Math Problem Statement

Data concerning a recent period’s activity in the Prep Department, the first processing department in a company that uses process costing, appear below:

Materials	Conversion

Equivalent units in ending work in process inventory 2,060 910 Cost per equivalent unit $ 13.86 $ 4.93 A total of 21,500 units were completed and transferred to the next processing department during the period.

Required: Compute the cost of ending work in process inventory for materials, conversion, and in total. Compute the cost of the units completed and transferred out for materials, conversion, and in total. Note: For all requirements, round your final answers to the nearest whole dollar amount.

Solution

We can break this down into two parts to calculate the cost of ending work in process (WIP) inventory and the cost of units completed and transferred out.

1. Cost of Ending Work in Process (WIP) Inventory

The formula for the cost of ending work in process inventory is:

Cost of Ending WIP Inventory=Equivalent Units in Ending WIP×Cost per Equivalent Unit\text{Cost of Ending WIP Inventory} = \text{Equivalent Units in Ending WIP} \times \text{Cost per Equivalent Unit}

For Materials:

Cost of Ending WIP (Materials)=2,060×13.86=28,611.60\text{Cost of Ending WIP (Materials)} = 2,060 \times 13.86 = 28,611.60

For Conversion:

Cost of Ending WIP (Conversion)=910×4.93=4,486.30\text{Cost of Ending WIP (Conversion)} = 910 \times 4.93 = 4,486.30

Total Cost of Ending WIP:

Total Cost of Ending WIP=28,611.60+4,486.30=33,097.90\text{Total Cost of Ending WIP} = 28,611.60 + 4,486.30 = 33,097.90

Rounding to the nearest dollar:

  • Cost of Ending WIP for Materials: $28,612
  • Cost of Ending WIP for Conversion: $4,486
  • Total Cost of Ending WIP: $33,098

2. Cost of Units Completed and Transferred Out

The formula for the cost of units completed and transferred out is:

Cost of Units Completed and Transferred Out=Units Completed and Transferred Out×Cost per Equivalent Unit\text{Cost of Units Completed and Transferred Out} = \text{Units Completed and Transferred Out} \times \text{Cost per Equivalent Unit}

Given that 21,500 units were completed and transferred:

For Materials:

Cost of Units Transferred Out (Materials)=21,500×13.86=297,990\text{Cost of Units Transferred Out (Materials)} = 21,500 \times 13.86 = 297,990

For Conversion:

Cost of Units Transferred Out (Conversion)=21,500×4.93=105,995\text{Cost of Units Transferred Out (Conversion)} = 21,500 \times 4.93 = 105,995

Total Cost of Units Transferred Out:

Total Cost of Units Transferred Out=297,990+105,995=403,985\text{Total Cost of Units Transferred Out} = 297,990 + 105,995 = 403,985

Rounding to the nearest dollar:

  • Cost of Units Transferred Out for Materials: $297,990
  • Cost of Units Transferred Out for Conversion: $105,995
  • Total Cost of Units Transferred Out: $403,985

Final Summary:

  1. Cost of Ending Work in Process Inventory:

    • Materials: $28,612
    • Conversion: $4,486
    • Total: $33,098
  2. Cost of Units Completed and Transferred Out:

    • Materials: $297,990
    • Conversion: $105,995
    • Total: $403,985

Would you like more details on any of these calculations, or have any questions?

Here are five related questions for further exploration:

  1. How do you calculate equivalent units in process costing?
  2. What is the difference between direct materials and conversion costs?
  3. How does the weighted-average method differ from the FIFO method in process costing?
  4. What factors could cause an increase in the cost per equivalent unit?
  5. How does ending work in process affect financial statements?

Tip: Always check if the rounding of costs affects final totals, especially when dealing with large unit volumes.

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Math Problem Analysis

Mathematical Concepts

Process Costing
Equivalent Units
Cost Allocation

Formulas

Cost of Ending WIP Inventory = Equivalent Units in Ending WIP × Cost per Equivalent Unit
Cost of Units Completed and Transferred Out = Units Completed and Transferred Out × Cost per Equivalent Unit

Theorems

Process Costing Methodology

Suitable Grade Level

College-level Accounting/Finance