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Sagot :
To determine the cost per equivalent unit for the Assembly Department's direct materials and conversion costs, and the total unit cost for the current period, we need to consider both the Weighted-Average method and the FIFO method.
### 1. Weighted-Average Method
#### Step-by-Step Solution:
1. Compute the total units to account for:
[tex]\[ \text{Total units} = \text{Beginning WIP units} + \text{Started in June units} \][/tex]
[tex]\[ \text{Total units} = 35,000 + 230,000 = 265,000 \][/tex]
2. Compute the equivalent units for direct materials:
[tex]\[ \text{Equivalent units for materials} = \text{Completed and transferred out units} + (\text{Ending WIP units} \times \text{Ending material completion percent}) \][/tex]
[tex]\[ \text{Equivalent units for materials} = 225,000 + (40,000 \times 0.75) = 225,000 + 30,000 = 255,000 \][/tex]
3. Compute the equivalent units for conversion costs:
[tex]\[ \text{Equivalent units for conversion} = \text{Completed and transferred out units} + (\text{Ending WIP units} \times \text{Ending conversion completion percent}) \][/tex]
[tex]\[ \text{Equivalent units for conversion} = 225,000 + (40,000 \times 0.25) = 225,000 + 10,000 = 235,000 \][/tex]
4. Compute the total costs:
[tex]\[ \text{Total material cost} = \text{Beginning material cost} + \text{Current period material cost} \][/tex]
[tex]\[ \text{Total material cost} = 183,600 + 1,346,400 = 1,530,000 \][/tex]
[tex]\[ \text{Total conversion cost} = \text{Beginning conversion cost} + \text{Current period conversion cost} \][/tex]
[tex]\[ \text{Total conversion cost} = 65,800 + 874,200 = 940,000 \][/tex]
5. Compute the cost per equivalent unit:
[tex]\[ \text{Cost per equivalent unit for materials} = \frac{\text{Total material cost}}{\text{Equivalent units for materials}} \][/tex]
[tex]\[ \text{Cost per equivalent unit for materials} = \frac{1,530,000}{255,000} = 6.00 \][/tex]
[tex]\[ \text{Cost per equivalent unit for conversion} = \frac{\text{Total conversion cost}}{\text{Equivalent units for conversion}} \][/tex]
[tex]\[ \text{Cost per equivalent unit for conversion} = \frac{940,000}{235,000} = 4.00 \][/tex]
6. Compute the total unit cost:
[tex]\[ \text{Total unit cost} = \text{Cost per equivalent unit for materials} + \text{Cost per equivalent unit for conversion} \][/tex]
[tex]\[ \text{Total unit cost} = 6.00 + 4.00 = 10.00 \][/tex]
### 2. FIFO Method
#### Step-by-Step Solution:
1. Compute the units started and completed during the period:
[tex]\[ \text{Units started and completed} = \text{Completed and transferred out units} - \text{Beginning WIP units} \][/tex]
[tex]\[ \text{Units started and completed} = 225,000 - 35,000 = 190,000 \][/tex]
2. Compute the equivalent units for direct materials:
[tex]\[ \text{Equivalent units for materials} = \text{Units started and completed} + (\text{Ending WIP units} \times \text{Ending material completion percent}) \][/tex]
[tex]\[ \text{Equivalent units for materials} = 190,000 + (40,000 \times 0.75) = 190,000 + 30,000 = 220,000 \][/tex]
3. Compute the equivalent units for conversion costs:
[tex]\[ \text{Equivalent units for conversion} = (\text{Beginning WIP units} \times (1 - \text{Beginning conversion completion percent})) + \text{Units started and completed} + (\text{Ending WIP units} \times \text{Ending conversion completion percent}) \][/tex]
[tex]\[ \text{Equivalent units for conversion} = (35,000 \times (1 - 0.40)) + 190,000 + (40,000 \times 0.25) \][/tex]
[tex]\[ \text{Equivalent units for conversion} = (35,000 \times 0.60) + 190,000 + 10,000 \][/tex]
[tex]\[ \text{Equivalent units for conversion} = 21,000 + 190,000 + 10,000 = 221,000 \][/tex]
4. Compute the costs added during the current period:
[tex]\[ \text{Added material cost} = \text{Current period material cost} = 1,346,400 \][/tex]
[tex]\[ \text{Added conversion cost} = \text{Current period conversion cost} = 874,200 \][/tex]
5. Compute the cost per equivalent unit:
[tex]\[ \text{Cost per equivalent unit for materials} = \frac{\text{Added material cost}}{\text{Equivalent units for materials}} \][/tex]
[tex]\[ \text{Cost per equivalent unit for materials} = \frac{1,346,400}{220,000} = 6.12 \][/tex]
[tex]\[ \text{Cost per equivalent unit for conversion} = \frac{\text{Added conversion cost}}{\text{Equivalent units for conversion}} \][/tex]
[tex]\[ \text{Cost per equivalent unit for conversion} = \frac{874,200}{221,000} = 3.96 \][/tex]
6. Compute the total unit cost:
[tex]\[ \text{Total unit cost} = \text{Cost per equivalent unit for materials} + \text{Cost per equivalent unit for conversion} \][/tex]
[tex]\[ \text{Total unit cost} = 6.12 + 3.96 = 10.08 \][/tex]
### Summary:
- Weighted-Average Method:
- Cost per equivalent unit for materials: [tex]\(6.00\)[/tex]
- Cost per equivalent unit for conversion: [tex]\(4.00\)[/tex]
- Total unit cost: [tex]\(10.00\)[/tex]
- FIFO Method:
- Cost per equivalent unit for materials: [tex]\(6.12\)[/tex]
- Cost per equivalent unit for conversion: [tex]\(3.96\)[/tex]
- Total unit cost: [tex]\(10.08\)[/tex]
### 1. Weighted-Average Method
#### Step-by-Step Solution:
1. Compute the total units to account for:
[tex]\[ \text{Total units} = \text{Beginning WIP units} + \text{Started in June units} \][/tex]
[tex]\[ \text{Total units} = 35,000 + 230,000 = 265,000 \][/tex]
2. Compute the equivalent units for direct materials:
[tex]\[ \text{Equivalent units for materials} = \text{Completed and transferred out units} + (\text{Ending WIP units} \times \text{Ending material completion percent}) \][/tex]
[tex]\[ \text{Equivalent units for materials} = 225,000 + (40,000 \times 0.75) = 225,000 + 30,000 = 255,000 \][/tex]
3. Compute the equivalent units for conversion costs:
[tex]\[ \text{Equivalent units for conversion} = \text{Completed and transferred out units} + (\text{Ending WIP units} \times \text{Ending conversion completion percent}) \][/tex]
[tex]\[ \text{Equivalent units for conversion} = 225,000 + (40,000 \times 0.25) = 225,000 + 10,000 = 235,000 \][/tex]
4. Compute the total costs:
[tex]\[ \text{Total material cost} = \text{Beginning material cost} + \text{Current period material cost} \][/tex]
[tex]\[ \text{Total material cost} = 183,600 + 1,346,400 = 1,530,000 \][/tex]
[tex]\[ \text{Total conversion cost} = \text{Beginning conversion cost} + \text{Current period conversion cost} \][/tex]
[tex]\[ \text{Total conversion cost} = 65,800 + 874,200 = 940,000 \][/tex]
5. Compute the cost per equivalent unit:
[tex]\[ \text{Cost per equivalent unit for materials} = \frac{\text{Total material cost}}{\text{Equivalent units for materials}} \][/tex]
[tex]\[ \text{Cost per equivalent unit for materials} = \frac{1,530,000}{255,000} = 6.00 \][/tex]
[tex]\[ \text{Cost per equivalent unit for conversion} = \frac{\text{Total conversion cost}}{\text{Equivalent units for conversion}} \][/tex]
[tex]\[ \text{Cost per equivalent unit for conversion} = \frac{940,000}{235,000} = 4.00 \][/tex]
6. Compute the total unit cost:
[tex]\[ \text{Total unit cost} = \text{Cost per equivalent unit for materials} + \text{Cost per equivalent unit for conversion} \][/tex]
[tex]\[ \text{Total unit cost} = 6.00 + 4.00 = 10.00 \][/tex]
### 2. FIFO Method
#### Step-by-Step Solution:
1. Compute the units started and completed during the period:
[tex]\[ \text{Units started and completed} = \text{Completed and transferred out units} - \text{Beginning WIP units} \][/tex]
[tex]\[ \text{Units started and completed} = 225,000 - 35,000 = 190,000 \][/tex]
2. Compute the equivalent units for direct materials:
[tex]\[ \text{Equivalent units for materials} = \text{Units started and completed} + (\text{Ending WIP units} \times \text{Ending material completion percent}) \][/tex]
[tex]\[ \text{Equivalent units for materials} = 190,000 + (40,000 \times 0.75) = 190,000 + 30,000 = 220,000 \][/tex]
3. Compute the equivalent units for conversion costs:
[tex]\[ \text{Equivalent units for conversion} = (\text{Beginning WIP units} \times (1 - \text{Beginning conversion completion percent})) + \text{Units started and completed} + (\text{Ending WIP units} \times \text{Ending conversion completion percent}) \][/tex]
[tex]\[ \text{Equivalent units for conversion} = (35,000 \times (1 - 0.40)) + 190,000 + (40,000 \times 0.25) \][/tex]
[tex]\[ \text{Equivalent units for conversion} = (35,000 \times 0.60) + 190,000 + 10,000 \][/tex]
[tex]\[ \text{Equivalent units for conversion} = 21,000 + 190,000 + 10,000 = 221,000 \][/tex]
4. Compute the costs added during the current period:
[tex]\[ \text{Added material cost} = \text{Current period material cost} = 1,346,400 \][/tex]
[tex]\[ \text{Added conversion cost} = \text{Current period conversion cost} = 874,200 \][/tex]
5. Compute the cost per equivalent unit:
[tex]\[ \text{Cost per equivalent unit for materials} = \frac{\text{Added material cost}}{\text{Equivalent units for materials}} \][/tex]
[tex]\[ \text{Cost per equivalent unit for materials} = \frac{1,346,400}{220,000} = 6.12 \][/tex]
[tex]\[ \text{Cost per equivalent unit for conversion} = \frac{\text{Added conversion cost}}{\text{Equivalent units for conversion}} \][/tex]
[tex]\[ \text{Cost per equivalent unit for conversion} = \frac{874,200}{221,000} = 3.96 \][/tex]
6. Compute the total unit cost:
[tex]\[ \text{Total unit cost} = \text{Cost per equivalent unit for materials} + \text{Cost per equivalent unit for conversion} \][/tex]
[tex]\[ \text{Total unit cost} = 6.12 + 3.96 = 10.08 \][/tex]
### Summary:
- Weighted-Average Method:
- Cost per equivalent unit for materials: [tex]\(6.00\)[/tex]
- Cost per equivalent unit for conversion: [tex]\(4.00\)[/tex]
- Total unit cost: [tex]\(10.00\)[/tex]
- FIFO Method:
- Cost per equivalent unit for materials: [tex]\(6.12\)[/tex]
- Cost per equivalent unit for conversion: [tex]\(3.96\)[/tex]
- Total unit cost: [tex]\(10.08\)[/tex]
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