Matrix Inc. calculates cost for an equivalent unit of production using the weighted-average method. Data for July:

Work-in-process inventory, July 1 (40,000 units):
Direct materials (92% completed) $122,800
Conversion (58% completed) 77,250
Balance in work in process inventory, July 1 $200,050
Units started during July 94,000
Units completed and transferred 109,600
Work-in-process inventory, July 31:
Direct materials (92% completed) 24,400
Conversion (58% completed) Cost incurred during July:
Direct materials $184,000
Conversion costs 292,000

Required:
a. Cost per equivalent unit for materials under the weighted-average method is calculated to be:
b. Cost per equivalent unit for conversion under the FIFO method is calculated to be:

a. $2.32

b. $2.92

Explanation:

Part a

Equivalent Units

Completed and Transferred 109,600 x 100%    109,600

Ending Work In Process 24,400 x 92%               22,448

Equivalent Units with respect to Materials         132,048

Total Materials Cost

Materials cost Beginning Work in Process       $122,800

Add Material Cost incurred during the year     $184,000

Total Material Costs                                           $306,800

Cost per equivalent unit  = Total Materials Cost  ÷ Equivalent Units

                                          = $306,800 ÷ 132,048

                                          = $2.32

Part b

Equivalent Units

To finish OWIP 40,000 x 42%                                           16,800

Started and Completed  (109,000 - 40,000) x 100        69,000

Closing Work in Progress 24,400 x 58%                          14,152

Equivalent units with respect to conversion cost           99,952

Total Conversion Cost

Conversion Cost incurred during the year    $292,000

Total Material Costs

Cost per equivalent unit  = Total Conversion Cost  ÷ Equivalent Units

                                          = $292,000 ÷ 99,952

                                          = $2.92

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