Chapter 3, Problem 4PB

Work in process account data for two months; cost of production reports

Pittsburgh Aluminum Company uses a process cost system to record the costs of manufacturing rolled aluminum, which consists of the smelting and rolling processes. Materials are entered from smelting at the beginning of the rolling process. The inventory of Work in Process—Rolling on September 1 and debits to the account during September were as follows:

During September, 2,600 units in process on September 1 were completed, and of the 28,900 units entering the department, all were completed except 2,900 units that were 4⁄5 completed.

Charges to Work in Process—Rolling for October were as follows:

During October, the units in process at the beginning of the month were completed, and of the 31,000 units entering the department, all were completed except 2,000 units that were 2⁄5 completed.

Instructions

1. 1. Enter the balance as of September 1 in a four-column account for Work in Process—Rolling. Record the debits and the credits in the account for September. Construct a cost of production report and present computations for determining (A) equivalent units of production for materials and conversion, (B) costs per equivalent unit, (C) cost of goods finished, differentiating between units started in the prior period and units started and finished in September, and (D) work in process inventory.
2. 2. Provide the same information for October by recording the October transactions in the four-column work in process account. Construct a cost of production report, and present the October computations (A through D) listed in part (1).
3. 3. Comment on the change in costs per equivalent unit for August through October for direct materials and conversion cost.

To determine

Prepare the four-column account for work in process inventory balancerolling departmentfrom September to October of Company PA.

Explanation of Solution

Process costs

It is a method of cost accounting, which is used where the production is continuous, and the product needs various processes to complete. This method is used to ascertain the cost of the product at each process or stage of production.

Equivalents units for production

The activity of a processing department in terms of fully completed units is known as equivalent units. It includes the completed units of direct materials and conversion cost of beginning work in process, units completed and transferred out, and ending work in process.

Production cot report

A production cost report is a comprehensive report prepared for each department separately at the end of a particular period, which represents the physical flow and cost flow of product for the concerned department.

Prepare the four column account for work in process inventory balance rolling department from September to October of Company PA as shown below:

Work in Process - Rolling
Date	Item	Debit	Credit	Balance
				Debit	Credit
Sept 1	Balance, 2,600 units			$45,825
Sept 30	Smelting department	$462,400		$508,225
Sept 30	Direct labor	$158,920		$667,145
Sept 30	Factory overhead	$101,402		$768,547
Sept 30	Finished goods		$702,195	$66,352
Sept 30	Balance, 2,900 units			$66,352
Oct 31	Smelting department	$511,500		$577,852
Oct 31	Direct labor	$162,850		$740,702
Oct 31	Factory overhead	$104,494		$845,196
Oct 31	Finished goods		$805,156	$40,040
Oct 31	Balance, 2,000 units			$40,040

Table (1)

Conclusion

Hence, Work in process inventory ending balance for the month of September is $66,352 and for the month of October is $40,040.

To determine

Prepare the equivalents units for production of direct materials and conversion cost of Company PA.

Explanation of Solution

Prepare the equivalent units for production of direct materials and conversion cost of Company PA as shown below:

Figure (1)

Working notes:

Calculate opening work in process inventory for conversion percentage to complete as shown below:

  $\begin{array}{c}\begin{array}{l}\text{Opening work in process}\\ \text{ inventory for Conversion}\end{array})\text{=}\text{1}-\frac{1}{4}\\ =\frac{3}{4}\\ =75\%\end{array}$

Calculate units started and completed in September as shown below:

  $\begin{array}{c}\text{Units started and completed in September}\text{=}\left(\begin{array}{l}\text{Received from Smelting Department}\\ -\text{Ending work in process inventory}\end{array}\right)\\ \text{=}28\text{,900}\text{units }-2,900\text{units}\\ \text{=}26\text{,000}\text{units}\end{array}$

Calculate ending work in process inventory units as shown below:

  $\begin{array}{c}\text{Ending work in process inventory for conversion =}2,900\text{units }\times \frac{4}{5}\\ \text{=}2,320\text{units}\end{array}$

Total units to be assigned to costs is calculated by adding opening work in process inventory, units started and completed and ending work in process inventory.

Conclusion

Therefore, direct material equivalent units for production is 28,900 units and conversion cost equivalent units for production is 30,270 units.

To determine

Prepare the cost per equivalent unit for direct material and conversion cost of Company PA.

Explanation of Solution

Calculate the cost per equivalent unit for direct material and conversion cost of Company PA as shown below:

  $\begin{array}{c}\begin{array}{l}\text{Equivalent cost per unit }\\ \text{of direct materials }\end{array})\text{=}\frac{\text{Cost of Direct materials}}{\text{Equivalent units of direct materials}}\\ =\frac{\$462,400}{28,900\text{units}}\\ =\$16.00\text{per unit}\end{array}$

  $\begin{array}{c}\begin{array}{l}\text{Equivalent cost per unit }\\ \text{of Conversion cost }\end{array})\text{=}\frac{\text{Cost of Conversion cost}}{\text{Equivalent units of conversion}}\\ =\frac{\$260,322}{30,270\text{units}}\\ =\$8.60\text{per unit}\end{array}$

Working note:

Calculate conversion cost for the month of September of Company PA as shown below:

  $\begin{array}{c}\text{Conversion cost =}\text{Direct labor cost +}\text{Factory overhead cost}\\ \text{=}\text{\$158,920}\text{+}\text{\$101,402}\\ \text{=}\text{\$260,322}\end{array}$

Equivalent cost per unit for direct materials is calculated by dividing direct material cost by equivalent units for direct materials. Equivalent cost per unit for conversion cost is calculated by dividing conversion cost by equivalent units for conversion.

Conclusion

Therefore, equivalent cost per unit for direct material is $16.00 per unit and for conversion cost is $8.60 per unit.

To determine

Prepare the cost of goods finished, between units stared in the prior period and units started and finished in September of Company PA.

Explanation of Solution

Prepare the cost of goods finished, between units stared in the prior period and units started and finished in September of Company PA as shown below:

Figure (2)

Costs transferred to finished goods is calculated by adding opening inventory in September balance, to complete opening work in process inventory in September, andcost of units started and completed in September.

Conclusion

Hence, cost of completed work in process inventory in September 1 is $62,595, cost for started and completed in September is $639,600, and transferred to finished goods is $702,195.

To determine

Prepare the ending work in process inventory cost of the month September for the Company PA.

Explanation of Solution

Prepare the ending work in process inventory cost of the month September for the Company PA as shown below:

Figure (3)

Ending work in process inventory cost is calculated by adding ending direct material cost and ending conversion costs.

Conclusion

Hence, ending work in process inventory cost for the month of September is $66,352.

To determine

Prepare the production cost report of rolling department for the month of September of Company PA.

Explanation of Solution

Prepare the production cost report of rolling department for the month of September for Company PA as shown below:

Figure (4)

Conclusion

Therefore, cost of production report for rolling department during the month of September for Company PA is $768,547.

To determine

Prepare the equivalents units for production of direct materials and conversion cost during the month of October for Company PA.

Explanation of Solution

Prepare the equivalents units for production of direct materials and conversion cost during the month of October for Company PA as shown below:

Figure (5)

Working notes:

Calculate opening work in process inventory for conversion percentage to complete as shown below:

  $\begin{array}{c}\begin{array}{l}\text{Opening work in process}\\ \text{ inventory for Conversion}\end{array})\text{=}\text{1}-\frac{4}{5}\\ =\frac{4}{5}\\ =20\%\end{array}$

Calculate units started and completed in October as shown below:

  $\begin{array}{c}\text{Units started and completed in May}\text{=}\left(\begin{array}{l}\text{Received from smelting department}\\ -\text{Ending work in process inventory}\end{array}\right)\\ \text{=}31\text{,000}\text{units }-2,000\text{units}\\ \text{=}29,000\text{units}\end{array}$

Calculate ending work in process inventory units as shown below:

$\begin{array}{c}\text{Ending work in process inventory for conversion =}30\text{0}\text{units }\times \frac{2}{5}\\ \text{=}800\text{units}\end{array}$

Total units to be assigned to costs is calculated by adding opening work in process inventory, units started and completed and ending work in process inventory.

Conclusion

Therefore, direct material equivalent units for production is 31,000 units and conversion cost equivalent units for production is 30,380 units.

To determine

Prepare the cost per equivalent unit for direct material and conversion cost during the month of Octoberfor Company PA.

Explanation of Solution

Calculate the cost per equivalent unit for direct material and conversion cost during the month of October for Company PA as shown below:

  $\begin{array}{c}\begin{array}{l}\text{Equivalent cost per unit }\\ \text{of direct materials }\end{array})\text{=}\frac{\text{Cost of Direct materials}}{\text{Equivalent units of direct materials}}\\ =\frac{\$511,500}{31,000\text{units}}\\ =\$16.50\text{per unit}\end{array}$

  $\begin{array}{c}\begin{array}{l}\text{Equivalent cost per unit }\\ \text{of Conversion cost }\end{array})\text{=}\frac{\text{Cost of Conversion cost}}{\text{Equivalent units of conversion}}\\ =\frac{\$267,344}{30,380\text{units}}\\ =\$8.80\text{per unit}\end{array}$

Working note:

Calculate conversion cost for the month of September of Company PA as shown below:

  $\begin{array}{c}\text{Conversion cost =}\text{Direct labor cost +}\text{Factory overhead cost}\\ \text{=}\text{\$162,850}\text{+}\text{\$104,494}\\ \text{=}\text{\$267,344}\end{array}$

Equivalent cost per unit for direct materials is calculated by dividing direct material cost by equivalent units for direct materials. Equivalent cost per unit for conversion cost is calculated by dividing conversion cost by equivalent units for conversion.

Conclusion

Therefore, equivalent cost per unit for direct material is $16.50 per unit and for conversion cost is $8.80 per unit.

To determine

Prepare the cost of goods finished, between units stared in the prior period and units started and finished in October of Company PA.

Explanation of Solution

Prepare the cost of goods finished, between units stared in the prior period and units started and finished in October of Company PA as shown below:

Figure (6)

Costs transferred to finished goods is calculated by adding opening inventory in September balance, to complete opening work in process inventory in September, and cost of units started and completed in September.

Conclusion

Hence, cost of completed work in process inventory in October 1 is $71,456, cost for started and completed in October is $733,700, and transferred to finished goods is $805,156.

To determine

Prepare the ending work in process inventory cost of the month October for the Company PA.

Explanation of Solution

Prepare the ending work in process inventory cost of the month October for the Company PA as shown below:

Figure (7)

Ending work in process inventory cost is calculated by adding ending direct material cost and ending conversion costs.

Conclusion

Hence, ending work in process inventory cost for the month of October is $40,040.

To determine

Prepare the production cost report of rolling department for the month of October of Company PA.

Explanation of Solution

Prepare the production cost report of rolling department for the month of October of Company PA as shown below:

Figure (8)

Conclusion

Therefore, cost of production report for Rolling department during the month of October for Company PA is $845,196.

To determine

Mention the change in cost per equivalent unit for August through October for direct materials and conversion costs.

Explanation of Solution

The cost per equivalent unit for direct material in August is $15.50 per unit, in September is $16.00 per unit, and in October is $16.50 per unit. Constantly direct material cost per unit is increased from August to October. Likewise, the cost per equivalent unit for conversion cost in August is $8.50 per unit, in September is $8.60 per unit, and in October$8.80 per unit. Constantly conversion cost per unit is increased from August to October. The Company PA scrutinizes for their underlying reasons, and any required remedial actions would be taken.