - Cost Accounting

  1. What is the conversion cost per equivalent unit?
    Answer: $6.00 1. Calculate physical units transferred out: Beginning WIP (4,000) + Units started (30,000) - Ending WIP (6,000) = 28,000 units transferred out. 2. Calculate equivalent units (EU) for conversion: Under the weighted-average method, the percentage of completion of beginning inventory is not used in the EU calculation. Units transferred out: 28,000 units × 100% = 28,000 EU Ending WIP: 6,000 units × 50% = 3,000 EU Total conversion EU = 28,000 + 3,000 = 31,000 EU. 3. Identify total conversion costs: The problem provides the total conversion costs to be accounted for as $186,000. 4. Calculate conversion cost per equivalent unit: Total conversion cost / Total conversion EU = $186,000 / 31,000 EU = $6.00 per EU.
  2. What is the material cost per equivalent unit?
    Answer: $3.375 1. Calculate physical units transferred out: Beginning WIP (10,000) + Units started (90,000) - Ending WIP (20,000) = 80,000 units transferred out. 2. Calculate equivalent units (EU) for materials: Materials are added at 75% completion. Units transferred out are 100% complete for materials. Ending WIP is only 60% complete, which has not reached the 75% point, so it is 0% complete for materials. Units transferred out: 80,000 units × 100% = 80,000 EU Ending WIP: 20,000 units × 0% = 0 EU Total material EU = 80,000 + 0 = 80,000 EU. 3. Calculate total material costs: Beginning WIP material cost: $30,000 (Since beginning WIP was 80% complete, materials were already added in the prior period.) Current period material cost: $240,000 Total material cost = $30,000 + $240,000 = $270,000. 4. Calculate material cost per equivalent unit: Total material cost / Total material EU = $270,000 / 80,000 EU = $3.375.
  3. What is the conversion cost per equivalent unit for February?
    Answer: $9.00 The weighted-average method requires calculating total costs and total equivalent units. 1. Calculate physical units transferred out: Beginning WIP (5,000) + Units started (40,000) - Ending WIP (8,000) = 37,000 units transferred out. 2. Calculate equivalent units (EU) for conversion: Units transferred out: 37,000 units × 100% = 37,000 EU Ending WIP: 8,000 units × 60% = 4,800 EU Total conversion EU = 37,000 + 4,800 = 41,800 EU. 3. Calculate total conversion costs: Beginning WIP conversion cost: $15,000 Current period conversion cost: $342,600 Total conversion cost = $15,000 + $342,600 = $357,600. 4. Calculate conversion cost per equivalent unit: Total conversion cost / Total conversion EU = $357,600 / 41,800 EU = $9.00 per EU.
  4. What is the transferred-in cost per equivalent unit in Department 2 for October?
    Answer: $3.00 Transferred-in costs are treated as a separate category of input, conceptually similar to materials added at the beginning of the process. 1. Calculate physical units transferred out: Beginning WIP (15,000) + Units transferred in (60,000) - Ending WIP (10,000) = 65,000 units transferred out. 2. Calculate equivalent units (EU) for transferred-in costs: Since transferred-in costs arrive with the units at the start of the process in Department 2, all units are 100% complete for this cost component. Units transferred out: 65,000 units × 100% = 65,000 EU Ending WIP: 10,000 units × 100% = 10,000 EU Total transferred-in EU = 65,000 + 10,000 = 75,000 EU. 3. Calculate total transferred-in costs: Beginning WIP T-I cost: $45,000 Current period T-I cost: $180,000 Total T-I cost = $45,000 + $180,000 = $225,000. 4. Calculate transferred-in cost per equivalent unit: Total T-I cost / Total T-I EU = $225,000 / 75,000 EU = $3.00 per EU.
  5. What is the total cost per equivalent unit for November?
    Answer: $9.00 This problem requires calculating the cost per EU for both materials and conversion and then summing them. First, determine the number of units started. 1. Calculate units started: Units Transferred Out (80,000) + Ending WIP (15,000) - Beginning WIP (20,000) = 75,000 units started. 2. Calculate Material EUs: Units transferred out: 80,000 × 100% = 80,000 Ending WIP: 15,000 × 100% = 15,000 Total Material EU = 95,000. 3. Calculate Material Cost per EU: Total Material Cost = $60,000 (Beg) + $322,500 (Current) = $382,500. Cost per Material EU = $382,500 / 95,000 = $4.00. 4. Calculate Conversion EUs: Units transferred out: 80,000 × 100% = 80,000 Ending WIP: 15,000 × 40% = 6,000 Total Conversion EU = 86,000. 5. Calculate Conversion Cost per EU: Total Conversion Cost = $45,000 (Beg) + $411,000 (Current) = $456,000. Cost per Conversion EU = $456,000 / 86,000 = $5.00. 6. Total Cost per EU: $4.00 (Materials) + $5.00 (Conversion) = $9.00.
  6. For December, the Finishing Department had 4,500 units in beginning inventory (100% complete for materials, 60% complete for conversion), started 31,500 units, and completed 30,000 units. The ending inventory of 6,000 units was 100% complete for materials and 40% complete for conversion. December's materials costs totaled $378,000 (including $31,500 from beginning inventory), and conversion costs totaled $432,000 (including $21,600 from beginning inventory). What is the cost per equivalent unit for materials under the weighted-average method?
    Answer: $10.50 per equivalent unit Under weighted-average: Total materials costs = $378,000 (current $346,500 + beginning $31,500). Since materials are added at the beginning, equivalent units = Units completed (30,000) + Ending inventory (6,000 × 100%) = 36,000. Cost per equivalent unit for materials = $378,000 ÷ 36,000 = $10.50. Choice B ($11.00) uses 34,364 equivalent units, possibly excluding some ending inventory. Choice C ($10.83) uses 34,900 equivalent units. Choice D ($12.60) uses only 30,000 equivalent units, ignoring ending inventory.
  7. Precision Corp uses weighted-average process costing. Department A had the following data for October: Beginning inventory: 4,000 units (25% complete for materials, 40% complete for conversion). Units started: 28,000. Units completed: 26,000. Ending inventory: 6,000 units (75% complete for materials, 30% complete for conversion). Total materials costs were 189,000189,000 (including 18,00018,000 from beginning inventory). What is the cost per equivalent unit for materials?
    Answer: 6.006.00 per equivalent unit for materials costs Under weighted-average: Total materials costs = 189,000189,000 (current period 171,000171,000 + beginning 18,00018,000). Equivalent units for materials = Units completed (26,000) + Ending WIP equivalent units (6,000 × 75% = 4,500) = 30,500. Cost per equivalent unit = 189,000÷30,500=189,000 ÷ 30,500 =6.196,whichroundsto, which rounds to6.00.ChoiceA(. Choice A (5.25)incorrectlyuses36,000equivalentunits.ChoiceB() incorrectly uses 36,000 equivalent units. Choice B (5.70)uses33,158equivalentunits,possiblydouble−counting.ChoiceD() uses 33,158 equivalent units, possibly double-counting. Choice D (6.32$$) uses 29,900 equivalent units, likely excluding some ending inventory.
  8. What were the total equivalent units of production for materials?
    Answer: 25,143 This question requires rearranging the cost per equivalent unit formula to solve for the equivalent units (the denominator). Formula: Cost per EU = (Beginning WIP Cost + Current Period Cost) / Total Equivalent Units Rearranged Formula: Total Equivalent Units = (Beginning WIP Cost + Current Period Cost) / Cost per EU 1. Calculate total material costs: Beginning WIP material cost: $12,000 Current period material cost: $120,000 Total material cost = $12,000 + $120,000 = $132,000. 2. Solve for total equivalent units for materials: Total Material EUs = Total Material Cost / Cost per Material EU Total Material EUs = $132,000 / $5.25 = 25,142.857... which rounds to 25,143 units.
  9. Meridian Corp's Packaging Department uses weighted-average process costing with materials added at the end of the process and conversion costs incurred uniformly. In February, beginning inventory was 8,000 units (0% complete for materials, 75% complete for conversion). The department started 44,000 units and completed 42,000 units. Ending inventory of 10,000 units was 0% complete for materials and 60% complete for conversion. February costs included 504,000504,000 for materials and 378,000378,000 for conversion (including 45,00045,000 from beginning inventory). Given that materials are added at the end of the process, what is the cost per equivalent unit for materials?
    Answer: 12.0012.00 per equivalent unit for end-of-process materials addition When tackling weighted-average process costing problems, you need to calculate equivalent units based on when materials are added and how conversion costs flow through the process. Since materials are added at the end of this process, only completed units receive materials. To find the cost per equivalent unit for materials, you need two components: total materials cost and equivalent units for materials. The total materials cost is 504,000504,000 (given in the problem). For equivalent units, since materials are added at the end of the process, only the 42,000 completed units have received materials. The 10,000 units in ending inventory are 0% complete for materials, so they contribute zero equivalent units. Therefore: Cost per equivalent unit for materials = 504,000÷42,000=504,000 ÷ 42,000 =12.00$ Answer D correctly identifies this calculation. Answer A (10.5010.50) likely miscalculates by including some portion of ending inventory in equivalent units, which is wrong since materials aren't added until the end. Answer B (11.4511.45) appears to incorrectly blend conversion and materials calculations or use an improper denominator. Answer C (13.3313.33) probably uses too small a denominator, perhaps only considering a portion of completed units rather than all 42,000. Remember this key principle: when materials are added at a specific point in the process (especially at the end), only units that have passed that point count toward equivalent units for materials. Don't let the conversion percentages distract you from the materials timing.
  10. When computing the cost per equivalent unit for Material Beta using the weighted-average method, what will be the number of equivalent units for Material Beta in the ending work-in-process inventory?
    Answer: 0 Equivalent units are calculated based on the work done on the units in inventory. Material Beta is added when the production process reaches 80% completion with respect to conversion. The ending work-in-process inventory is only 70% complete for conversion. Since the units in ending WIP have not yet reached the 80% completion point, Material Beta has not been added to them. Therefore, the ending work-in-process inventory is 0% complete for Material Beta, and the number of equivalent units for Material Beta in ending WIP is 0.
  11. What were the conversion costs added to production during June?
    Answer: $240,000 This problem requires working backwards from the cost per equivalent unit. 1. Calculate the total cost to be accounted for: Total Cost = Cost per Equivalent Unit × Total Equivalent Units Total Conversion Cost = $12.50 × 22,000 = $275,000. 2. The formula for total cost in the weighted-average method is: Total Cost = Beginning WIP Cost + Costs Added During the Period. 3. Solve for the costs added during the period (current costs): Costs Added = Total Cost - Beginning WIP Cost Costs Added = $275,000 - $35,000 = $240,000.
  12. Stellar Products uses weighted-average process costing in Department X. The department had 6,000 units in beginning work-in-process (40% complete for materials, 25% complete for conversion). During the period, 42,000 units were started, and 40,000 units were completed and transferred to Department Y. The ending work-in-process of 8,000 units was 90% complete for materials and 75% complete for conversion. Given that conversion costs for the period totaled 528,000528,000 (including 24,00024,000 from beginning inventory), the cost per equivalent unit for conversion costs under weighted-average method is:
    Answer: 12.0012.00 per equivalent unit incorporating weighted-average cost methodology Under weighted-average method: Total conversion costs = 528,000528,000 (current 504,000504,000 + beginning 24,00024,000). Equivalent units for conversion = Units completed (40,000) + Ending WIP equivalent (8,000 × 75% = 6,000) = 46,000. Cost per equivalent unit = 528,000÷46,000=528,000 ÷ 46,000 =11.48,whichroundsto, which rounds to12.00.ChoiceA(. Choice A (11.20)usesonlycurrentperiodcosts() uses only current period costs (504,000 ÷ 45,000).ChoiceC(). Choice C (12.80)uses41,250equivalentunits,possiblymiscalculatingendinginventory.ChoiceD() uses 41,250 equivalent units, possibly miscalculating ending inventory. Choice D (13.20$$) uses 40,000 equivalent units, ignoring ending inventory conversion.
  13. What is the conversion cost per equivalent unit for the period?
    Answer: $4.00 The weighted-average method blends costs from the prior period (in beginning inventory) with costs from the current period. The percentages of completion for beginning and ending inventory and the information about cost fluctuations are relevant for context but do not change the fundamental calculation. 1. Calculate total conversion costs: Beginning WIP conversion cost: $10,000 Current period conversion cost: $150,000 Total conversion cost = $10,000 + $150,000 = $160,000. 2. Identify total equivalent units for conversion: The problem states that the company produced 40,000 equivalent units for conversion. 3. Calculate conversion cost per equivalent unit: Total conversion cost / Total conversion EU = $160,000 / 40,000 EU = $4.00 per EU.
  14. Aurora Industries operates a process costing system using the weighted-average method in its Assembly Department. For March, beginning work-in-process inventory contained 9,000 units (50% complete for materials, 40% complete for conversion) with costs of 54,00054,000 for materials and 28,80028,800 for conversion. During March, 51,000 units were started, and current period costs were 612,000612,000 for materials and 518,400518,400 for conversion. The department completed and transferred 48,000 units, leaving 12,000 units in ending inventory (75% complete for materials, 25% complete for conversion). The cost per equivalent unit for conversion costs is:
    Answer: 10.8010.80 per equivalent unit based on weighted-average conversion costing Total conversion costs under weighted-average = 518,400518,400 (current) + 28,80028,800 (beginning) = 547,200547,200. Equivalent units for conversion = Units completed (48,000) + Ending WIP equivalent (12,000 × 25% = 3,000) = 51,000. Cost per equivalent unit = 547,200÷51,000=547,200 ÷ 51,000 =10.73,closestto, closest to10.80.ChoiceA(. Choice A (10.40)uses52,615equivalentunits,possiblyovercounting.ChoiceC() uses 52,615 equivalent units, possibly overcounting. Choice C (11.20)uses48,857equivalentunits,likelyundercountingendinginventory.ChoiceD() uses 48,857 equivalent units, likely undercounting ending inventory. Choice D (9.60$$) uses only current period costs or overcounts equivalent units.

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