To determine the equivalent units of production with respect to direct materials and conversion costs, we analyze the progress of units through the Converting Department. We use the weighted-average method for equivalent units, which takes into account the work done during the period and the work in progress at the beginning and end of the period.

Let's break down the calculations:

1. Direct Materials

Since direct materials are added at the beginning of the process, all units in the process (whether they are beginning work in process, completed, or ending work in process) will have 100% of the direct materials added.

Formula for equivalent units for direct materials: \text{Equivalent Units for Direct Materials} = \text{Units Transferred Out} + \text{Ending Work in Process (100% for materials)}

• Units Transferred Out = 19,200 units
• Ending Work in Process = 1,040 units

So, $\text{Equivalent Units for Direct Materials} = 19,200 + 1,040 = 20,240 \text{ units}$

2. Conversion Costs

Conversion costs include labor and overhead, which are applied throughout the production process. Therefore, we need to account for the percentage completion of units in the beginning and ending work in process inventories.

Formula for equivalent units for conversion costs: $\text{Equivalent Units for Conversion Costs} = \text{Units Transferred Out} + (\text{Ending Work in Process} \times \text{Percentage Complete}) - (\text{Beginning Work in Process} \times \text{Percentage Complete})$

• Units Transferred Out = 19,200 units (100% complete)
• Beginning Work in Process = 920 units, 40% complete
• Ending Work in Process = 1,040 units, 30% complete

Now calculate the equivalent units for each component:

• Equivalent Units from Beginning Work in Process = $920 \times 40\% = 368$ units
• Equivalent Units from Ending Work in Process = $1,040 \times 30\% = 312$ units

So, $\text{Equivalent Units for Conversion Costs} = 19,200 + 312 - 368 = 19,144 \text{ units}$

Summary of Equivalent Units

Cost Component	Equivalent Units
Direct Materials	20,240
Conversion Costs	19,144

Would you like further breakdown or explanations on any step?

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Additional Questions for Deeper Understanding:

1. What is the purpose of calculating equivalent units in production costing?
2. How does the weighted-average method differ from the FIFO method in process costing?
3. Why do direct materials often have a different completion percentage compared to conversion costs?
4. How does knowing the equivalent units of production help in financial reporting?
5. How might changes in the percentage completion of ending work in process impact equivalent units?

Tip:

Equivalent units provide insight into the amount of work done on incomplete units, aiding in accurate cost allocation between completed and in-process units.