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Sagot :
Let's break down each part of the problem and provide detailed, step-by-step solutions.
### Step-by-Step Solution:
#### a. Calculate the number of units started and completed this period for the Forming department.
To find the number of units started and completed this period, we need to identify the units that began and finished during the same period. This can be calculated by subtracting the beginning work in process from the completed units.
Calculation
[tex]\[ \text{Units started and completed} = \text{Units completed and transferred out} - \text{Beginning work in process units} \][/tex]
Given:
[tex]\[ \text{Units completed and transferred out} = 295,000 \][/tex]
[tex]\[ \text{Beginning work in process units} = 25,000 \][/tex]
Therefore:
[tex]\[ \text{Units started and completed} = 295,000 - 25,000 = 270,000 \][/tex]
The number of units started and completed this period is 270,000 units.
#### b. Calculate the equivalent units of production for both direct materials and conversion for the Forming department.
Equivalent units of production (EUP) account for the work done on incomplete units. We consider both the completed units and the ending work in process inventory, adjusted by their percent completion.
Equivalent Units for Direct Materials (DM):
[tex]\[ \text{Equivalent units (DM)} = \text{Units completed and transferred out} + \text{(Ending work in process units} \times \text{ Percent completion for DM)} \][/tex]
Given:
[tex]\[ \text{Units completed and transferred out} = 295,000 \][/tex]
[tex]\[ \text{Ending work in process units} = 30,000 \][/tex]
[tex]\[ \text{Percent completion for DM in ending WIP} = 80.8\% \][/tex]
Therefore:
[tex]\[ \text{Equivalent units (DM)} = 295,000 + (30,000 \times 0.808) = 295,000 + 24,240 = 319,240 \][/tex]
Equivalent Units for Conversion (C):
[tex]\[ \text{Equivalent units (C)} = \text{Units completed and transferred out} + \text{(Ending work in process units} \times \text{ Percent completion for C)} \][/tex]
Given:
[tex]\[ \text{Units completed and transferred out} = 295,000 \][/tex]
[tex]\[ \text{Ending work in process units} = 30,000 \][/tex]
[tex]\[ \text{Percent completion for C in ending WIP} = 30.8\% \][/tex]
Therefore:
[tex]\[ \text{Equivalent units (C)} = 295,000 + (30,000 \times 0.308) = 295,000 + 9,240 = 304,240 \][/tex]
The equivalent units of production are 319,240 units for direct materials and 304,240 units for conversion.
#### c. Calculate the costs per equivalent unit of production for both direct materials and conversion for the Forming department.
First, we need to determine the total costs for direct materials and conversion by adding the beginning work-in-process costs to the costs added during the period. Then, we divide these total costs by the equivalent units of production calculated above.
Total Cost for Direct Materials (DM):
[tex]\[ \text{Total direct materials cost} = \text{Beginning direct materials cost} + \text{Added direct materials cost} \][/tex]
Given:
[tex]\[ \text{Beginning direct materials cost} = \$44,800 \][/tex]
[tex]\[ \text{Added direct materials cost} = \$896,700 \][/tex]
Therefore:
[tex]\[ \text{Total direct materials cost} = \$44,800 + \$896,700 = \$941,500 \][/tex]
Total Cost for Conversion (C):
[tex]\[ \text{Total conversion cost} = \text{Beginning conversion cost} + \text{Added conversion cost} \][/tex]
Given:
[tex]\[ \text{Beginning conversion cost} = \$15,300 \][/tex]
[tex]\[ \text{Added conversion cost} = \$1,231,200 \][/tex]
Therefore:
[tex]\[ \text{Total conversion cost} = \$15,300 + \$1,231,200 = \$1,246,500 \][/tex]
Cost per Equivalent Unit for Direct Materials (DM):
[tex]\[ \text{Cost per equivalent unit (DM)} = \frac{\text{Total direct materials cost}}{\text{Equivalent units (DM)}} \][/tex]
Therefore:
[tex]\[ \text{Cost per equivalent unit (DM)} = \frac{\$941,500}{319,240} \approx \$2.949 \][/tex]
Cost per Equivalent Unit for Conversion (C):
[tex]\[ \text{Cost per equivalent unit (C)} = \frac{\text{Total conversion cost}}{\text{Equivalent units (C)}} \][/tex]
Therefore:
[tex]\[ \text{Cost per equivalent unit (C)} = \frac{\$1,246,500}{304,240} \approx \$4.097 \][/tex]
The costs per equivalent unit of production are approximately [tex]$2.949 for direct materials and $[/tex]4.097 for conversion.
### Summary of Results:
- Units started and completed this period: 270,000 units
- Equivalent units of production:
- Direct Materials: 319,240 units
- Conversion: 304,240 units
- Cost per equivalent unit:
- Direct Materials: [tex]$2.949 - Conversion: $[/tex]4.097
### Step-by-Step Solution:
#### a. Calculate the number of units started and completed this period for the Forming department.
To find the number of units started and completed this period, we need to identify the units that began and finished during the same period. This can be calculated by subtracting the beginning work in process from the completed units.
Calculation
[tex]\[ \text{Units started and completed} = \text{Units completed and transferred out} - \text{Beginning work in process units} \][/tex]
Given:
[tex]\[ \text{Units completed and transferred out} = 295,000 \][/tex]
[tex]\[ \text{Beginning work in process units} = 25,000 \][/tex]
Therefore:
[tex]\[ \text{Units started and completed} = 295,000 - 25,000 = 270,000 \][/tex]
The number of units started and completed this period is 270,000 units.
#### b. Calculate the equivalent units of production for both direct materials and conversion for the Forming department.
Equivalent units of production (EUP) account for the work done on incomplete units. We consider both the completed units and the ending work in process inventory, adjusted by their percent completion.
Equivalent Units for Direct Materials (DM):
[tex]\[ \text{Equivalent units (DM)} = \text{Units completed and transferred out} + \text{(Ending work in process units} \times \text{ Percent completion for DM)} \][/tex]
Given:
[tex]\[ \text{Units completed and transferred out} = 295,000 \][/tex]
[tex]\[ \text{Ending work in process units} = 30,000 \][/tex]
[tex]\[ \text{Percent completion for DM in ending WIP} = 80.8\% \][/tex]
Therefore:
[tex]\[ \text{Equivalent units (DM)} = 295,000 + (30,000 \times 0.808) = 295,000 + 24,240 = 319,240 \][/tex]
Equivalent Units for Conversion (C):
[tex]\[ \text{Equivalent units (C)} = \text{Units completed and transferred out} + \text{(Ending work in process units} \times \text{ Percent completion for C)} \][/tex]
Given:
[tex]\[ \text{Units completed and transferred out} = 295,000 \][/tex]
[tex]\[ \text{Ending work in process units} = 30,000 \][/tex]
[tex]\[ \text{Percent completion for C in ending WIP} = 30.8\% \][/tex]
Therefore:
[tex]\[ \text{Equivalent units (C)} = 295,000 + (30,000 \times 0.308) = 295,000 + 9,240 = 304,240 \][/tex]
The equivalent units of production are 319,240 units for direct materials and 304,240 units for conversion.
#### c. Calculate the costs per equivalent unit of production for both direct materials and conversion for the Forming department.
First, we need to determine the total costs for direct materials and conversion by adding the beginning work-in-process costs to the costs added during the period. Then, we divide these total costs by the equivalent units of production calculated above.
Total Cost for Direct Materials (DM):
[tex]\[ \text{Total direct materials cost} = \text{Beginning direct materials cost} + \text{Added direct materials cost} \][/tex]
Given:
[tex]\[ \text{Beginning direct materials cost} = \$44,800 \][/tex]
[tex]\[ \text{Added direct materials cost} = \$896,700 \][/tex]
Therefore:
[tex]\[ \text{Total direct materials cost} = \$44,800 + \$896,700 = \$941,500 \][/tex]
Total Cost for Conversion (C):
[tex]\[ \text{Total conversion cost} = \text{Beginning conversion cost} + \text{Added conversion cost} \][/tex]
Given:
[tex]\[ \text{Beginning conversion cost} = \$15,300 \][/tex]
[tex]\[ \text{Added conversion cost} = \$1,231,200 \][/tex]
Therefore:
[tex]\[ \text{Total conversion cost} = \$15,300 + \$1,231,200 = \$1,246,500 \][/tex]
Cost per Equivalent Unit for Direct Materials (DM):
[tex]\[ \text{Cost per equivalent unit (DM)} = \frac{\text{Total direct materials cost}}{\text{Equivalent units (DM)}} \][/tex]
Therefore:
[tex]\[ \text{Cost per equivalent unit (DM)} = \frac{\$941,500}{319,240} \approx \$2.949 \][/tex]
Cost per Equivalent Unit for Conversion (C):
[tex]\[ \text{Cost per equivalent unit (C)} = \frac{\text{Total conversion cost}}{\text{Equivalent units (C)}} \][/tex]
Therefore:
[tex]\[ \text{Cost per equivalent unit (C)} = \frac{\$1,246,500}{304,240} \approx \$4.097 \][/tex]
The costs per equivalent unit of production are approximately [tex]$2.949 for direct materials and $[/tex]4.097 for conversion.
### Summary of Results:
- Units started and completed this period: 270,000 units
- Equivalent units of production:
- Direct Materials: 319,240 units
- Conversion: 304,240 units
- Cost per equivalent unit:
- Direct Materials: [tex]$2.949 - Conversion: $[/tex]4.097
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