To solve this problem using the weighted-average method, we need to compute:

1. The equivalent units for materials and conversion costs.
2. The cost per equivalent unit for direct materials and conversion costs.

Let’s go through each step in detail.

Step 1: Compute Equivalent Units

For the weighted-average method, we calculate equivalent units by combining work done in the beginning WIP inventory and the units started and completed during the current period.

1. Units started and completed:
   Total units = Beginning WIP + Units started
   = 6,000 + 44,400 = 50,400 units.

2. Ending WIP units:
   Ending inventory is given as 15,000 units, which means the units started and completed this period are: $\text{Units started and completed} = 50,400 - 15,000 = 35,400$

Now, calculate the equivalent units for materials and conversion costs.

Equivalent Units for Direct Materials

For direct materials, we have:

• Beginning WIP (6,000 units) at 40% complete: $6,000 \times 0.40 = 2,400$ equivalent units.
• Units started and completed (35,400 units): 100% complete.
• Ending WIP (15,000 units) at 75% complete: $15,000 \times 0.75 = 11,250$ equivalent units.

Total equivalent units for materials: $2,400 + 35,400 + 11,250 = 49,050 \text{ equivalent units}$

Equivalent Units for Conversion Costs

For conversion costs, we have:

• Beginning WIP (6,000 units) at 15% complete: $6,000 \times 0.15 = 900$ equivalent units.
• Units started and completed (35,400 units): 100% complete.
• Ending WIP (15,000 units) at 35% complete: $15,000 \times 0.35 = 5,250$ equivalent units.

Total equivalent units for conversion costs: $900 + 35,400 + 5,250 = 41,550 \text{ equivalent units}$

Step 2: Calculate Cost per Equivalent Unit

Now, use the total costs and equivalent units calculated above to determine the cost per equivalent unit.

Total Costs for Direct Materials and Conversion Costs

• Direct materials: Beginning WIP ($22,553) + Current period costs ($131,392) = $153,945
• Conversion costs: Beginning WIP ($7,405) + Current period costs ($61,700) = $69,105

Cost per Equivalent Unit for Direct Materials

$\text{Cost per equivalent unit for materials} = \frac{\text{Total materials cost}}{\text{Equivalent units for materials}} = \frac{153,945}{49,050} = 3.14$

Cost per Equivalent Unit for Conversion Costs

$\text{Cost per equivalent unit for conversion costs} = \frac{\text{Total conversion cost}}{\text{Equivalent units for conversion}} = \frac{69,105}{41,550} = 1.66$

Summary of Answers

1. Equivalent units for materials: 49,050
2. Equivalent units for conversion: 41,550
3. Cost per equivalent unit for materials: $3.14
4. Cost per equivalent unit for conversion: $1.66

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Would you like a further breakdown of any steps?

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1. How does the weighted-average method differ from the FIFO method in cost calculations?
2. Why is it important to calculate equivalent units in process costing?
3. What are common challenges in determining percentages for completion?
4. How does ending WIP affect total equivalent units?
5. How might changes in direct material and conversion percentages impact unit costs?

Tip: In process costing, understanding equivalent units helps accurately spread total costs over partially completed and fully completed units.