Math Problem Statement

A company gives us the following information about their inventories at the beginning and end of the year:

Beginning work in process: 9000 units. (With 100% of DM and 47% of MOH).

Finished goods beginning inventory: 6200 units.

Ending work in process: 0 units

Finished goods ending inventory: 4700 units.

The company has sold 37000 units. How many equivalent units belong to Conversion costs?

Solution

To determine the equivalent units for Conversion Costs (MOH + Direct Labor), we follow these steps:

Step 1: Definitions

  • Equivalent Units: The units completed or partially completed, expressed in terms of fully completed units.
  • Conversion Costs: The costs incurred for Direct Labor and Manufacturing Overhead (MOH) to convert raw materials into finished products.

Step 2: Data Breakdown

  • Beginning Work in Process (WIP): 9,000 units
    • 100% Direct Materials
    • 47% Conversion Costs
  • Ending WIP: 0 units (meaning all units in WIP at the start of the year were completed during the year).
  • Finished Goods Beginning Inventory: 6,200 units
  • Finished Goods Ending Inventory: 4,700 units
  • Units Sold: 37,000 units

Step 3: Total Units Produced

We calculate the total units completed during the year: Units Completed=Units Sold+Ending Finished Goods InventoryBeginning Finished Goods Inventory\text{Units Completed} = \text{Units Sold} + \text{Ending Finished Goods Inventory} - \text{Beginning Finished Goods Inventory} Units Completed=37,000+4,7006,200=35,500 units.\text{Units Completed} = 37,000 + 4,700 - 6,200 = 35,500 \text{ units.}

Step 4: Equivalent Units for Conversion Costs

  1. Conversion of Beginning WIP:

    • Beginning WIP: 9,000 units, which were 47% complete for conversion costs.
    • Remaining Conversion Costs to complete: 100%47%=53%100\% - 47\% = 53\%.
    • Equivalent units needed to complete beginning WIP for conversion costs: 9,000×0.53=4,770 equivalent units.9,000 \times 0.53 = 4,770 \text{ equivalent units.}
  2. Newly Started and Completed Units:

    • Total Units Completed: 35,500.
    • Units already in Beginning WIP: 9,000.
    • Units started and completed during the year: 35,5009,000=26,500 units.35,500 - 9,000 = 26,500 \text{ units.}
    • These units are 100% complete for conversion costs: 26,500×1=26,500 equivalent units.26,500 \times 1 = 26,500 \text{ equivalent units.}
  3. Ending WIP:

    • Since Ending WIP is 0 units, no equivalent units are needed for conversion costs in ending WIP.

Step 5: Total Equivalent Units

The total equivalent units for conversion costs are: Total Equivalent Units=Equivalent Units for Beginning WIP+Equivalent Units for Newly Started and Completed Units\text{Total Equivalent Units} = \text{Equivalent Units for Beginning WIP} + \text{Equivalent Units for Newly Started and Completed Units} Total Equivalent Units=4,770+26,500=31,270 equivalent units.\text{Total Equivalent Units} = 4,770 + 26,500 = 31,270 \text{ equivalent units.}

Final Answer:

The equivalent units for conversion costs are 31,270.

Let me know if you'd like further clarification or more detailed steps! 😊


Here are 5 questions to expand your understanding:

  1. What are the differences between Direct Materials and Conversion Costs?
  2. How do beginning and ending inventories affect equivalent unit calculations?
  3. Why is it important to calculate equivalent units in manufacturing accounting?
  4. What would happen to the equivalent unit calculation if ending WIP was not zero?
  5. How does the percentage completion of WIP inventory impact the overall cost accounting?

Tip: Always double-check percentage completion levels for accuracy when working with equivalent unit problems—they are crucial for precise cost allocation!

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Math Problem Analysis

Mathematical Concepts

Cost Accounting
Equivalent Units
Manufacturing Overhead
Direct Labor

Formulas

Units Completed = Units Sold + Ending Finished Goods Inventory - Beginning Finished Goods Inventory
Equivalent Units = Units × Percentage Completion
Total Equivalent Units = Equivalent Units for Beginning WIP + Equivalent Units for Newly Started and Completed Units

Theorems

Concept of Equivalent Units in Process Costing

Suitable Grade Level

Undergraduate Level (Accounting/Finance)