Chapter 8, Problem 53P

a.

To determine

Prepare a production cost report using the weighted-average method.

Explanation of Solution

Weighted average cost method:

Weighted average cost method is the method to find out the equivalent units in the process costing. Under this method work done on all completed units taken as 100% whether these units are from beginning inventory or units introduced in the process. The work done on the ending inventory is calculated as per work done on it with respect to the completed units.

Compute the total units of prior department, materials, labor and manufacturing overhead:

Particulars	Physical units	Prior department	Materials	Labor	Manufacturing overhead
Beginning work-in-process inventory	75,000
Units started this period	375,000
Total units	450,000
Completed and transferred out
Beginning work-in-process inventory	75,000
Started and currently completed	225,000
Total transferred out	300,000	300,000	300,000	300,000	300,000
Units in ending work-in-process inventory	150,000	150,000	135,000(1)	105,000(2)	52,500(3)
Total units	450,000	450,000	435,000	405,000	352,500

Table: (1)

Compute the cost per equivalent unit for prior department, materials, labor and manufacturing overhead:

Particulars	Total	Prior department	Materials	Labor	Manufacturing overhead
Costs in beginning work-in-process inventory	$ 382,800	$ 192,000	$ 120,000	$ 43,200	$ 27,600
Add: Current period costs	$ 1,865,400	$ 960,000	$ 576,000	$ 216,000	$ 113,400
Total costs	$ 2,248,200	$ 1,152,000	$ 696,000	$ 259,200	$ 141,000
Cost per equivalent unit:
Prior department		$ 2.56(4)
Materials			$ 1.60(5)
Labor				$ 0.64(6)
Manufacturing overhead					$ 0.40(7)

Table: (2)

Compute the transferred out, ending inventory and total costs for prior department, materials, labor and manufacturing overhead:

Particulars	Total	Prior department	Materials	Labor	Manufacturing overhead
Transferred out:
Prior department	$ 768,000	$768,000(8)
Materials	$ 480,000		$480,000(9)
Labor	$ 192,000			$192,000(10)
Manufacturing overhead	$ 120,000				$120,000(11)
Total costs	$ 1,560,000
Work-in-process ending inventory
Prior department	$ 384,000	$384,000(12)
Materials	$ 216,000		$216,000(13)
Labor	$ 67,200			$67,200(14)
Manufacturing overhead	$ 21,000				$21,000(15)
Total ending work-in-process inventory	$ 688,200
Total costs	$ 2,248,200	$ 1,152,000	$ 696,000	$ 259,200	$ 141,000

Table: (3)

Working note 1:

Compute the units in ending work-in-process inventory:

$\begin{array}{c}\text{Ending}\text{work-in-process}\text{inventory}\text{=}\text{Completion}\text{rate}\\ \text{×}\text{Total}\text{units}\text{in}\text{ending}\text{inventory}\text{(WIP)}\\ =90\%\times 150,000\\ =135,000\end{array}$

Working note 2:

Compute the units in ending work-in-process inventory:

$\begin{array}{c}\text{Ending}\text{work-in-process}\text{inventory}\text{=}\text{Completion}\text{rate}\\ \text{×}\text{Total}\text{units}\text{in}\text{ending}\text{inventory}\text{(WIP)}\\ =70\%\times 150,000\\ =105,000\end{array}$

Working note 3:

Compute the units in ending work-in-process inventory:

$\begin{array}{c}\text{Ending}\text{work-in-process}\text{inventory}\text{=}\text{Completion}\text{rate}\\ \text{×}\text{Total}\text{units}\text{in}\text{ending}\text{inventory}\text{(WIP)}\\ =35\%\times 150,000\\ =52,500\end{array}$

Working note 4:

Compute the cost per equivalent unit:

$\begin{array}{c}\text{Cost}\text{per}\text{equivalen}\text{unit}\text{=}\frac{\text{Total}\text{cost}}{\text{Total}\text{units}\text{accounted}\text{for}}\\ \text{=}\frac{\text{\$1,152,000}}{\text{450,000}}\\ \text{=}\text{\$2}\text{.56}\end{array}$

Working note 5:

Compute the cost per equivalent unit:

$\begin{array}{c}\text{Cost}\text{per}\text{equivalen}\text{unit}\text{=}\frac{\text{Total}\text{cost}}{\text{Total}\text{units}\text{accounted}\text{for}}\\ \text{=}\frac{\text{\$696,000}}{\text{435,000}}\\ \text{=}\text{\$1}\text{.60}\end{array}$

Working note 6:

Compute the cost per equivalent unit:

$\begin{array}{c}\text{Cost}\text{per}\text{equivalen}\text{unit}\text{=}\frac{\text{Total}\text{cost}}{\text{Total}\text{units}\text{accounted}\text{for}}\\ \text{=}\frac{\text{\$259,200}}{\text{405,000}}\\ \text{=}\text{\$0}\text{.64}\end{array}$

Working note 7:

Compute the cost per equivalent unit:

$\begin{array}{c}\text{Cost}\text{per}\text{equivalen}\text{unit}\text{=}\frac{\text{Total}\text{cost}}{\text{Total}\text{units}\text{accounted}\text{for}}\\ \text{=}\frac{\text{\$141,000}}{\text{352,500}}\\ \text{=}\text{\$0}\text{.40}\end{array}$

Working note 8:

Compute the transferred out costs:

$\begin{array}{c}\text{Transferred}\text{out}\text{cost}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Transferred}\text{out}\text{units}\\ \text{=}\text{\$2}\text{.56}\left(4\right)\times \text{300,000}\\ \text{=}\text{\$768,000}\end{array}$

Working note 9:

Compute the transferred out costs:

$\begin{array}{c}\text{Transferred}\text{out}\text{cost}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Transferred}\text{out}\text{units}\\ \text{=}\text{\$1}\text{.60}\left(5\right)\times \text{300,000}\\ \text{=}\text{\$480,000}\end{array}$

Working note 10:

Compute the transferred out costs:

$\begin{array}{c}\text{Transferred}\text{out}\text{cost}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Transferred}\text{out}\text{units}\\ \text{=}\text{\$0}\text{.64}\left(6\right)\times \text{300,000}\\ \text{=}\text{\$192,000}\end{array}$

Working note 11:

Compute the transferred out costs:

$\begin{array}{c}\text{Transferred}\text{out}\text{cost}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Transferred}\text{out}\text{units}\\ \text{=}\text{\$0}\text{.40}\left(7\right)\times \text{300,000}\\ \text{=}\text{\$120,000}\end{array}$

Working note 12:

Compute the costs assigned to ending work-in-process inventory:

$\begin{array}{c}\text{Cost}\text{of}\text{ending}\text{inventory}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Units}\text{in}\text{ending}\text{inventory}\\ \text{=}\text{\$2}\text{.56}\left(4\right)\times \text{150,000}\\ \text{=}\text{\$384,000}\end{array}$

Working note 13:

Compute the costs assigned to ending work-in-process inventory:

$\begin{array}{c}\text{Cost}\text{of}\text{ending}\text{inventory}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Units}\text{in}\text{ending}\text{inventory}\\ \text{=}\text{\$1}\text{.60}\left(5\right)\times \text{135,000}\\ \text{=}\text{\$216,000}\end{array}$

Working note 14:

Compute the costs assigned to ending work-in-process inventory:

$\begin{array}{c}\text{Cost}\text{of}\text{ending}\text{inventory}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Units}\text{in}\text{ending}\text{inventory}\\ \text{=}\text{\$0}\text{.64}\left(6\right)\times 105\text{,000}\\ \text{=}\text{\$67,200}\end{array}$

Working note 15:

Compute the costs assigned to ending work-in-process inventory:

$\begin{array}{c}\text{Cost}\text{of}\text{ending}\text{inventory}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Units}\text{in}\text{ending}\text{inventory}\\ \text{=}\text{\$0}\text{.40}\left(7\right)\times 52\text{,500}\\ \text{=}\text{\$21,000}\end{array}$

b.

To determine

Determine whether the targets assigned by the management have been achieved or not. Write a short report on the same.

Explanation of Solution

Cost per equivalent unit:

Total amount accounted for and total units accounted are considered Compute the cost per equivalent unit.

Computed cost per equivalent units:

Particulars	Cost per equivalent unit
Materials	$ 1.60
Labor	$ 0.64
Manufacturing overhead	$ 0.40

Table: (4)

Targeted cost per equivalent units:

Particulars	Cost per equivalent unit
Materials	$ 1.60
Labor	$ 0.80
Manufacturing overhead	$ 0.36

Table: (5)

Relevance of reported computed result and targeted result for materials, labor and manufacturing overhead:

Only the target determined by the management for materials has been achieved. For labor and manufacturing overhead, the cost per equivalent unit has not achieved. The targeted cost per equivalent unit for labor was $0.80 but the actual cost per equivalent unit has been computed to $0.64. Thus, the target has been achieved and reduced further when computed using weighted-average method for labor.

And, the target set by the management for manufacturing overhead was $0.36 and the cost per equivalent unit has been computed to $0.40. The target has not been met by 11% difference approximately.