In the realm of production and cost accounting, understanding how to compute cost per equivalent unit and allocate costs to various units of production is crucial for effective financial management. In this scenario, we are presented with data from Stone Incorporated’s first production department for the month of April. The goal is to calculate the cost per equivalent unit for both direct materials and conversion costs, and then apply the weighted average method to assign April’s costs to the department’s output, including units transferred to the next department and the ending work in process inventory.
Cost per Equivalent Unit Calculation
Cost per equivalent unit is a fundamental metric that helps us determine the cost of a single unit of production, taking into account both direct materials and conversion costs. To calculate this, we need to consider the costs incurred during the period and the equivalent units of production.
Equivalent Units of Production (EUP) is a measure that considers both completed units and the work in process at the end of the period, accounting for the percentage of completion for both direct materials and conversion costs.
Let’s begin by calculating the equivalent units for direct materials and conversion costs:
Direct Materials Equivalent Units
Beginning Work in Process (BWIP) Inventory: 71,000 units * 65% = 46,150 equivalent units
Units Started and Completed: 355,000 units
Ending Work in Process (EWIP) Inventory: 93,000 units * 90% = 83,700 equivalent units
Total Direct Materials Equivalent Units: 46,150 + 355,000 + 83,700 = 484,850 equivalent units
Conversion Costs Equivalent Units
Beginning Work in Process (BWIP) Inventory: 71,000 units * 35% = 24,850 equivalent units
Units Started and Completed: 355,000 units
Ending Work in Process (EWIP) Inventory: 93,000 units * 40% = 37,200 equivalent units
Total Conversion Costs Equivalent Units: 24,850 + 355,000 + 37,200 = 417,050 equivalent units
Now that we have computed the equivalent units, we can calculate the cost per equivalent unit for both direct materials and conversion costs.
Cost per Equivalent Unit
Direct Materials Cost per EUP:
Total Direct Materials Cost = Beginning WIP Inventory + Costs Added This Period Total Direct Materials Cost = $165,239 + $1,106,991 = $1,272,230
Cost per EUP for Direct Materials = Total Direct Materials Cost / Total Direct Materials Equivalent Units Cost per EUP for Direct Materials = $1,272,230 / 484,850 EUP ≈ $2.62 per EUP
Conversion Cost per EUP:
Total Conversion Costs = Beginning WIP Inventory + Costs Added This Period Total Conversion Costs = $42,407 + $800,823 = $843,230
Cost per EUP for Conversion Costs = Total Conversion Costs / Total Conversion Costs Equivalent Units Cost per EUP for Conversion Costs = $843,230 / 417,050 EUP ≈ $2.02 per EUP
Assignment of Costs Using the Weighted Average Method
The weighted average method allocates the total costs to the units completed and transferred out during the period and the ending work in process inventory. We already have the total costs incurred during April, which is $2,115,460.
Costs assigned to units transferred out:
Units Transferred Out = 355,000
Cost per Unit Transferred Out = Cost per EUP for Direct Materials + Cost per EUP for Conversion Costs
Cost per Unit Transferred Out = $2.62 + $2.02 = $4.64 per unit
Total Cost for Units Transferred Out = Units Transferred Out * Cost per Unit Transferred Out
Total Cost for Units Transferred Out = 355,000 * $4.64 ≈ $1,647,200
Costs assigned to ending work in process (EWIP) inventory:
EWIP Equivalent Units = 83,700 (Direct Materials) + 37,200 (Conversion Costs) = 120,900 EUP
Cost per Unit in EWIP Inventory = Cost per EUP for Direct Materials + Cost per EUP for Conversion Costs
Cost per Unit in EWIP Inventory = $2.62 + $2.02 = $4.64 per unit
Total Cost for EWIP Inventory = EWIP Equivalent Units * Cost per Unit in EWIP Inventory
Total Cost for EWIP Inventory = 120,900 * $4.64 ≈ $561,936
In conclusion, using the weighted average method, we have allocated April’s costs as follows:
$1,647,200 to units transferred to the next department.
$561,936 to the ending work in process (EWIP) inventory.
This accounting process allows Stone Incorporated to accurately track and assign costs to their production output, helping them make informed financial decisions and maintain effective cost control within their production department.
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