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21.3 Explain and Compute Equivalent Units and Total Cost of Production in an Initial Processing Stage

Equivalent Units Concept​

Equivalent units represent the number of complete units that could have been produced given the amount of work actually performed on partially completed units.

Purpose:

  • Account for work done on partially completed units
  • Calculate accurate unit costs
  • Allocate costs between completed and in-process units

Why Equivalent Units Are Needed​

In process costing, units are often in various stages of completion at period end:

  • Some units completed
  • Some units partially completed
  • Need to account for work done on all units

Example:

  • 1,000 units completed (100% complete)
  • 200 units 50% complete
  • Equivalent units: 1,000 + (200 × 50%) = 1,100 equivalent units

Calculating Equivalent Units​

Formula: Equivalent Units = Units Completed + (Units in Process × Percentage Complete)

Example:

  • Units completed: 800
  • Units in process: 200 (60% complete)
  • Equivalent units: 800 + (200 × 60%) = 800 + 120 = 920 equivalent units

Separate Calculation for Materials and Conversion​

Materials and conversion costs are often at different completion levels, so equivalent units are calculated separately.

Materials Equivalent Units:

  • Materials may be added at beginning of process
  • If added at beginning: Units in process = 100% complete for materials
  • If added throughout: Need to determine percentage

Conversion Equivalent Units:

  • Conversion (labor + overhead) occurs throughout process
  • Units in process are partially complete for conversion
  • Calculate based on completion percentage

Process Cost Report - Initial Stage​

A process cost report (also called production cost report) summarizes:

  1. Physical flow of units
  2. Equivalent units
  3. Costs to account for
  4. Cost per equivalent unit
  5. Cost allocation

Example: Initial Processing Stage​

Luxembourg Bakery - Mixing Department (Initial Stage):

Physical Flow:

  • Units started: 1,000
  • Units completed: 800
  • Units in process (end): 200 (100% complete for materials, 60% complete for conversion)

Costs:

  • Direct materials: €650
  • Direct labor: €200
  • Manufacturing overhead: €150
  • Total: €1,000

Step 1: Calculate Equivalent Units

Materials:

  • Completed: 800 units × 100% = 800
  • In process: 200 units × 100% = 200
  • Total equivalent units: 1,000

Conversion:

  • Completed: 800 units × 100% = 800
  • In process: 200 units × 60% = 120
  • Total equivalent units: 920

Step 2: Calculate Cost per Equivalent Unit

Materials: €650 ÷ 1,000 = €0.65 per equivalent unit

Conversion: €350 ÷ 920 = €0.38 per equivalent unit (rounded)

Total: €0.65 + €0.38 = €1.03 per equivalent unit

Step 3: Allocate Costs

To Completed Units:

  • Materials: 800 × €0.65 = €520
  • Conversion: 800 × €0.38 = €304
  • Total: €824

To Units in Process:

  • Materials: 200 × €0.65 = €130
  • Conversion: 120 × €0.38 = €46
  • Total: €176

Verification: €824 + €176 = €1,000 ✓

Process Cost Report Format​

═══════════════════════════════════════════════════════
PROCESS COST REPORT - MIXING DEPARTMENT
Period: November 2024
═══════════════════════════════════════════════════════

PHYSICAL FLOW:
───────────────────────────────────────────────────────
Units started                                   1,000
Units completed                                   800
Units in process (end)                            200
───────────────────────────────────────────────────────
Total units accounted for                       1,000

EQUIVALENT UNITS:
───────────────────────────────────────────────────────
                    Materials    Conversion
Completed              800          800
In Process (200 @ 100%, 60%)  200        120
───────────────────────────────────────────────────────
Total Equivalent Units       1,000        920

COSTS:
───────────────────────────────────────────────────────
                    Materials    Conversion    Total
Costs to Account For:
  Beginning WIP         €0          €0        €0
  Current Costs        650         350     1,000
───────────────────────────────────────────────────────
Total Costs           €650        €350    €1,000

COST PER EQUIVALENT UNIT:
───────────────────────────────────────────────────────
Materials:    €650 ÷ 1,000 = €0.65
Conversion:   €350 ÷ 920   = €0.38
───────────────────────────────────────────────────────
Total Cost per Unit: €1.03

COST ALLOCATION:
───────────────────────────────────────────────────────
Completed Units (800):
  Materials:    800 × €0.65 = €520
  Conversion:   800 × €0.38 = €304
  Total                        €824

Units in Process (200):
  Materials:    200 × €0.65 = €130
  Conversion:   120 × €0.38 = €46
  Total                        €176
───────────────────────────────────────────────────────
Total Costs Accounted For              €1,000
═══════════════════════════════════════════════════════

When Materials Are Added at Different Stages​

Materials Added at Beginning:

  • All units in process are 100% complete for materials
  • Materials equivalent units = Total units (completed + in process)

Materials Added Throughout:

  • Units in process are partially complete for materials
  • Calculate materials equivalent units based on completion

Materials Added at End:

  • Units in process are 0% complete for materials
  • Only completed units have materials

Luxembourg Compliance Note​

In Luxembourg:

  • Equivalent units must be calculated accurately
  • Separate calculation for materials and conversion
  • Process cost reports should be maintained
  • Use PCN accounts properly
  • Cost allocation must be reasonable
  • Support cost of goods sold calculations

Think It Through​

Why do we calculate equivalent units separately for materials and conversion? What happens if we don't account for partially completed units?