Chapter 6, Problem 9E

A company manufactures a liquid product called Crystal. The basic ingredients are put into process in Department 1. In Department 2, other materials are added that increase the number of units being processed by 50%. The factory has only two departments.

Calculate the following for each department: (a) unit cost for the month for materials, labor, and factory overhead, (b) cost of the units transferred, and (c) cost of the ending work in process.

To determine

Compute unit cost for materials, labor and factory overhead, cost of the units transferred and cost of the ending work in process-department 1.

Explanation of Solution

Compute equivalent unit of production.

Particulars	Units
Units finished and transferred out	14,000
Ending work in process	1,000
Total	15,000

Table (1)

a. Compute unit cost.

Particulars	Amount ($)
Materials	6
Labor	2
Factory overhead	1
Total	9

Table (2)

Working Notes:

Calculate the cost of work in process, end of month-material.

$\begin{array}{c}\left(\begin{array}{l}\text{Cost of work in process,}\\ \text{end of process-Material}\end{array}\right)=\frac{\text{Material cost}}{\text{Equivalent units of production}}\\ =\frac{\$90,000}{15,000}\\ =\$6\end{array}$

Calculate the cost of work in process, end of month-labor.

$\begin{array}{c}\left(\begin{array}{l}\text{Cost of work in process,}\\ \text{end of process-labor}\end{array}\right)=\frac{\text{Labor cost}}{\text{Equivalent units of production}}\\ =\frac{\$30,000}{15,000}\\ =\$2\end{array}$

Calculate the cost of work in process, end of month-factory overhead.

$\begin{array}{c}\left(\begin{array}{l}\text{Cost of work in process,}\\ \text{end of process-Factory}\\ \text{overhead}\end{array}\right)=\frac{\text{Factory overhead cost}}{\text{Equivalent units of production}}\\ =\frac{\$15,000}{15,000}\\ =\$1\end{array}$

b. Compute cost of units finished and transferred.

$\begin{array}{c}\text{Unit cost of material}=\frac{\text{Units transferred}}{\text{Toatl unit cost}}\\ =\frac{14,000}{\$9}\\ =\$126,000\end{array}$

c. Compute total work in process, end of month.

Particulars	Amount ($)
Materials	6,000
Labor	2,000
Factory overhead	1,000
Total	9,000

Table (3)

Working Notes:

Calculate the cost of work in process-material.

$\begin{array}{c}\left(\begin{array}{l}\text{Cost of work in process}\\ \left(\text{Material}\right)\end{array}\right)=\left(\begin{array}{l}\text{Units in process}\\ \times \text{Stage of completion}\\ \times \text{Unit cost of material}\end{array}\right)\\ =\left(4,000\times \frac{1}{4}\times \$6\right)\\ =\$6,000\end{array}$

Calculate the cost of work in process-labor.

$\begin{array}{c}\left(\begin{array}{l}\text{Cost of work in process}\\ \left(\text{Labor}\right)\end{array}\right)=\left(\begin{array}{l}\text{Units in process}\\ \times \text{Stage of completion}\\ \times \text{Unit cost of material}\end{array}\right)\\ =\left(4,000\times \frac{1}{4}\times \$2\right)\\ =\$2,000\end{array}$

Calculate the cost of work in process-factory overhead.

$\begin{array}{c}\left(\begin{array}{l}\text{Cost of work in process}\\ \left(\text{Factory overhead}\right)\end{array}\right)=\left(\begin{array}{l}\text{Units in process}\\ \times \text{Stage of completion}\\ \times \text{Unit cost of factory overhead}\end{array}\right)\\ =\left(4,000\times \frac{1}{4}\times \$1\right)\\ =\$1,000\end{array}$

To determine

Compute unit cost for materials, labor and factory overhead, cost of the units transferred and cost of the ending work in process-department 2.

Explanation of Solution

Compute equivalent unit of production- department 2.

Particulars	Units
Units finished and transferred out	15,000
Ending work in process	3,000
Total	18,000

Table (4)

a. Compute unit cost-department 2.

Particulars	Amount ($)
Materials	2
Labor	0.75
Factory overhead	0.25
Total	3

Table (5)

Working Notes:

Calculate the cost of work in process, end of month-material.

$\begin{array}{c}\left(\begin{array}{l}\text{Cost of work in process,}\\ \text{end of process-Material}\end{array}\right)=\frac{\text{Material cost}}{\text{Equivalent units of production}}\\ =\frac{\$36,000}{18,000}\\ =\$2\end{array}$

Calculate the cost of work in process, end of month-labor.

$\begin{array}{c}\left(\begin{array}{l}\text{Cost of work in process,}\\ \text{end of process-labor}\end{array}\right)=\frac{\text{Labor cost}}{\text{Equivalent units of production}}\\ =\frac{\$13,500}{18,000}\\ =\$0.75\end{array}$

Calculate the cost of work in process, end of month-factory overhead.

$\begin{array}{c}\left(\begin{array}{l}\text{Cost of work in process,}\\ \text{end of process-Factory}\\ \text{overhead}\end{array}\right)=\frac{\text{Factory overhead cost}}{\text{Equivalent units of production}}\\ =\frac{\$4,500}{18,000}\\ =\$0.25\end{array}$

b. Compute cost of units finished and transferred- department 2.

Particulars	Amount ($)
Cost in department 1	90,000
Cost in department 2	45,000
Total	135,000

Table (6)

Working Notes:

Calculate the cost in department 1.

$\begin{array}{c}\text{Cost in department 1}=\left(\begin{array}{l}\text{Unit cost transferred}\\ \times \text{Adjusted unit cost}\end{array}\right)\\ =15,000\times \$6\left(1\right)\\ =\$90,000\end{array}$

(1) Calculate the adjusted unit cost.

 $\begin{array}{c}\text{Adjusted unit cost}=\frac{\text{Units from department 1}}{\text{New quantity}}\\ =\frac{\$126,000}{21,000\left(2\right)}\\ =\$6\end{array}$

(2) Calculate the new quantity.

Particulars	Amount ($)
Units from department	14,000
Units added	7,000
New quantity	21,000

Table (7)

Calculate the cost in department 2.

$\begin{array}{c}\text{Cost in department 2}=\left(\begin{array}{l}\text{Unit cost transferred}\\ \times \text{Total unit cost}\end{array}\right)\\ =15,000\times \$3\\ =\$45,000\end{array}$

c. Compute work in process, end of month- department 2.

Particulars	Amount ($)	Amount ($)
Cost in department 1		36,000
Cost in department 2
Materials	6,000
Labor	2,000
Factory overhead	1,000	9,000
Total		45,000

Table (8)

Working Notes:

Calculate the cost of work in process-material.

$\begin{array}{c}\left(\begin{array}{l}\text{Cost of work in process}\\ \left(\text{Material}\right)\end{array}\right)=\left(\begin{array}{l}\text{Units in process}\\ \times \text{Stage of completion}\\ \times \text{Unit cost of material}\end{array}\right)\\ =\left(6,000\times \frac{1}{2}\times \$2\right)\\ =\$6,000\end{array}$

Calculate the cost of work in process-labor.

$\begin{array}{c}\left(\begin{array}{l}\text{Cost of work in process}\\ \left(\text{Labor}\right)\end{array}\right)=\left(\begin{array}{l}\text{Units in process}\\ \times \text{Stage of completion}\\ \times \text{Unit cost of material}\end{array}\right)\\ =\left(6,000\times \frac{1}{2}\times \$0.75\right)\\ =\$2,250\end{array}$

Calculate the cost of work in process-factory overhead.

$\begin{array}{c}\left(\begin{array}{l}\text{Cost of work in process}\\ \left(\text{Factory overhead}\right)\end{array}\right)=\left(\begin{array}{l}\text{Units in process}\\ \times \text{Stage of completion}\\ \times \text{Unit cost of factory overhead}\end{array}\right)\\ =\left(6,000\times \frac{1}{2}\times \$0.25\right)\\ =\$750\end{array}$