Process Costing with Opening and Closing WIP; Equivalent Units (using FIFO) and Cost allocation

Process Costing is a method used in industries where production is continuous, and goods pass through multiple processes or stages before completion. In process costing, the costs are accumulated for each stage of the process, and the total costs are assigned to units produced. However, when there is Work-in-Progress (WIP)—either at the beginning or end of a period—it adds a layer of complexity to cost allocation.

Opening WIP represents incomplete units from the previous period, while Closing WIP refers to units that remain incomplete at the end of the current period.

Components of Process Costing with WIP:

1. Opening Work-in-Progress (Opening WIP):

The costs and partially completed units that were not finished in the previous period and carried over to the current period. These costs typically include materials, labor, and overheads incurred in the previous period.

2. Closing Work-in-Progress (Closing WIP):

Units that remain incomplete at the end of the current period. These will become the opening WIP for the following period and need to be valued based on the costs incurred up to the point of incompletion.

3. Costs Added During the Period:

The costs (materials, labor, and overheads) incurred during the current period.

4. Finished Goods:

The completed units during the period that are ready for transfer to the next process or for sale.

Methods of Process Costing with WIP:

There are two primary methods used to allocate costs when there is opening and closing WIP:

1. Weighted Average Method

Under the Weighted Average Method, the opening WIP is combined with the costs of the current period to determine the total cost per equivalent unit. This method assumes that both the opening WIP and the new production are treated as part of the same pool.

Key Features:

• Opening WIP and current period costs are combined.
• The cost per equivalent unit is calculated based on the total units (including opening WIP and new units).
• Simple to apply, but it may not be as precise in terms of cost allocation.

Calculation Steps:

1. Step 1: Calculate Equivalent UnitsEquivalent units are used to convert partially completed units into a measure of full units.

Equivalent Units = Units Completed + Equivalent Units of Closing WIP

2. Step 2: Calculate Total Costs

Add the opening WIP costs and the current period costs to get the total cost.

Total Costs = Opening WIP Costs + Costs Incurred During the Period

3. Step 3: Calculate Cost per Equivalent Unit

Cost per Equivalent Unit =Total Costs / Equivalent Units

4. Step 4: Allocate Costs

Allocate costs to completed units and closing WIP using the cost per equivalent unit.

Example:

Suppose a company has:

• Opening WIP: 500 units (50% complete for materials and 30% for conversion)
• Units started during the period: 4,000 units
• Units completed: 3,700 units
• Closing WIP: 800 units (40% complete for materials and 20% for conversion)
• Opening WIP Costs: $5,000 (Materials $3,000, Conversion $2,000)
• Current period costs: $40,000 (Materials $30,000, Conversion $10,000)

Calculation of Equivalent Units:

Calculation of Total Cost and Cost per Equivalent Unit:

• Total Costs:

Total Materials Costs = 3,000 + 30,000 = 33,000

Total Conversion Costs = 2,000 + 10,000 = 12,000

• Cost per Equivalent Unit:

Material Cost per Equivalent Unit = 33,000 / 4,020 = 8.21

Conversion Cost per Equivalent Unit = 12,000 / 3,860 = 3.11

Allocation of Costs:

• Completed Units (3,700 units):

Total Cost of Completed Units = 3,700 × (8.21 + 3.11) = 41,180.00

• Closing WIP (800 units):

Cost of Closing WIP = (320×8.21) + (160×3.11) = 2,627.20 + 497.60 = 3,124.80

2. First In, First Out (FIFO) Method

FIFO Method separates the costs of opening WIP from the current period’s costs. The units in opening WIP are completed first, and any additional costs incurred during the current period are treated separately.

Key Features:

• Opening WIP units are treated separately from the units started and completed during the current period.
• Provides a more accurate measure of current period costs and efficiencies.
• More complex than the weighted average method.

Calculation Steps:

1. Step 1: Calculate Equivalent Units for Current Period Production Only

Equivalent units are based on the work done during the current period.

Equivalent Units = Units Started and Completed + Equivalent Units of Closing WIP

2. Step 2: Calculate Current Period Costs

Exclude the opening WIP costs. Use only the costs incurred during the current period.

3. Step 3: Calculate Cost per Equivalent Unit for Current Period

Cost per Equivalent Unit = Current Period Costs / Equivalent Units (current period only)

4. Step 4: Allocate Costs
   • Completed units from opening WIP
   • Units started and completed during the current period
   • Closing WIP

Example:

Using the same data as in the previous example, under the FIFO method:

1. Units Started and Completed:

Units Started and Completed = 3,700 – 500 = 3,200

2. Equivalent Units (for work done in the current period):

3. Costs Allocation:
   • Cost of Completed Units (500 from Opening WIP + 3,200 started and completed).
   • Cost of Closing WIP.

Advantages of Process Costing with WIP:

1. Provides a clear understanding of costs at each production stage.
2. Accurately allocates costs to completed units and WIP, ensuring cost control.
3. Facilitates comparison between periods.

Disadvantages:

1. Can be complex, especially with varying degrees of completion in WIP.
2. Requires precise data on costs and completion percentages.
3. May be challenging to allocate costs in cases of significant production variation.