Question

Collins Company has the following data for the Assembly Department for August:

Unit in process at the beginning of august	900
Units started in august	2,000
Units completed and transferred	2,100
Units in process at the end of august	800

Conversion costs are added evenly throughout the process. The company uses the weighted-average method. Compute the equivalent units of production for direct materials and conversion costs for each independent scenario:

1. Units in process at the end of August are 20% complete; materials are added at the beginning of the process.

2. Units in process at the end of August are 80% complete; materials are added at the beginning of the process.

3. Units in process at the end of August are 20% complete; materials are added at the end of the process.

4. Units in process at the end of August are 80% complete; materials are added at the halfway point.

Short answer

Cases	EUP for direct material	EUP for conversion cost
Units in process at the end of August are 20% complete; materials are added at the beginning of the process.	2,900	2,260
Units in process at the end of August are 80% complete; materials are added at the beginning of the process.	2,900	2,740
Units in process at the end of August are 20% complete; materials are added at the end of the process.	2,100	2,260
Units in process at the end of August are 80% complete; materials are added at the halfway point.	2,900	2,740

Step-by-step solution

Meaning of Manufacturing Process

The manufacturing process means the procedure undertaken by the manufacturing companies for converting the raw material into the finished goodsby using the machinery, labor, etc. Manufacturing is integral to the economy.

Equivalent unit of production for direct materials when the unit in process at the end of August is 20%

$$\begin{gathered} \mathbf{EUP}\mathbf{=}\left(\mathbf{Completedunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{Inprocessunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right) \\ \mathbf{=}\left(\mathbf{2}\mathbf{,}\mathbf{100}\mathbf{\times }\mathbf{100}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{800}\mathbf{\times }\mathbf{100}\mathbf{\%}\right) \\ \mathbf{=}\mathbf{2}\mathbf{,}\mathbf{900} \end{gathered}$$

Equivalent unit of production for conversion cost when the unit in process at the end of August is 20%

$$\begin{gathered} \mathbf{EUP}\mathbf{=}\left(\mathbf{Completedunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{Inprocessunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right) \\ \mathbf{=}\left(\mathbf{2}\mathbf{,}\mathbf{100}\mathbf{\times }\mathbf{100}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{800}\mathbf{\times }\mathbf{20}\mathbf{\%}\right) \\ \mathbf{=}\mathbf{2}\mathbf{,}\mathbf{260} \end{gathered}$$

Equivalent unit of production for direct materials when the unit in process at the end of August is 80%

$$\begin{gathered} \mathbf{EUP}\mathbf{=}\left(\mathbf{Completedunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{Inprocessunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right) \\ \mathbf{=}\left(\mathbf{2}\mathbf{,}\mathbf{100}\mathbf{\times }\mathbf{100}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{800}\mathbf{\times }\mathbf{100}\mathbf{\%}\right) \\ \mathbf{=}\mathbf{2}\mathbf{,}\mathbf{900} \end{gathered}$$

Equivalent unit of production for conversion cost when the unit in process at the end of August is 80%

$$\begin{gathered} \mathbf{EUP}\mathbf{=}\left(\mathbf{Completedunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{Inprocessunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right) \\ \mathbf{=}\left(\mathbf{2}\mathbf{,}\mathbf{100}\mathbf{\times }\mathbf{100}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{800}\mathbf{\times }\mathbf{80}\mathbf{\%}\right) \\ \mathbf{=}\mathbf{2}\mathbf{,}\mathbf{740} \end{gathered}$$

Equivalent unit of production for direct materials when the unit in process at the end of August is 20%, and the materials are added at the end of the process.

$$\begin{gathered} \mathbf{EUP}\mathbf{=}\left(\mathbf{Completedunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{Inprocessunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right) \\ \mathbf{=}\left(\mathbf{2}\mathbf{,}\mathbf{100}\mathbf{\times }\mathbf{100}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{800}\mathbf{\times }\mathbf{0}\mathbf{\%}\right) \\ \mathbf{=}\mathbf{2}\mathbf{,}\mathbf{100} \end{gathered}$$

Equivalent unit of production for conversion cost when the unit in process at the end of August is 20%,and the materials are added at the end of the process.

$$\begin{gathered} \mathbf{EUP}\mathbf{=}\left(\mathbf{Completedunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{Inprocessunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right) \\ \mathbf{=}\left(\mathbf{2}\mathbf{,}\mathbf{100}\mathbf{\times }\mathbf{100}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{800}\mathbf{\times }\mathbf{20}\mathbf{\%}\right) \\ \mathbf{=}\mathbf{2}\mathbf{,}\mathbf{260} \end{gathered}$$

Equivalent unit of production for direct materials when the unit in process at the end of August is 80%, and the materials are added at the halfway point

$$\begin{gathered} \mathbf{EUP}\mathbf{=}\left(\mathbf{Completedunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{Inprocessunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right) \\ \mathbf{=}\left(\mathbf{2}\mathbf{,}\mathbf{100}\mathbf{\times }\mathbf{100}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{800}\mathbf{\times }\mathbf{100}\mathbf{\%}\right) \\ \mathbf{=}\mathbf{2}\mathbf{,}\mathbf{900} \end{gathered}$$

Equivalent unit of production for conversion cost when the unit in process at the end of August is 80%,and the materials are added at the Halfway point

$$\begin{gathered} \mathbf{EUP}\mathbf{=}\left(\mathbf{Completedunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{Inprocessunits}\mathbf{\times }\mathbf{Completion}\mathbf{\%}\right) \\ \mathbf{=}\left(\mathbf{2}\mathbf{,}\mathbf{100}\mathbf{\times }\mathbf{100}\mathbf{\%}\right)\mathbf{+}\left(\mathbf{800}\mathbf{\times }\mathbf{80}\mathbf{\%}\right) \\ \mathbf{=}\mathbf{2}\mathbf{,}\mathbf{740} \end{gathered}$$