Chapter 3, Problem 6E

1.

To determine

To compute: Equivalent unit of production according to weighted average method.

Explanation of Solution

For direct material:

Given,
Completed goods are 295,000 units.
Work in progress is 24,000 units.

Formula for calculating equivalent unit of production (direct material),

$\text{Equivalent}\text{Unit}\text{of}\text{Production}\text{(Direct}\text{Material)}=\left(\begin{array}{l}\text{Completed}\text{Goods}\\ +\text{Work}\text{in}\text{Progress}\end{array}\right)$

Substitute 295,000 units for completed goods and 24,000 units for work in progress.

$\begin{array}{c}\text{Equivalent}\text{Unit}\text{of}\text{Production}=295,000+24,000\\ =319,000\end{array}$

Hence, equivalent unit of production (direct material) is 319,000 units.

Working note:

Calculation for work in progress,

$\begin{array}{c}\text{Work}\text{in}\text{progress}=\text{Unfinsihed}\text{goods}\times \text{Finished}\text{percentage}\\ =30,000\times \frac{80}{100}\\ =24,000\end{array}$

For conversion:

Given,
Completed goods are 295,000 units.
Work in progress is 9,000 units.

Formula for calculating equivalent unit of production (conversion),

$\text{Equivalent}\text{Unit}\text{of}\text{Production}\text{(Conversion)}=\left(\begin{array}{l}\text{Completed}\text{Goods}\\ +\text{Work}\text{in}\text{progress}\end{array}\right)$

Substitute, 295,000 units for completed goods and 9,000 units for work in progress in the above equation,

$\begin{array}{c}\text{Equivalent}\text{Unit}\text{of}\text{Production}=295,000+9,000\\ =304,000\end{array}$

Hence, equivalent unit of production (conversion) is 304,000 units.

Working note:

Calculation for work in progress,

$\begin{array}{c}\text{Work}\text{in}\text{progress}=\text{Unfinsihed}\text{goods}\times \text{Finished}\text{percentage}\\ =30,000\times \frac{30}{100}\\ =9,000\end{array}$

2.

To determine

To compute: Cost per equivalent unit of production.

Explanation of Solution

For direct material:

Given,
Total direct material cost is $1,276,000.
Total EUP (Direct Material) is 319,000 units.

Formula for calculating cost per equivalent unit of production,

$\text{Cost}\text{per}\text{EUP}\text{(Direct}\text{Material)}=\frac{\text{Total}\text{Direct}\text{Material}\text{Cost}}{\text{Total}\text{EUP}\text{(Direct}\text{Material)}}$

Substitute, $1,276,000 for total direct material cost and 319,000 units for total EUP (direct material).

$\begin{array}{c}\text{Cost}\text{per}\text{EUP}\text{(Direct}\text{Material)}=\frac{\$1,276,000}{319,000}\\ =\$4\end{array}$

Hence, cost per EUP (Direct Material) is $4.

Working note:

Calculation for total direct material cost,

$\begin{array}{c}\text{Total}\text{Direct}\text{Material}\text{Cost}=\left(\begin{array}{l}\text{Direct}\text{Material}\text{In}\text{the}\text{opening}\text{inventory}\\ +\text{Direct}\text{matrial}\text{used}\text{during}\text{the}\text{month}\end{array}\right)\\ =\$44,800+\$1,231,200\\ =\$1,276,000\end{array}$

For conversion:

Given,
Total conversion cost is $912,000.
Total EUP (Conversion) is 304,000 units.

Formula for calculating cost per equivalent unit of production,

$\text{Cost}\text{per}\text{EUP}\text{(Conversion)}=\frac{\text{Total}\text{Direct}\text{Material}\text{Cost}}{\text{Total}\text{EUP}\text{(Conversion)}}$

Substitute $912,000 for total conversion cost and 304,000 units for total EUP (conversion).

$\begin{array}{c}\text{Cost}\text{per}\text{EUP}\text{(Direct}\text{Material)}=\frac{\$912,000}{304,000}\\ =\$3\end{array}$

Hence, cost per EUP (conversion) is $3.

Working note:

Calculation for total direct material cost,

$\begin{array}{c}\text{Total}\text{conversion}\text{cost}=\left(\begin{array}{l}\text{Conversion}\text{cost}\text{in}\text{the}\text{opening}\text{inventory}\\ +\text{Conversion}\text{cost}\text{used}\text{during}\text{the}\text{month}\end{array}\right)\\ =\$15,300+\$896,700\\ =\$912,000\end{array}$

3.

To determine

To compute: Assign cost to forming department.

Explanation of Solution

Given,
Direct material cost for completed goods is $1,280,000.
Conversion cost for completed goods is $885,000.

For completed goods:

Formula for calculating the cost of unit completed,

$\text{Cost}\text{of}\text{Units}\text{Completed}=\left(\begin{array}{l}\text{Direct}\text{Material}\text{Cost}\text{for}\text{Completed}\text{Goods}\\ +\text{Conversion}\text{Cost}\text{for}\text{Completed}\text{Goods}\end{array}\right)$

Substitute, $1,280,000 for direct material cost for completed goods and $885,000 for conversion cost for completed goods.

$\begin{array}{c}\text{Cost}\text{of}\text{Units}\text{Completed}=\$1,280,000+\$885,000\\ =\$2,165,000\end{array}$

Hence, cost of unit completed is $2,165,000.

Working notes:

Calculation for direct material cost for completed goods,

$\begin{array}{c}\text{Direct}\text{Material}\text{Cost}\text{for}\text{Completed}\text{Goods}=\left(\begin{array}{l}\text{Completed}\text{Goods}\\ \times \text{Cost}\text{per}\text{EUP}\text{(Direct}\text{Material)}\end{array}\right)\\ =295,000\times \$4\\ =\$1,280,000\end{array}$

Calculation for conversion cost for completed goods,

$\begin{array}{c}\text{Conversion}\text{Cost}\text{for}\text{Completed}\text{Goods}=\left(\begin{array}{l}\text{Completed}\text{Goods}\\ \times \text{Cost}\text{per}\text{EUP}\text{(Conversion)}\end{array}\right)\\ =295,000\times \$3\\ =\$885,000\end{array}$

For work in process (end):

Given,
Direct material cost for work in process (end) is $96,000.
Conversion cost for work in process (end) is $27,000.

Formula for calculating the cost of work in process (end),

$\text{Cost}\text{of}\text{work in process}\left(\text{end}\right)=\left(\begin{array}{l}\text{Direct}\text{Material}\text{Cost}\text{for}\text{Completed}\text{Goods}\\ +\text{Conversion}\text{Cost}\text{for}\text{Completed}\text{Goods}\end{array}\right)$

Substitute, $96,000 for direct material cost for work in process (end) and $27,000 for conversion cost for work in process (end).

$\begin{array}{c}\text{Cost}\text{of}\text{work in process }\left(\text{end}\right)=\$96,000+\$27,000\\ =\$123,000\end{array}$

Hence, cost of work in process (end) is $123,000.

Working notes:

Calculation for direct material cost for work in process (end),

$\begin{array}{c}\left[\begin{array}{l}\text{Direct}\text{Material}\text{Cost}\text{for}\\ \text{work in process }\left(\text{end}\right)\end{array}\right]=\left[\begin{array}{l}\text{EUP}\text{(Direct}\text{Material)}\text{for}\text{work in process }\left(\text{end}\right)\\ \times \text{Cost}\text{per}\text{EUP}\text{(Direct}\text{Material)}\end{array}\right]\\ =24,000\times \$4\\ =\$96,000\end{array}$

Calculation for conversion cost for work in process (end),

$\begin{array}{c}\left[\begin{array}{l}\text{Conversion}\text{Cost}\text{for}\\ \text{Completed}\text{Goods}\end{array}\right]=\left[\begin{array}{l}\text{EUP}\text{(Conversion)}\text{for}\text{work in process }\left(\text{end}\right)\\ \times \text{Cost}\text{per}\text{EUP}\text{(Conversion)}\end{array}\right]\\ =9,000\times \$3\\ =\$27,000\end{array}$