Chapter 6, Problem 34E

1.

To determine

Calculate the costs per equivalent unit for both the weighted-average method and FIFO method.

Explanation of Solution

Equivalent units: Equivalent units are the number of units that could have been performed given the amount of work actually performed, and for both partially complete units and complete units, the quantity of other production inputs used.

Calculate the costs per equivalent unit for direct materials using weighted-average method:

$\begin{array}{c}\text{Cost per equivalent unit = }\left(\frac{\begin{array}{l}\left(\text{Completed direct materials, Beginning}\right)\text{ + }\\ \left(\text{Current costs of direct materials}\right)\end{array}}{\left(\begin{array}{l}\text{Units completed and transferred out+}\\ \left(\text{Completed direct materials, Ending}\right)\end{array}\right)}\right)\\ \text{=}\frac{\$60,000+\$120,000}{\left(70,000\text{units}\right)+\left(30,000\text{units}\times \text{100\%}\right)}\\ =\frac{\$180,000}{100,000\text{units}}\\ \text{=\$1}\text{.80}\end{array}$

Hence, the costs per equivalent unit for direct materials using weighted-average method is $1.80.

Calculate the costs per equivalent unit for conversion using weighted-average method:

$\begin{array}{c}\text{Cost per equivalent unit = }\left(\frac{\begin{array}{l}\left(\text{Completed conversion, Beginning}\right)\text{ + }\\ \left(\text{Current costs of conversion}\right)\end{array}}{\left(\begin{array}{l}\text{Units completed and transferred out+}\\ \left(\text{Completed conversion, Ending}\right)\end{array}\right)}\right)\\ \text{=}\frac{\$24,000+\$300,000}{\left(70,000\text{units}\right)+\left(30,000\text{units}\times 8\text{0\%}\right)}\\ =\frac{\$324,000}{94,000\text{units}}\\ \text{=\$3}\text{.4468}\end{array}$

Hence, the costs per equivalent unit for conversion using weighted-average method is $3.4468.

Calculate the costs per equivalent unit for direct materials using FIFO method:

$\begin{array}{c}\text{Cost per equivalent unit = }\left(\frac{\text{ Current costs of direct materials}}{\left(\begin{array}{l}\text{Units completed and transferred out+}\\ \left(\text{Completed direct materials, Ending}\right)-\\ \left(\text{Completed direct materials, Beginning}\right)\end{array}\right)}\right)\\ \text{=}\frac{\$120,000}{\left[\begin{array}{l}\left(70,000\text{units}\right)+\left(30,000\text{units}\times \text{100\%}\right)-\\ \left(30,000\text{units}\times \text{100\%}\right)\end{array}\right]}\\ =\frac{\$120,000}{70,000\text{units}}\\ \text{=\$1}\text{.7143}\end{array}$

Hence, the costs per equivalent unit for direct materials using FIFO method is $1.7143.

Calculate the costs per equivalent unit for conversion using FIFO method:

$\begin{array}{c}\text{Cost per equivalent unit = }\left(\frac{\text{ Current costs of conversion}}{\left(\begin{array}{l}\text{Units completed and transferred out+}\\ \left(\text{Completed conversion, Ending}\right)-\\ \left(\text{Completed conversion, Beginning}\right)\end{array}\right)}\right)\\ \text{=}\frac{\$300,000}{\left[\begin{array}{l}\left(70,000\text{units}\right)+\left(30,000\text{units}\times 8\text{0\%}\right)-\\ \left(30,000\text{units}\times 4\text{0\%}\right)\end{array}\right]}\\ =\frac{\$300,000}{82,000\text{units}}\\ \text{=\$3}\text{.6585}\end{array}$

Hence, the costs per equivalent unit for conversion using FIFO method is $3.6585.

2.

To determine

Explain the difference between the equivalent unit costs of FIFO method and weighted-average method.

Explanation of Solution

Due to the per unit amount differences in current costs and beginning work-in-process, there are differences between the equivalent unit costs of FIFO method and weighted-average method. The cost per equivalent unit is based on current costs only, under the FIFO method, while in the weighted-average method, these differences are averaged together.