Math Problem Statement

EXHIBIT 4.docx

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Solution

To answer the questions from the document regarding equivalent units of production, cost per equivalent unit, and the cost of units transferred out, we'll use the Weighted-Average Method.

Data for Calculations:

  1. Beginning Work in Process Inventory:

    • Units in process: 500
    • Completion with respect to materials: 15%
    • Completion with respect to conversion: 55% (Requirement 2) and 95% (Requirement 3).
  2. Costs in the Beginning Work in Process Inventory:

    • Materials cost: $3,617
    • Conversion cost: $22,357
  3. Units Started into Production: 16,700

  4. Costs Added to Production:

    • Materials cost: $798,118
    • Conversion cost: $1,352,603
  5. Ending Work in Process Inventory:

    • Units in process: 500
    • Completion with respect to materials: 50%
    • Completion with respect to conversion: 30%

Steps to Solve:

  1. Equivalent Units of Production:

    • Equivalent units = Units completed and transferred + (Ending WIP units × % completion).

    For materials:

    • Units transferred: 16,700 - 500 (Ending WIP) = 16,200
    • Ending WIP equivalent for materials: 500×50%=250500 \times 50\% = 250
    • Total equivalent units for materials = 16,200 + 250 = 16,450

    For conversion:

    • Units transferred: 16,200
    • Ending WIP equivalent for conversion: 500×30%=150500 \times 30\% = 150
    • Total equivalent units for conversion = 16,200 + 150 = 16,350
  2. Cost per Equivalent Unit:

    • Cost per equivalent unit=Total costEquivalent units\text{Cost per equivalent unit} = \frac{\text{Total cost}}{\text{Equivalent units}}

    For materials:

    • Total materials cost = $3,617 (beginning) + $798,118 (added) = $801,735
    • Cost per equivalent unit = 801,73516,450=48.74\frac{801,735}{16,450} = 48.74

    For conversion:

    • Total conversion cost = $22,357 (beginning) + $1,352,603 (added) = $1,374,960
    • Cost per equivalent unit = 1,374,96016,350=84.08\frac{1,374,960}{16,350} = 84.08
  3. Cost of Units Transferred Out:

    • Cost of units transferred = Equivalent units transferred×Cost per unit\text{Equivalent units transferred} \times \text{Cost per unit}

    For materials:

    • 16,200×48.74=789,58816,200 \times 48.74 = 789,588

    For conversion:

    • 16,200×84.08=1,362,09616,200 \times 84.08 = 1,362,096

    Total cost transferred out = $789,588 + $1,362,096 = $2,151,684

These are the core calculations needed to solve the problem. Would you like further details on any part of this, or help with the next steps? Here are some related questions:


  1. How does the change from 55% to 95% for conversion completion affect the costs?
  2. What is the total cost of the ending work in process inventory for materials and conversion?
  3. How would this method compare with the FIFO method?
  4. What other departments might have similar production calculations?
  5. How are equivalent units affected by the percentage completion for materials and conversion?

Tip: Keep track of the costs and equivalent units in separate tables in Excel. This can make the process easier to visualize!

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Math Problem Analysis

Mathematical Concepts

Cost Accounting
Weighted-Average Method
Equivalent Units of Production
Cost Allocation

Formulas

Equivalent units = Units completed + (Ending WIP × % completion)
Cost per equivalent unit = Total cost / Equivalent units

Theorems

Weighted-Average Cost Allocation Method

Suitable Grade Level

Undergraduate (Accounting or Business Studies)