Chapter 20, Problem 21QS

To determine

Concept Introduction:

Equivalent Units of Production:

The equivalent units of production can be defined as the units which are partially completed to be counted as fully completed units based on their percentage of work done on them.

For example, the units in ending inventory are 1,000 units and 60 % completed. Thus, the equivalent units for ending inventory will be = 1,000 units X 60 % = 600 units.

First-in, first-out (FIFO):

In FIFO method of inventory, the cost of goods sold and ending inventory are valued at the older prices. The cost of goods sold are valued at the older prices and the inventory which remains unsold are with the newest prices. This method says that, the inventory first purchased is first sold the ending inventory consists of the latest purchases.

Cost per equivalent unit:

Cost per equivalent unit can be defined as the costs that are incurred during the process to the equivalent units of production. In FIFO method, only the costs that are added during the process are assigned to the equivalent units of production for materials and conversion.

Cost per equivalent unit can be calculated as under –

$Costperequivalentunits=\frac{Totalcostaddedduringtheprocess}{Equivalentunitsofproduction}$

Requirement 1

To compute:

The roasting department’s equivalent units of production for materials for the month using FIFO method.

Answer to Problem 21QS

Solution:

	Materials
Equivalent Units	18,000 units

Explanation of Solution

The equivalent units of production for Materials can be calculated as under –

First, units added and completed 100 % from the process will be calculated.

$Unitsaddedandcompleted100\%=Unitstransferredout–Beginninginventoryunits$

Given,

• Units transferred out = 17,000 units ( 2,000 units + 18,000 units – 3,000 units)

• Beginning inventory units = 2,000 units

$\begin{array}{l}Unitsaddedandcompleted100\%=Unitstransferredout–Beginninginventoryunits\hfill \\ Unitsaddedandcompleted100\%=\text{ 17},000units–2,000units\hfill \\ Unitsaddedandcompleted100\%=\text{ 15},000units\hfill \end{array}$

Out of total units transferred, 15,000 units were added and completed and transferred out during the process.

Equivalent units of production as FIFO method will be calculated as under –

Equivalent units of production -FIFO
	Direct Materials
Units to complete - Beginning Inventory
Direct Materials (2,000 X 30%)	600
Units completed and transferred out	15,000
Units completed - Ending Inventory
Direct Materials (3,000 X 80%)	2,400
Equivalent units of production	18,000

The above calculations can be explained as under –

For beginning inventory –

Given,

• Units in beginning inventory = 2,000 units

• For direct material completed percentage = 70 %

$Equivalentunitsfor\text{ Beginni}nginventory=UnitsinbeginninginventoryX\left(1–percentofcompletion\right)$

Units to be counted from beginning inventory for materials –

$\begin{array}{l}Equivalentunits=2,000unitsX\left(1–\text{ 7}0\%\right)\hfill \\ Equivalentunits=2,000unitsX\text{ 3}0\%\hfill \\ Equivalentunits=\text{ 6}00units\hfill \end{array}$

For units added, completed and transferred out –

15,000 units calculated as above

For ending inventory –

Given,

• Units in ending inventory = 3,000 units

• For direct material completed percentage = 80 %

$\text{Equivalent units for ending inventory }=UnitsinbeginninginventoryX\text{ Percent of completion}$

Equivalent units for ending inventory for materials –

$\begin{array}{l}Unitstobecountedascompleted=\text{ 3},000unitsX\text{ 80\%}\hfill \\ Unitstobecountedascompleted=2,400units\hfill \\ \hfill \end{array}$

Total equivalent units for production for materials will be calculated as under –

$\begin{array}{l}Totalequivalentunitsforproduction=Beginningequivalentunits+Completedandtransferred\\ +Endingequivalentunits\end{array}$

Given,

For materials –

• Beginning equivalent units = 600 units

• Completed and transferred = 15,000 units

• Ending equivalent units = 2,400 units

$\begin{array}{l}Totalequivalentunitsforproduction=\text{ 600 units + 15,000 units }+\text{ 2,400 units }\\ Totalequivalentunitsforproduction=18,000\text{ units}\end{array}$

Conclusion

Thus, the roasting department’s equivalent units of production for materials for the month using FIFO method have been calculated.

To determine

Requirement 2

To compute:

The roasting department’s cost per equivalent unit of production for materials for the month using FIFO method.

Answer to Problem 21QS

Solution:

The roasting department’s cost per equivalent unit of production for materials for the month using FIFO method = $ 1.55 per unit

Explanation of Solution

The cost per equivalent unit for materials is calculated as under –

Cost per Equivalent unit - FIFO
	Direct Materials
Costs incurred during the period	27,900
Equivalent units of production	18,000
Cost per Equivalent unit	1.55

Given,

For materials –

• Costs incurred during the period = $ 27,900

• Equivalent units of production = 18,000 units

$\begin{array}{l}Costperequivalentunits=\frac{Totalcostaddedduringtheprocess}{Equivalentunitsofproduction}\\ Costperequivalentunits=\frac{\text{\$27,900}}{\text{18,000 }units}\\ Costperequivalentunits=\$1.55perunit\end{array}$

Conclusion

Thus, the roasting department’s cost per equivalent unit of production for materials for the month using FIFO method has been calculated.