At the beginning of the month, the Painting Department of Skye Manufacturing had 20,000 units in inventory, \( 70 \% \) complete as to materials, and \( 20 \% \) complete as to conversion. The cost of the beginning inventory, \( \$ 28,650 \), consisted of \( \$ 22,400 \) of material costs and \( \$ 6,250 \) of comversion costs. During the month the department started 115,000 units and transferred 120,000 units to the next manufacturing department. Costs added is the current month consisted of \( \$ 229,600 \) of materials costs and \( \$ 540,500 \) of conversion costs. At the end of the month, the department had 15,000 units in inventory, \( 40 \% \) complete as to materials and \( 10 \% \) complete as to conversion. If Skye Manufacturing uses the weighted average method of process costing, compute the costs per equivalent unit of materials and conversion respectively for the Painting Department.

To determine the costs per equivalent unit of materials and conversion for Skye Manufacturing's Painting Department using the weighted average method, we first need to calculate the total equivalent units for both materials and conversion costs. **Total Units to Account For:** - Beginning Inventory: 20,000 units - Units Started: 115,000 units - Total Units: 20,000 + 115,000 = 135,000 units **Units Transferred Out:** - Transferred to Next Department: 120,000 units **Ending Inventory:** - Remaining Units: 135,000 - 120,000 = 15,000 units **Equivalent Units Calculation:** 1. **Materials:** - Units Transferred Out: 120,000 (100% complete) - Ending Inventory: 15,000 units × 40% complete = 6,000 equivalent units - Total Equivalent Units for Materials = 120,000 + 6,000 = 126,000 units 2. **Conversion:** - Units Transferred Out: 120,000 (100% complete) - Ending Inventory: 15,000 units × 10% complete = 1,500 equivalent units - Total Equivalent Units for Conversion = 120,000 + 1,500 = 121,500 units **Total Costs Calculation:** - **Materials:** - Beginning Inventory Cost: $22,400 - Costs Added: $229,600 - Total Material Costs = $22,400 + $229,600 = $252,000 - **Conversion:** - Beginning Inventory Cost: $6,250 - Costs Added: $540,500 - Total Conversion Costs = $6,250 + $540,500 = $546,750 **Costs per Equivalent Unit Calculation:** 1. **Cost per Equivalent Unit for Materials:** \[ \text{Cost per Equivalent Unit for Materials} = \frac{\text{Total Material Costs}}{\text{Equivalent Units for Materials}} = \frac{252,000}{126,000} = \$2.00 \] 2. **Cost per Equivalent Unit for Conversion:** \[ \text{Cost per Equivalent Unit for Conversion} = \frac{\text{Total Conversion Costs}}{\text{Equivalent Units for Conversion}} = \frac{546,750}{121,500} \approx \$4.50 \] Thus, the costs per equivalent unit for materials and conversion in the Painting Department are **$2.00** and **$4.50**, respectively.