Chapter 8, Problem 53P

To determine

Compute the cost of goods transferred out in August and the cost of work-in-process ending inventory.

Explanation of Solution

Cost of units in ending work-in-process:

Cost of ending units in work-in-process is found out by multiplying equivalent unit in ending inventory by equivalent cost of ending inventory with respect to materials cost and conversion costs.

Conversion costs:

The total production cost or converting the product from raw material to final product that is ready to be transferred as finished goods, work-in-process or has started are taken into consideration for conversion costs.

Compute the total units for prior department, materials and conversion costs:

Particulars	Physical units	Prior department	Materials	Conversion costs
Beginning work-in-process inventory	12,500
Units started this period	127,500
Total units	140,000
Completed and transferred out
Beginning work-in-process inventory	12,500	0	5,000 (1)	7,500(2)
Started and currently completed	107,500	107,500	107,500	107,500
Units in ending work-in-process inventory	20,000	20,000	18,000 (3)	10,000 (4)
Total units	140,000	127,500	130,500	125,000

Table: (1)

Compute the cost per equivalent unit for prior department, materials and conversion costs:

Particulars	Total	Prior department	Materials	Conversion costs
Costs in beginning work-in-process inventory	$ 323,400	$ 98,000	$ 164,400	$ 61,000
Current period costs	$ 3,306,600	$ 2,142,000	$ 939,600	$ 225,000
Total costs	$ 3,630,000	$ 2,240,000	$ 1,104,000	$ 286,000
Cost per equivalent unit
Prior department		$ 16.80(5)
Materials			$ 7.20(6)
Conversion				$ 1.80(7)

Table: (2)

Compute the total costs for prior department, materials and conversion costs:

Particulars	Total	Prior department	Materials	Conversion costs
Transferred out:
Costs from beginning inventory	$ 323,400	$ 98,000	$ 164,400	$ 61,000
Current costs beginning work-in-process inventory
Prior department	$ 0	$ 0
Materials	$ 36,000		$ 36,000(8)
Conversion	$ 13,500			$ 13,500(9)
Total costs	$ 372,900
Current costs of units started and completed
Prior department	$ 1,806,000	$ 1,806,000(10)
Materials	$ 774,000		$ 774,000(11)
Conversion	$ 193,500			$ 193,500(12)
Total costs of units started and completed	$ 2,773,500
Total costs	$ 3,146,400	$ 1,806,000	$ 810,000	$ 207,000
Current costs work-in-process ending inventory
Prior department	$ 336,000	$ 336,000(13)
Materials	$ 129,600		$ 129,600(14)
Conversion	$ 18,000			$ 18,000(15)
Total ending work-in-process inventory	$ 483,600
Total costs accounted for	$ 3,630,000	$ 2,240,000	$ 1,104,000	$ 286,000

Table: (3)

Working note 1:

Compute the units completed and transferred out from beginning inventory of materials:

$\begin{array}{l}\text{Beginning}\text{inventory}\text{=}\left(\text{1}-\text{Completion}\text{rate}\right)\text{×}\text{}\text{Beginning}\text{inventory}\text{(WIP)}\\ \text{=}\left(1-60\%\right)\times 12,500\\ =5,000\end{array}$

Working note 2:

Compute the units completed and transferred out from beginning inventory of conversion costs:

$\begin{array}{c}\text{Beginning}\text{inventory}\text{=}\left(\text{1}-\text{Completion}\text{rate}\right)\text{×}\text{Beginning}\text{inventory}\text{(WIP)}\\ \text{=}\left(1-40\%\right)\times 12,500\\ =7,500\end{array}$

Working note 3:

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

$\begin{array}{c}\text{Ending}\text{inventory}\text{=}\text{Completion}\text{rate}\text{×}\text{Ending}\text{inventory}\text{(Physical}\text{units)}\\ \text{=}\text{90\%}\text{×}\text{20,000}\\ \text{=}\text{18,000}\end{array}$

Working note 4:

Compute the units in ending work-in-process inventory for conversion costs:

$\begin{array}{c}\text{Ending}\text{inventory}\text{=}\text{Completion}\text{rate}\text{×}\text{Ending}\text{inventory}\text{(Physical}\text{units)}\\ \text{=}5\text{0\%}\text{×}\text{20,000}\\ \text{=}\text{10,000}\end{array}$

Working note 5:

Compute the cost per equivalent unit for prior department costs:

$\begin{array}{c}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{=}\frac{\text{Current}\text{period}\text{costs}}{\text{Total}\text{units}\text{accounted}\text{for}}\\ =\frac{\$2,142,000}{127,500}\\ =\$16.80\end{array}$

Working note 6:

Compute the cost per equivalent unit for prior department costs:

$\begin{array}{c}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{=}\frac{\text{Current}\text{period}\text{costs}}{\text{Total}\text{units}\text{accounted}\text{for}}\\ =\frac{\$939,600}{130,500}\\ =\$7.20\end{array}$

Working note 7:

Compute the cost per equivalent unit for prior department costs:

$\begin{array}{c}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{=}\frac{\text{Current}\text{period}\text{costs}}{\text{Total}\text{units}\text{accounted}\text{for}}\\ =\frac{\$225,,000}{125,500}\\ =\$16.80\end{array}$

Working note 8:

Compute the current costs added to complete beginning work-in-process inventory:

$\begin{array}{c}\text{Current}\text{costs}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Beginning}\text{inventory}\text{(WIP)}\\ \text{=}\text{\$7}\text{.20}\text{×}\text{5,000}\\ \text{=}\text{36,000}\end{array}$

Working note 9:

Compute the current costs added to complete beginning work-in-process inventory:

$\begin{array}{c}\text{Current}\text{costs}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Beginning}\text{inventory}\text{(WIP)}\\ \text{=}\text{\$1}\text{.80}\text{×}7\text{,500}\\ \text{=}13\text{,500}\end{array}$

Working note 10:

Compute the current costs of units started and completed:

$\begin{array}{c}\text{Cost}\text{of}\text{units}\text{completed}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Started}\text{and}\text{completed}\text{units}\\ \text{=}\text{\$16}\text{.80}\text{×}\text{107,500}\\ \text{=}\text{\$1,806,000}\end{array}$

Working note 11:

Compute the current costs of units started and completed:

$\begin{array}{c}\text{Cost}\text{of}\text{units}\text{completed}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Started}\text{and}\text{completed}\text{units}\\ \text{=}\text{\$7}\text{.20}\text{×}\text{107,500}\\ \text{=}\text{\$774,000}\end{array}$

Working note 12:

Compute the current costs of units started and completed:

$\begin{array}{c}\text{Cost}\text{of}\text{units}\text{completed}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Started}\text{and}\text{completed}\text{units}\\ \text{=}\text{\$1}\text{.80}\text{×}\text{107,500}\\ \text{=}\text{\$193,500}\end{array}$

Working note 13:

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

$\begin{array}{c}\text{Cost}\text{of}\text{ending}\text{inventory}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Ending}\text{inventory}\\ \text{=}\text{\$16}\text{.80}\text{×}\text{20,000}\\ \text{=}\$336,000\end{array}$

Working note 14:

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

$\begin{array}{c}\text{Cost}\text{of}\text{ending}\text{inventory}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Ending}\text{inventory}\\ \text{=}\text{\$7}\text{.20}\text{×}18\text{,000}\\ \text{=}\$129,600\end{array}$

Working note 15:

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

$\begin{array}{c}\text{Cost}\text{of}\text{ending}\text{inventory}\text{=}\text{Cost}\text{per}\text{equivalent}\text{unit}\text{×}\text{Ending}\text{inventory}\\ \text{=}\text{\$1}\text{.80}\text{×}1\text{0,000}\\ \text{=}\$18,000\end{array}$