Index Corporation uses the FIFO method in its process costing system. The first processing department, the Forming Department, started the month with 17,000 units in its beginning work in process inventory that were 10% complete with respect to conversion costs. The conversion cost in this beginning work in process inventory was $9,010. An additional 76,000 units were started into production during the month and 83,000 units were completed and transferred to the next processing department. There were 10,000 units in the ending work in process inventory of the Forming Department that were 70% complete with respect to conversion costs. A total of $445,915 in conversion costs were incurred in the department during the month.
Required:1. The cost per equivalent unit for conversion costs for the month is closest to . a. $5,150b. $5,300c. $5,867d. $5,050

Cost per equivalent unit= $5.152  

Explanation:

Cost per equivalent unit = Total conversion cost / Total equivalent unit

Fully worked = 76,000 - 10,000 = 66,000  units

Fully worked represents units started and completed in the same period.

Equivalent units

Item                                  Units                                   Equivalent unit

Opening inventory      17,000        90% × 17,000 =       15,300

Fully worked                 66,0000    100% × 66,000 =     66,000

Closing inventory          10,000       70% ×   10,000 =     7,000

Total equivalent units                                                       88,300

Note also at that the degree of completion for opening inventory is the simply the balance of work remaining to be done.

For example, for materials, 10% of work has been done on the opening inventory in the last period, hence the balance of 90% would be done this period

Cost per equivalent unit = Total conversion cost / Total equivalent unit

= $( 9,010 + 445,915)/ 88300 units  =  $5.152

Cost per equivalent unit= $5.152            

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