Equivalent Units of Production - Managerial Accounting

1. What are the equivalent units of production for conversion costs for the month?
   Answer: 30,800 Under the FIFO method, equivalent units are based on work done in the current period only. The calculation has three components: 1. Work to complete beginning WIP: 8,000 units were 70% complete, so 30% of the work remains. EUP = 8,000 × 30% = 2,400 units. 2. Units started and completed: Total completed (34,000) - Beginning WIP (8,000) = 26,000 units. These are 100% worked on this period, so EUP = 26,000 units. 3. Work done on ending WIP: 6,000 units × 40% = 2,400 units. Total equivalent units for conversion costs = 2,400 + 26,000 + 2,400 = 30,800 units.
2. What are the equivalent units of production for direct materials for June?
   Answer: 90,000 Under the weighted-average method, equivalent units for materials are the sum of units completed and transferred out and the equivalent units in ending WIP. Since materials are added at the beginning of the process, any unit in ending WIP is 100% complete with respect to materials. 1. Units completed and transferred out: 70,000 units. These are fully complete for materials. 2. Equivalent units in ending WIP for materials: 20,000 units * 100% (since materials are added at the start) = 20,000 units. 3. Total EUP for materials: 70,000 + 20,000 = 90,000 units. Distractor A is incorrect. This is the number of units started during the period (75,000). Distractor C is incorrect. This result represents the equivalent units for conversion costs: 70,000 + (20,000 * 30%) = 76,000. Distractor D is incorrect. This result is obtained by using the FIFO method for materials: (15,000 0% to complete) + (55,000 started and completed) + (20,000 100% in EWIP) = 0 + 55,000 + 20,000 = 75,000. The value 85,000 comes from (70,000 completed) + (15,000 BWIP), an incorrect calculation.
3. What are the equivalent units for direct materials for June?
   Answer: 30,000 Under the weighted-average method, EUP = (Units Transferred Out) + (Equivalent Units in Ending WIP). 1. Units Transferred Out: 25,000 units. These are 100% complete for materials because they passed the 50% addition point. 2. Equivalent Units in Ending WIP: 5,000 units are 80% complete. Since this is past the 50% point where materials are added, these units have received all their materials. Therefore, they are 100% complete for materials. EUP = 5,000 * 100% = 5,000. 3. Total EUP for materials: 25,000 + 5,000 = 30,000 units. Distractor A is incorrect. This calculation (25,000) completely ignores the units in ending WIP. Distractor B is incorrect. This represents the equivalent units for conversion costs: 25,000 + (5,000 * 80%) = 29,000. Distractor D is incorrect. This result (20,000) might come from incorrectly assuming the 10,000 units in beginning WIP (40% complete) did not receive materials last period and subtracting them from the units transferred out.
4. In October, the Purification Department had 6,000 units in beginning work-in-process inventory that were 80% complete for materials and 60% complete for conversion costs. During the month, 28,000 units were received from the previous department, and 30,000 units were completed and transferred to finished goods. The ending work-in-process inventory consisted of 4,000 units that were 90% complete for materials and 45% complete for conversion costs. Materials are added continuously throughout the purification process, and conversion costs are incurred uniformly. What are the equivalent units of production for materials using the weighted-average method?
   Answer: $33,600$ equivalent units Under weighted-average method, equivalent units = Units completed and transferred + (Ending WIP × % complete for materials). Units completed and transferred = 30,000. Ending WIP equivalent units for materials = 4,000 × 90% = 3,600. Total equivalent units for materials = 30,000 + 3,600 = 33,600. Choice B incorrectly uses a different percentage. Choice C ignores the percentage completion of ending WIP. Choice D includes all units without considering completion percentages.
5. What are the equivalent units for direct materials?
   Answer: 22,000 Under FIFO, we calculate work done this period. Materials are added at 25% completion. 1. Work on beginning WIP: The 5,000 beginning units were 40% complete. This means they passed the 25% material addition point in the prior period. Thus, 0% of material work was done this period. EUP = 5,000 * 0% = 0. 2. Units started and completed: Total completed = 27,000. BWIP = 5,000. So, units started and completed = 27,000 - 5,000 = 22,000. These units were started and fully completed, so they received 100% of their materials this period. EUP = 22,000. 3. Work on ending WIP: The 8,000 ending units are 20% complete. They have not yet reached the 25% material addition point. Therefore, 0% of material work has been done on them. EUP = 8,000 * 0% = 0. 4. Total EUP for materials: 0 + 22,000 + 0 = 22,000 units. Distractor A is incorrect. This is the number of units started (30,000). This would be the EUP if materials were added at the beginning of the process. Distractor C is incorrect. This is the number of units completed (27,000). This would be the EUP if all ending WIP units had passed the material addition point. Distractor D is incorrect. This is the weighted-average EUP: 27,000 completed (all past 25%) + 8,000 EWIP (not past 25%) = 27,000 + 0 = 27,000. 35,000 is total physical units.
6. What are the equivalent units of production for materials?
   Answer: 9,000 First, determine the number of units completed. Units to account for = 2,000 BWIP + 10,000 started = 12,000. Units completed = 12,000 - 3,000 EWIP = 9,000. Materials are added at the end of the process (i.e., at 100% completion). Under FIFO, we only count work done this period. 1. Work on beginning WIP: 2,000 units. These units were completed this period, so they reached 100% completion. Thus, they received their materials this period. EUP = 2,000 * 100% = 2,000. 2. Units started and completed: 9,000 total completed - 2,000 from BWIP = 7,000. These were also completed and thus received their materials this period. EUP = 7,000 * 100% = 7,000. 3. Work on ending WIP: 3,000 units. These are only 70% complete. They have not reached the end of the process, so they have received 0% of their materials. EUP = 3,000 * 0% = 0. 4. Total EUP for materials: 2,000 + 7,000 + 0 = 9,000 units. This is simply the number of units completed during the period. Distractor A is incorrect. This is the total number of physical units to account for. Distractor B is incorrect. This is the number of units started. Distractor D is incorrect. This is the weighted-average EUP for materials (9,000 completed + 0 from EWIP = 9,000). The value 11,000 is a miscalculation.
7. What was the percentage of completion for conversion costs in the ending work-in-process inventory?
   Answer: 50% The formula for weighted-average equivalent units is: EUP = (Units Transferred Out) + (Ending WIP Units * % Completion). We are given: - Total EUP = 45,000 - Units Transferred Out = 40,000 - Ending WIP Units = 10,000 We need to solve for the percentage of completion (let's call it P): 45,000 = 40,000 + (10,000 * P) 5,000 = 10,000 * P P = 5,000 / 10,000 P = 0.50 or 50%. Distractor B is incorrect. This would imply total EUP of 40,000 + 10,000 = 50,000. Distractor C is incorrect. This result comes from incorrectly dividing total EUP by total units accounted for or a similar misstep, such as 45,000 / (40,000 + 10,000) = 0.90, or dividing EUP in EWIP by total EUP: 5,000/45,000. The 45% is likely derived from dividing total EUP by ending WIP physical units (45,000/10,000) which has no meaning. Distractor D is incorrect. This would imply EUP in ending WIP of 7,500 and total EUP of 47,500.
8. How many physical units were in the ending work-in-process inventory?
   Answer: 5,000 Transferred-in costs are always considered 100% complete for any unit that has entered a department. The EUP calculation for transferred-in costs under the weighted-average method is: EUP = (Units Transferred Out) + (Physical units in Ending WIP * 100%). We are given: - EUP for Transferred-in = 60,000 - Units Transferred Out = 55,000 We can solve for the physical units in Ending WIP (EWIP): 60,000 = 55,000 + (EWIP * 100%) 60,000 = 55,000 + EWIP EWIP = 5,000 physical units. The information about conversion and material completion percentages is extraneous. Distractor A is incorrect. If EWIP were 10,000 units, the transferred-in EUP would be 55,000 + 10,000 = 65,000. Distractor C is incorrect. This result (2,500) might be obtained by incorrectly applying the 50% conversion completion rate to the calculation: 5,000 physical units * 50%. Distractor D is incorrect. The information is sufficient to solve the problem.
9. What is the difference between the equivalent units calculated under the FIFO method and the weighted-average method for conversion costs?
   Answer: 2,000 The difference between equivalent units under the weighted-average method and the FIFO method is always equal to the equivalent units of work already performed on the beginning work-in-process inventory. Difference = Beginning WIP physical units * Percentage of completion Difference = 8,000 units * 25% Difference = 2,000 equivalent units. The weighted-average method will have 2,000 more equivalent units than the FIFO method because it includes this prior-period work in its calculation. Distractor A is incorrect. This represents the equivalent units in the ending WIP inventory (5,000 units * 60%). Distractor C is incorrect. This represents the work needed to complete the beginning WIP (8,000 units * 75% = 6,000). Distractor D is incorrect. This is the number of physical units in the ending WIP.
10. Delta Dynamics operates a process costing system in its Fabrication Department, where three different materials are added at specific points and conversion costs are incurred uniformly. Material A is added at the beginning (0% complete), Material B when units reach 30% completion, and Material C when units are 80% complete. At the end of the current period, the department had 7,200 units in ending work-in-process that were 50% complete and 2,800 units in ending work-in-process that were 85% complete. Using the weighted-average method, what are the equivalent units for Material B from the ending work-in-process inventory only?
    Answer: $10,000$ equivalent units Material B is added when units reach 30% completion. For ending WIP: Units at 50% completion have passed the 30% addition point, so all 7,200 units are 100% complete for Material B. Units at 85% completion have also passed the 30% point, so all 2,800 units are 100% complete for Material B. Total equivalent units for Material B from ending WIP = (7,200 × 100%) + (2,800 × 100%) = 7,200 + 2,800 = 10,000. Choice A only counts the 85% complete units. Choice B only counts the 50% complete units. Choice C applies completion percentages incorrectly.
11. What are the total equivalent units for conversion costs for November?
    Answer: 60,000 Under the weighted-average method, the calculation for equivalent units is straightforward: it combines work from the prior period with work from the current period. 1. Units completed and transferred out: These units are considered 100% complete, regardless of when the work was done. EUP = 48,000 units. 2. Equivalent units in ending WIP: 15,000 physical units * 80% completion = 12,000 EUP. 3. Total EUP for conversion: 48,000 + 12,000 = 60,000 units. The information about beginning WIP (12,000 units, 20% complete) is irrelevant for the weighted-average EUP calculation. Distractor B is incorrect. This result (57,600) is calculated using the FIFO method: (12,000 BWIP 80% to complete) + (36,000 started & completed) + (15,000 EWIP 80%) = 9,600 + 36,000 + 12,000 = 57,600. Distractor C is incorrect. This is a miscalculation, perhaps from an arithmetic error in calculating the ending WIP EUP. Distractor D is incorrect. This only includes the units completed and transferred out, ignoring the work done on the ending work-in-process inventory.
12. What are the equivalent units for conversion costs?
    Answer: 18,600 First, account for physical units: 20,000 started = 16,000 completed + 3,000 EWIP + 1,000 spoiled units. Under weighted-average, equivalent units include work done on all units, including spoiled units. 1. Units completed and transferred out: 16,000 units × 100% = 16,000 EUP. 2. Equivalent units in ending WIP: 3,000 units × 60% = 1,800 EUP. 3. Equivalent units for normal spoilage: The 1,000 spoiled units reached the 80% inspection point. Work done = 1,000 units × 80% = 800 EUP. 4. Total EUP for conversion: 16,000 + 1,800 + 800 = 18,600 units.
13. How many physical units were completed and transferred out of the Polishing Department in July?
    Answer: 52,000 This problem requires working backward. The formula for weighted-average EUP is: Total EUP = (Units Transferred Out) + (Equivalent Units in Ending WIP). First, calculate the equivalent units in ending WIP: EUP in EWIP = 8,000 physical units * 75% completion = 6,000 EUP. Now, plug the known values into the formula and solve for Units Transferred Out (T/O): 58,000 (Total EUP) = T/O + 6,000 (EUP in EWIP) T/O = 58,000 - 6,000 T/O = 52,000 units. Distractor A is incorrect. This is the number of units started during the period (50,000). Distractor B is incorrect. This result might come from an arithmetic error, such as subtracting the full physical units in EWIP (58,000 - 10,000 = 48,000). Distractor D is incorrect. This is the total number of physical units to account for (10,000 BWIP + 50,000 Started = 60,000).
14. How many physical units were in the beginning work-in-process inventory?
    Answer: 5,000 With materials added at the start, the FIFO EUP for materials equals the number of units started during the period. We can work backward to find the units started. 1. Given: FIFO EUP for materials = 40,000. Therefore, Units Started = 40,000. 2. We can use a physical unit reconciliation: Beginning WIP + Units Started = Units Completed + Ending WIP. 3. Let BWIP be the unknown. BWIP + 40,000 = 35,000 + 10,000. 4. BWIP + 40,000 = 45,000. 5. BWIP = 5,000 units. Distractor A is incorrect. This would imply 40,000 started = 35,000 completed + 10,000 EWIP, which is not possible. Distractor C is incorrect. This is the number of units in ending WIP. Distractor D is incorrect. If BWIP were 15,000, then 15,000 + 40,000 = 55,000 total units, which would not balance with 35,000 completed + 10,000 EWIP.
15. What are the equivalent units of production for materials in Department 2?
    Answer: 14,000 First, determine the number of units completed and transferred out. Units to account for = 3,000 (BWIP) + 15,000 (Transferred In) = 18,000. Units completed = 18,000 - 4,000 (EWIP) = 14,000. Under the weighted-average method, EUP = (Units Transferred Out) + (EUP in Ending WIP). 1. Units Transferred Out: 14,000 units. These are 100% complete, so they passed the 90% point and have received all materials. EUP = 14,000. 2. Equivalent Units in Ending WIP: The 4,000 units in ending WIP are only 80% complete. They have not yet reached the 90% point where materials are added. Therefore, they are 0% complete with respect to materials. EUP = 4,000 * 0% = 0. 3. Total EUP for materials: 14,000 + 0 = 14,000 units. Distractor B is incorrect. This is the total number of physical units to account for (3,000 + 15,000). Distractor C is incorrect. This is the number of units transferred in during the period. Distractor D is incorrect. This incorrectly assumes that because ending WIP has 0 EUP for materials, the total EUP is 0.
16. How many units were started and completed during the period?
    Answer: 12,000 This question requires a calculation that is a key component of the FIFO EUP computation. First, determine the total units completed and transferred out. Total units to account for = 5,000 (BWIP) + 20,000 (Started) = 25,000 units. Units completed = Total units to account for - Ending WIP units = 25,000 - 8,000 = 17,000 units. Second, determine how many of the completed units were started this period. Units started and completed = Total units completed - Units from beginning WIP Units started and completed = 17,000 - 5,000 = 12,000 units. Distractor A is incorrect. This is the total number of units completed and transferred out (17,000). Distractor B is incorrect. This is the number of units started during the period (20,000). Distractor D is incorrect. This is the total number of physical units to account for (25,000).
17. What are the equivalent units for transferred-in costs in the Finishing department for June?
    Answer: 25,000 Transferred-in costs are treated as 100% complete as soon as the units enter the new department. Under the weighted-average method, the EUP calculation is (Units Transferred Out) + (EUP in Ending WIP). 1. First, find the number of units transferred out: Units to account for = 5,000 (BWIP) + 20,000 (Transferred In) = 25,000. Units transferred out = 25,000 - 4,000 (EWIP) = 21,000. 2. Units Transferred Out: 21,000 units are 100% complete for transferred-in costs. 3. Equivalent Units in Ending WIP: 4,000 units are 100% complete for transferred-in costs. EUP = 4,000 * 100% = 4,000. 4. Total EUP for transferred-in costs: 21,000 + 4,000 = 25,000 units. Distractor A is incorrect. This is the number of physical units completed and transferred out (21,000). Distractor B is incorrect. This is the number of units transferred in from Molding during the period. Distractor D is incorrect. This is the EUP for conversion costs: 21,000 + (4,000 * 60%) = 21,000 + 2,400 = 23,400. 24,000 is a close miscalculation.
18. For the Finishing Department, what are the equivalent units for transferred-in costs for March?
    Answer: 25,000 Transferred-in costs are treated like materials added at the very beginning of the process in the new department. Under the FIFO method, the equivalent units for a cost added at the beginning is always equal to the number of units started (or in this case, transferred in) during the period. 1. Work to complete beginning WIP: Transferred-in costs for BWIP were incurred in the prior period. So, work done this period is 0. EUP = 5,000 * 0% = 0. 2. Units started and completed: Total started = 25,000. Ending WIP = 8,000. So, units started and completed = 25,000 - 8,000 = 17,000. EUP = 17,000. 3. Work done on ending WIP: The 8,000 ending units were transferred in this period. EUP = 8,000. 4. Total EUP for transferred-in costs: 0 + 17,000 + 8,000 = 25,000. This is equal to the number of units transferred in during the month. Distractor B is incorrect. This is the number of units completed and transferred out: 5,000 (BWIP) + 17,000 (Started and Completed) = 22,000. Distractor C is incorrect. This represents the weighted-average EUP for transferred-in costs: 22,000 (completed) + 8,000 (EWIP * 100%) = 30,000. Distractor D is incorrect. This is the total number of physical units accounted for (5,000 BWIP + 25,000 T/I = 30,000 = 22,000 T/O + 8,000 EWIP). The value 33,000 is a miscalculation.
19. What were the equivalent units of production for conversion costs during the period?
    Answer: 29,400 Under the FIFO method, we calculate the work done in the current period. 1. Work to complete beginning WIP: 6,000 units were 60% complete, so 40% of the work was done this period. EUP = 6,000 * 0.40 = 2,400. 2. Units started and completed: 30,000 total units were completed. 6,000 of these were from beginning inventory. So, 30,000 - 6,000 = 24,000 units were started and completed this period. EUP = 24,000 * 1.00 = 24,000. 3. Work done on ending WIP: 10,000 units were 30% complete. EUP = 10,000 * 0.30 = 3,000. 4. Total EUP for conversion: 2,400 + 24,000 + 3,000 = 29,400 units. Distractor B is incorrect. This is the weighted-average EUP: 30,000 (completed) + (10,000 * 30%) = 33,000. Distractor C is incorrect. This is the number of units transferred out, which ignores the work in beginning and ending WIP. Distractor D is incorrect. This result (28,600) comes from incorrectly using the percentage complete for beginning WIP instead of the percentage to be completed: (6,000 60%) + 24,000 + (10,000 10%) miscalculation. Another path is (6,000 60%) + (24,000) + (3,000) = 30,600. A common error is (30,000 completed) - (6,000 60% BWIP done) + (10,000 30% EWIP) = 30,000 - 3,600 + 3,000 = 29,400. Let's recheck. (6,000 0.4) + (24,000) + (10,000*0.3) = 2400+24000+3000=29400. Okay, A is correct. 28,600 might come from 24,000 + (10,000 0.3) + (6000 0.6) - 6000. It is a plausible miscalculation.
20. How many units were started (or transferred in) and completed during the period, assuming there was no beginning inventory?
    Answer: 60,000 This problem can be solved using the EUP formula for either materials or conversion. Let's use materials. Weighted-Average EUP = Units Transferred Out + EUP in Ending WIP. EUP for Materials = 80,000. EUP in Ending WIP for Materials = 20,000 units * 100% = 20,000. So, 80,000 = Units Transferred Out + 20,000. Units Transferred Out = 60,000. Since there was no beginning inventory, the units transferred out are the same as the units started and completed. We can verify this with the conversion cost data: EUP for Conversion = 74,000. EUP in Ending WIP for Conversion = 20,000 units * 70% = 14,000. So, 74,000 = Units Transferred Out + 14,000. Units Transferred Out = 60,000. Both calculations yield the same result. Distractor B is incorrect. This is the total EUP for materials. Distractor C is incorrect. This is the total EUP for conversion costs. Distractor D is incorrect. This result (54,000) comes from subtracting the ending WIP EUP for conversion from the materials EUP (80,000 - 14,000 - 20,000) or a similar flawed combination.

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