Equivalent Units (Weighted-Average) - Cost Accounting

1. Using the weighted-average method, what are the equivalent units of production for transferred-in costs and materials, respectively?
   Answer: 40,000 and 32,000 Under the weighted-average method, we calculate EUP for each cost component based on units completed and ending WIP. 1. Transferred-in (TI) Costs: TI costs are always 100% complete for all units in the department from the moment they are transferred in. * Units completed: 32,000 EUP * Ending WIP: 8,000 EUP (since they are 100% complete for TI) * Total EUP for TI Costs = $32,000 + 8,000 = 40,000$ 2. Materials: Materials are added at the end of the process (100% completion). * Units completed: These units reached 100% completion, so they received all materials. EUP = 32,000. * Ending WIP: These units are only 25% complete. They have not reached the end of the process, so they have received 0% of the materials. EUP = $8,000 \times 0\% = 0$. * Total EUP for Materials = $32,000 + 0 = 32,000$ Therefore, the EUPs are 40,000 for transferred-in costs and 32,000 for materials. Distractor Rationale: * A: This incorrectly calculates TI EUP using the conversion percentage for ending WIP ($32,000 + 8,000 \times 25\% = 34,000$). * C: This correctly calculates TI EUP but incorrectly calculates materials EUP by applying the conversion percentage ($32,000 + 8,000 \times 25\% = 34,000$). * D: This uses the number of units transferred in during the period (35,000) for TI EUP, which is incorrect. It also correctly calculates materials EUP.
2. Under the weighted-average method, how many equivalent units of conversion costs were produced?
   Answer: 96,000 First, calculate the number of units completed. * Units Completed = Beginning WIP + Units Started - Ending WIP * Units Completed = $10,000 + 90,000 - 5,000 = 95,000$ units. Next, calculate the EUP for conversion costs. * Units completed: $95,000 \times 100\% = 95,000$ EUP. * Equivalent units in ending WIP: $5,000 \times 20\% = 1,000$ EUP. * Total EUP for conversion costs: $95,000 + 1,000 = 96,000$ EUP. Distractor Rationale: * A: This is the number of units started during the period. * B: This is the number of units completed, but it omits the equivalent units in the ending WIP. * D: This is the total number of physical units to be accounted for ($10,000 + 90,000$).
3. Using the weighted-average method, what are the equivalent units of production for materials?
   Answer: 240,000 The cost information is irrelevant for calculating equivalent units of production. 1. Calculate units completed and transferred out: Beginning WIP + Units started - Ending WIP $40,000 + 200,000 - 30,000 = 210,000$ units. 2. Calculate equivalent units for materials: * Units completed and transferred out: $210,000 \times 100\% = 210,000$ EUP * Equivalent units in ending WIP (100% complete for materials): $30,000 \times 100\% = 30,000$ EUP * Total EUP for materials: $210,000 + 30,000 = 240,000$ EUP. Distractor Rationale: * A: This is the number of units started during the period. * B: This is the number of units completed and transferred out, but it ignores the equivalent units in ending WIP. * D: This result might come from adding beginning and ending WIP to units started (40,000 + 200,000 + 30,000), which is an incorrect summation of physical units.
4. Using the weighted-average method, what are the total equivalent units for conversion costs?
   Answer: 46,000 First, determine the number of units in ending WIP. * Ending WIP = Beginning WIP + Units Started - Units Completed * Ending WIP = $0 + 50,000 - 40,000 = 10,000$ units. Next, calculate the EUP for conversion costs. * Units completed and transferred out: $40,000 \times 100\% = 40,000$ EUP. * Equivalent units in ending WIP: $10,000 \text{ units} \times 60\% = 6,000$ EUP. * Total EUP for conversion costs: $40,000 + 6,000 = 46,000$ EUP. Since there is no beginning inventory, the weighted-average and FIFO methods would produce the same result in this specific case. Distractor Rationale: * A: This represents only the units completed, ignoring the work done on the ending inventory. * B: This result might come from an incorrect calculation of ending WIP units as $50,000 - 40,000 - 6,000$ or some other error. Let's try $40,000 + 10,000 \times 40\% = 44,000$, using the complement of the completion percentage. * D: This represents the total physical units started, not the equivalent units of production.
5. Using the weighted-average method, what are the equivalent units of production for conversion costs?
   Answer: 33,000 First, determine the number of good units completed. * Total units to account for = $7,000 + 28,000 = 35,000$ * Good units completed = Total units - Ending WIP - Normal Spoilage = $35,000 - 5,000 - 2,000 = 28,000$ units. Next, calculate the EUP for conversion costs. * Good units completed (100% complete): $28,000 \times 100\% = 28,000$ EUP. * Normal spoilage (inspected at 50%): $2,000 \times 50\% = 1,000$ EUP. * Ending WIP (80% complete): $5,000 \times 80\% = 4,000$ EUP. Since ending WIP is past the inspection point, these units were inspected and found to be good. * Total EUP = $28,000 + 1,000 + 4,000 = 33,000$ EUP. Distractor Rationale: * A: This result is obtained by ignoring the spoilage EUP and also miscalculating the ending WIP EUP using the beginning percentage ($28,000 + 5,000 \times 25\% = 29,250$). That's not right. Let's try again. $28,000 + (5,000 \times 80\%) - (2,000 \times 50\%) = 31,000$. Subtracting spoilage EUP is a possible error. * B: This result is obtained by ignoring spoilage EUP: $28,000 + 4,000 = 32,000$. * D: This represents the total physical units to account for, not the equivalent units of production.
6. Using the weighted-average method, what are the equivalent units for transferred-in costs?
   Answer: 100,000 First, analyze the flow of physical units. * Units to account for = Beginning WIP + Units transferred in = $20,000 + 80,000 = 100,000$ units. * Units accounted for = Good units completed + Normal spoilage + Ending WIP * We are given Good units completed = 95,000 and Ending WIP = 0. * Therefore, Normal spoilage = $100,000 - 95,000 - 0 = 5,000$ units. Now, calculate the EUP for transferred-in (TI) costs. * Under weighted-average, TI costs are 100% complete for all units that entered the department. * The EUP calculation includes good units completed, spoilage, and ending WIP. * Good units completed: 95,000 EUP * Normal spoilage: 5,000 EUP (since they were in the process, they are 100% complete for TI costs) * Ending WIP: 0 EUP * Total EUP for TI Costs = $95,000 + 5,000 + 0 = 100,000$ EUP. Alternatively, for TI costs, the EUP under weighted-average is always the total units to be accounted for if there is no ending WIP, or the units transferred-in plus beginning WIP. Distractor Rationale: * A: This is the number of units transferred in during the period, ignoring beginning WIP and spoilage. * B: This is the number of good units completed, ignoring the spoiled units which also consumed transferred-in resources. * D: This includes an incorrect unit count, possibly from adding spoilage twice or miscalculating the number of spoiled units.
7. Using the weighted-average method, what are the equivalent units for packaging costs?
   Answer: 30,600 First, verify the physical unit flow. * Units to account for: $1,000 \text{ Beg WIP} + 30,000 \text{ TI} = 31,000$ * Units accounted for: $28,000 \text{ Completed} + 2,000 \text{ End WIP} + 1,000 \text{ Spoilage} = 31,000$. The flow is correct. Next, calculate EUP for packaging costs. * Units completed and transferred out (good units): 28,000 units, 100% complete = 28,000 EUP. * Normal spoilage (inspected at 100%): 1,000 units, 100% complete = 1,000 EUP. * Ending WIP: 2,000 units, 80% complete = $2,000 \times 0.80 = 1,600$ EUP. * Total EUP = $28,000 + 1,000 + 1,600 = 30,600$ EUP. Distractor Rationale: * A: This represents the sum of good completed units and spoiled units ($28,000 + 1,000$), ignoring ending WIP. * B: This ignores the spoiled units ($28,000 + 1,600 = 29,600$). This is a very common error. * D: This is the total number of physical units accounted for, not the equivalent units.
8. Using the weighted-average method, what are the equivalent units of production for conversion costs for April?
   Answer: 92,000 The weighted-average method combines work done in the prior period with work done in the current period. The calculation has two parts: units completed and transferred out, and units in ending work-in-process. 1. Calculate units completed and transferred out: Beginning WIP + Units started - Ending WIP $15,000 + 85,000 - 20,000 = 80,000$ units. 2. Calculate equivalent units: * Units completed and transferred out: $80,000 \text{ units} \times 100\% = 80,000$ EUP * Equivalent units in ending WIP: $20,000 \text{ units} \times 60\% = 12,000$ EUP * Total EUP for conversion costs: $80,000 + 12,000 = 92,000$ EUP. Distractor Rationale: * A: This is the number of units completed and transferred out, but it ignores the equivalent units in ending WIP. * B: This result comes from a common FIFO method error: $(15,000 \times (1-0.40)) + (80,000 - 15,000) + (20,000 \times 0.60) = 9,000 + 65,000 + 12,000 = 86,000$. * D: This represents the total physical units to be accounted for (15,000 + 85,000), not the equivalent units of production.
9. What are the equivalent units of production for materials?
   Answer: 90,000 Under the weighted-average method, EUP for materials is the sum of materials in units completed and materials in ending WIP. 1. Units completed and transferred out: 70,000 units. Since they are completed, they contain 100% of the required materials. EUP = 70,000. 2. Units in ending WIP: 20,000 units. Materials are added at the beginning of the process, so any unit in WIP, regardless of its conversion completion, is 100% complete for materials. EUP = $20,000 \times 100\% = 20,000$. 3. Total EUP for materials: $70,000 + 20,000 = 90,000$. Distractor Rationale: * A: This represents only the units completed and transferred out, ignoring the materials in the ending WIP. * B: This is the number of units started during the month, which is not the same as EUP. * C: This incorrectly applies the conversion cost percentage to the ending WIP for materials: $70,000 + (20,000 \times 75\%) - 12,000$? No. Maybe $70,000 + 12,000$ beginning units = 82,000. This is a plausible misstep of adding beginning physical units.
10. If the company needs to calculate cost per equivalent unit separately for materials and conversion costs, what is the difference between equivalent units for materials and equivalent units for conversion costs?
    Answer: 2,800 equivalent units difference Ending WIP = 12,000 + 38,000 - 42,000 = 8,000 units. EUP for materials = 42,000 + (8,000 × 75%) = 42,000 + 6,000 = 48,000. EUP for conversion = 42,000 + (8,000 × 40%) = 42,000 + 3,200 = 45,200. Difference = 48,000 - 45,200 = 2,800. Choice B uses 80% for materials ending WIP. Choice C uses 70% for materials ending WIP. Choice D uses 55% for materials ending WIP.
11. What must have been the work done on the beginning inventory, as measured in equivalent units for conversion costs, under the weighted-average method's perspective?
    Answer: 0 equivalent units This is a conceptual question about the weighted-average method. The weighted-average method does not distinguish between work done in the previous period on beginning inventory and work done in the current period. It blends them together. The formula EUP = Units Completed + EUP in Ending WIP implicitly treats all completed units as if they were 100% worked on during the current period for EUP calculation purposes. Therefore, from the perspective of the weighted-average EUP calculation itself, the work done on beginning inventory in the prior period is not separated and is effectively treated as zero; all work is presumed to be part of the current period's effort that resulted in a completed unit. The calculation confirms this: EUP = 20,000 (completed) + (5,000 $\times$ 40%) = 20,000 + 2,000 = 22,000. The calculation does not require any information about beginning inventory's prior-period work. Distractor Rationale: * B: This is the EUP of the ending inventory, not the beginning inventory. * C: A student might try to back-calculate a beginning WIP quantity and percentage, but the method's core assumption makes this irrelevant for the EUP calculation. * D: While specific details of beginning WIP (units, % complete) are not given, the conceptual answer about how weighted-average treats this work is determinable.
12. Given the information, what must have been the percentage of completion of the ending work-in-process for conversion costs?
    Answer: 50% The problem can be solved using the EUP formula and algebra. * Total EUP = (Units completed) + (Ending WIP units $\times$ % Complete) We are given: * Total EUP = 85,000 * Units completed = 75,000 * Ending WIP units = 20,000 Let 'P' be the percentage of completion for ending WIP. * $85,000 = 75,000 + (20,000 \times P)$ * $10,000 = 20,000 \times P$ * $P = 10,000 / 20,000 = 0.50$, or 50%. Distractor Rationale: * A: This percentage would result in a total EUP of $75,000 + (20,000 \times 0.25) = 80,000$. * C: This is the percentage completion of the beginning inventory, which is irrelevant information for this calculation. * D: This percentage would result in a total EUP of $75,000 + (20,000 \times 0.75) = 90,000$.
13. How many units were started in the Forming Department during June?
    Answer: 40,000 This problem requires working backwards using the physical unit flow equation. * Physical Unit Flow: Beginning WIP + Units Started = Units Completed + Ending WIP We are given: * Beginning WIP = 8,000 * Units Completed = 42,000 * Ending WIP = 6,000 Let 'S' be the units started. Substitute the known values into the equation: * $8,000 + S = 42,000 + 6,000$ * $8,000 + S = 48,000$ * $S = 48,000 - 8,000$ * $S = 40,000$ The information about EUP for materials (48,000) and conversion percentages is consistent with the data but not needed to find the number of units started. It can be used as a check: EUP Materials = 42,000 completed + (6,000 ending $\times$ 100%) = 48,000. Distractor Rationale: * A: This results from subtracting beginning WIP from units completed ($42,000 - 8,000 = 34,000$), which represents 'units started and completed'. * C: This is the total number of units accounted for ($42,000 + 6,000$), not the number of units started. * D: This is the sum of all units listed ($42,000 + 8,000$), a common error in handling the unit flow equation.
14. What are the equivalent units of production for materials in Department B for June?
    Answer: 28,750 equivalent units Ending WIP = 6,000 + 25,000 - 28,000 = 3,000 units. Since materials are added uniformly in Department B, EUP for materials = Units completed + (Ending WIP × % complete for materials) = 28,000 + (3,000 × 25%) = 28,000 + 750 = 28,750. Choice B uses 60% completion. Choice C ignores ending WIP. Choice D assumes 100% material completion for ending WIP.
15. Using the weighted-average method, what are the equivalent units for Material X and Material Y, respectively?
    Answer: 60,000 and 50,000 We need to calculate the EUP for each material separately. 1. Material X (added at 20% point): * Units completed (50,000) are 100% complete for Material X. * Ending WIP (10,000 units) is 70% complete. Since this is past the 20% addition point, these units are 100% complete for Material X. * Total EUP for X = $50,000 + (10,000 \times 100\%) = 60,000$. 2. Material Y (added at 80% point): * Units completed (50,000) are 100% complete for Material Y. * Ending WIP (10,000 units) is 70% complete. Since this is before the 80% addition point, these units are 0% complete for Material Y. * Total EUP for Y = $50,000 + (10,000 \times 0\%) = 50,000$. Distractor Rationale: * A: This ignores the EUP in ending WIP for Material X. * C: This correctly calculates EUP for X, but incorrectly calculates EUP for Y by applying the conversion completion percentage ($50,000 + 10,000 \times 70\% = 57,000$). * D: This incorrectly calculates EUP for X using the conversion percentage and correctly calculates EUP for Y.
16. Under the weighted-average method of process costing, which of the following best describes the calculation of equivalent units of production for a given cost component?
    Answer: The work done on units transferred out during the period, plus the work done on the ending inventory. The weighted-average method calculates equivalent units by summing two components: 1. All units transferred out are treated as 100% complete for the period, regardless of when they were started. This represents the work done on units transferred out. 2. The work done on the units that remain in ending work-in-process inventory, calculated as (Physical Units $\times$ Percent Complete). This corresponds directly to option B. Distractor Rationale: * A: This describes the calculation for the FIFO (First-In, First-Out) method, which separates the work done on beginning inventory from the work on units started and completed. * C: This is an incorrect description. It ignores beginning inventory and doesn't properly account for the completion stage of units. * D: This is an oversimplification. It incorrectly uses total physical units as a base rather than separating completed units and ending WIP.
17. A department's production for May resulted in 60,000 equivalent units for direct materials and 54,000 equivalent units for conversion costs using the weighted-average method. A total of 50,000 physical units were completed and transferred out. All materials are added at the start of the process. How many physical units were in the ending work-in-process inventory?
    Answer: 10,000 The information about material equivalent units is the key to solving this problem. * Total EUP for Materials = (Units completed) + (EUP in ending WIP for materials) Since materials are added at the beginning of the process, any unit in ending WIP is 100% complete with respect to materials. Let 'EWIP' be the number of physical units in ending WIP. * $60,000 = 50,000 + (\text{EWIP} \times 100\%)$ * $60,000 = 50,000 + \text{EWIP}$ * $\text{EWIP} = 10,000$ units. The information about conversion cost EUP can be used to determine the percentage of completion for conversion costs in ending WIP ($54,000 = 50,000 + (10,000 \times P)$ -> $4,000 = 10,000P$ -> $P=40\%$), but this is not required by the question. Distractor Rationale: * A: This is the number of equivalent units for conversion costs in the ending inventory ($54,000 - 50,000 = 4,000$), not the number of physical units. * B: This is the difference between the material EUP and conversion EUP ($60,000 - 54,000 = 6,000$), which is not the number of ending WIP units. * D: This might be an arithmetic error, for instance, adding the differences (10,000 + 4,000) instead of solving.
18. What are the total equivalent units of production for conversion costs for both products combined?
    Answer: 48,200 equivalent units For conversion costs under weighted-average: Product X: 27,000 completed + (4,000 ending × 40%) = 27,000 + 1,600 = 28,600. Product Y: 18,000 completed + (2,000 ending × 80%) = 18,000 + 1,600 = 19,600. Total EUP = 28,600 + 19,600 = 48,200. Choice A uses incorrect completion percentages. Choice C understates ending WIP conversion. Choice D assumes 100% completion for ending WIP.
19. What are the equivalent units of production for conversion costs for March?
    Answer: 51,000 equivalent units Under weighted-average method, EUP for conversion costs = Units completed + (Ending WIP × % complete). Units completed = 48,000. Ending WIP = Beginning WIP + Started - Completed = 8,000 + 45,000 - 48,000 = 5,000 units. EUP = 48,000 + (5,000 × 60%) = 48,000 + 3,000 = 51,000. Choice B ignores ending WIP. Choice C incorrectly uses beginning WIP completion percentage. Choice D uses only units started.
20. What was the percentage of completion for the ending work-in-process inventory with respect to conversion costs?
    Answer: 40% First, determine the number of physical units in ending WIP. * Ending WIP = Beginning WIP + Units started - Units completed * Ending WIP = $10,000 + 60,000 - 55,000 = 15,000$ units. Next, use the total EUP formula to solve for the unknown percentage completion (let's call it 'P'). * Total EUP = (Units completed) + (Ending WIP units $\times$ P) * $61,000 = 55,000 + (15,000 \times P)$ * Subtract 55,000 from both sides: $6,000 = 15,000 \times P$ * Solve for P: $P = 6,000 / 15,000 = 0.40$, or 40%. Distractor Rationale: * A: This is the percentage of completion for the beginning WIP, irrelevant for this calculation. * C: This result would be obtained if there were 12,000 units in ending WIP ($6,000 / 12,000 = 0.50$), possibly due to a calculation error in physical units. * D: This result might come from an algebraic error, such as inverting the division or miscalculating the EUP in ending WIP as 9,000 ($9,000 / 15,000 = 0.60$).

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