Chapter 3, Problem 8E

1. a. Based upon the data in Exercise 17-7, determine the following for December:
   1. 1. Direct materials cost per equivalent unit
   2. 2. Conversion cost per equivalent unit
   3. 3. Cost of the beginning work in process completed during December
   4. 4. Cost of units started and completed during December
   5. 5. Cost of the ending work in process
2. b. Assuming that the direct materials cost is the same for November and December, did the conversion cost per equivalent unit increase, decrease, or remain the same in December?

To determine

Compute the following:

1. 1. Direct materials cost per equivalent unit.
2. 2. Conversion cost per equivalent unit.
3. 3. Cost of the beginning work in process completed during December.
4. 4. Cost of units started and completed during December.
5. 5. Cost of the ending work in process.

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.

1. 1. Calculate direct material cost per unit:

$\begin{array}{c}\text{Material cost per unit =}\frac{\text{Total}\text{direct materials cost}}{\text{ Direct materials units}}\\ =\frac{\$234,500}{134,000\text{units}}\\ =\$1.75\text{per unit}\end{array}$

Material cost per unit is calculated by dividing total direct material cost by direct material units. Therefore, material cost per unit is $1.75.

1. 2. Calculate conversion cost per unit:

$\begin{array}{c}\text{Conversion}\text{cost per unit =}\frac{\text{Total direct labor cost +}\text{Total factory overhead cost}}{\text{ Conversion units}}\\ =\frac{\$150,000+\$375,000}{125,000\text{units}}\\ =\$4.20\text{per unit}\end{array}$

A conversion cost per unit is calculated by dividing total direct labor and factory overhead cost by conversion units. Therefore, conversion cost per unit is $4.20.

1. 3. Calculate the cost of beginning work in process inventory completed during the period December  :

$\begin{array}{c}\begin{array}{l}\text{Beginning work in process inventory}\\ \text{completed during the period}\end{array})=\left(\begin{array}{l}\text{Beginning work in process inventory }\\ \text{costs +}\text{Conversion costs during the period}\end{array}\right)\\ =\$116,700+\$25,200(1)\\ =\$141,900\end{array}$

Working note (1):

Calculate beginning work in process inventory amount for Conversion costs during the period:

$\begin{array}{c}\text{Beginning work in process inventory =}\left(\begin{array}{l}\text{Openning}\text{equivalent units }\\ \text{for conversion}\times \text{Conversion cost per unit }\end{array}\right)\\ =6,000\text{units }\times \text{\$4}\text{.20}\text{per unit}\\ =\$25,200\end{array}$

Beginning work in process inventory completed during the period of December is calculated by adding beginning work in process costs balance and beginning work in process inventory for conversion costs. Hence, beginning work in process inventory completed during the period of December is $141,900.

1. 4. Calculate the cost of units started and completed during the period of:

$\begin{array}{c}\begin{array}{l}\text{Cost of units started }\\ \text{and completed }\\ \text{during the period March}\end{array})=\left(\begin{array}{l}\text{Units started and completed during the march}\\ \times \text{Material cost per unit}+\text{Conversion cost per unit}\end{array}\right)\\ =104,000(2)\text{units}\times \text{(\$1}\text{.75}+\text{\$4}\text{.20)}\\ =104,000\times \$5.95\\ =\$618,800\text{unit}s\end{array}$

Working note (2):

Calculate the units started and completed during the period of December:

$\begin{array}{c}\text{Started and completed units =}\left(\begin{array}{l}\text{Transferred to packing department units }\\ -\text{beginning inventory units}\end{array}\right)\\ \text{=}\text{128,000}\text{units }-24,000\text{units}\\ \text{=}104,00\text{0}\text{units}\end{array}$

Cost of units started and completed during the period of December is calculated by multiplying units started and completed during the period with total cost per unit (material and conversion cost). Hence, cost of units started and completed during the period of December is $618,800.

1. 5. Calculate cost of ending work in process inventory:

Particulars	Units (A)	Cost per unit (B)	Amount $\left(A\times B\right)$
Ending work in process inventory:
Direct materials	30,000	$1.75	$52,500
Conversion costs	15,000	$4.20	$63,000
Total			$115,500

Table (1)

Ending work in process inventory cost is calculated by adding total ending work in process inventory for direct materials and conversion costs. Therefore, total ending work in process inventory cost is $115,500.

To determine

Describe whether the conversion cost per equivalent unit would increase, decrease, or remains constant in the period of December, if the direct material cost is same in the period of November and December.

Explanation of Solution

Describe whether the conversion cost per equivalent unit would increase, decrease, or remains constant in the period of December, if the direct material cost is same in the period of November and December as shown below:

Particulars	Per unit
Conversion cost equivalent per unit for December	$4.20
Less: Conversion cost equivalent per unit for November  (5)	$4.15
Increase in conversion cost per equivalent unit	$0.05

Table (2)

Working note (3):

Calculate the conversion costs during the period of November:

Particulars	Units (A)	Cost per unit (B)	Amount (A × B)
Work in process inventory - Baking department, balance			$116,700
Less: Direct materials cost incurred in November	24,000	$1.75	$42,000
Conversion costs incurred in November			$74,700

Working note (4):

Calculate equivalent units for conversion:

$\begin{array}{c}\text{Equivalent units for conversion costs}=\left[\begin{array}{l}\text{Total conversion}\text{costs units}\\ \times \text{Percentage to complete}\end{array}\right]\\ =24\text{,000}\times \frac{3}{4}\\ =18,0\text{00}\text{Units}\end{array}$

Working note (5):

Calculate conversion cost per unit during the period of November:

$\begin{array}{c}\text{Conversion cost per unit}\text{=}\frac{\text{Conversion cost during the period of February}}{\text{Equivalents units for Conversion}}\\ =\frac{\$74,700(3)}{18,000\text{units (4)}}\\ =\$4.15\text{per unit}\end{array}$

Conversion cost per unit during the period of December is $4.20 per unit and it is greater than the conversion cost per unit during the period of November ($4.15 per unit). Hence, the conversion cost equivalent per unit has been increased by $0.05 per unit $\text{(\$4}\text{.20 per unit}–\text{\$4}\text{.15 per unit)}$ .