To compute the total production cost per equivalent unit for work done during the period, we need to calculate the cost per equivalent unit for both direct materials and conversion costs separately.
First, let's calculate the cost per equivalent unit for direct materials:
Beginning work in process:
Units: 10,000
Percent completed: 90%
Direct Materials Costs: $10,000
Units started and completed during the period: 50,000
Ending work in process:
Units: 20,000
Percent completed: 30%
Total equivalent units for direct materials:
Beginning work in process: 10,000 units × 90% = 9,000 equivalent units
Units started and completed: 50,000 equivalent units
Ending work in process: 20,000 units × 30% = 6,000 equivalent units
Total equivalent units for direct materials = 9,000 + 50,000 + 6,000 = 65,000 equivalent units
Total direct materials costs = $10,000 + $110,000 (costs added this period) = $120,000
Cost per equivalent unit for direct materials = Total direct materials costs / Total equivalent units for direct materials = $120,000 / 65,000 equivalent units
Next, let's calculate the cost per equivalent unit for conversion costs:
Beginning work in process:
Units: 10,000
Percent completed: 90%
Conversion Costs: $30,000
Units started and completed during the period: 50,000
Ending work in process:
Units: 20,000
Percent completed: 30%
Total equivalent units for conversion costs:
Beginning work in process: 10,000 units × 90% = 9,000 equivalent units
Units started and completed: 50,000 equivalent units
Ending work in process: 20,000 units × 30% = 6,000 equivalent units
Total equivalent units for conversion costs = 9,000 + 50,000 + 6,000 = 65,000 equivalent units
Total conversion costs = $30,000 + $200,000 (costs added this period) = $230,000
Cost per equivalent unit for conversion costs = Total conversion costs / Total equivalent units for conversion costs = $230,000 / 65,000 equivalent units
Therefore, the computed total production cost per equivalent unit for work done during the period is as follows:
Cost per equivalent unit for direct materials = $120,000 / 65,000 equivalent units
Cost per equivalent unit for conversion costs = $230,000 / 65,000 equivalent units