Question

Arna, Inc. uses the dollar-value LIFO method of computing its inventory. Data for the past 3 years follow.

Year Ended December 31 Inventory at Current-Year Cost Price Index

2016 $19,750 100

2017 22,140 108

2018 25,935 114

Compute the value of the 2017 and 2018 inventories using the dollar-value LIFO method.

Short answer

Using the dollar-value LIFO, the value of ending inventory at the end of 2017 and 2018 amounts to $20,560 and $23,125, respectively.

Step-by-step solution

Value of ending inventory for 2016 using dollar-value LIFO

As 2016 is the first year for converting dollar value LIFO and the index is also 100, the value of ending inventory at base year would be the same as given.

The computation would be as follow –

$$\begin{gathered} \mathbf{Ending}\mathbf{}\mathbf{inventory}\mathbf{}\mathbf{at}\mathbf{}\mathbf{base}\mathbf{}\mathbf{yaer}\mathbf{}\mathbf{prices}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{Inventory}\mathbf{}\mathbf{at}\mathbf{}\mathbf{current}\mathbf{}\mathbf{cost}}{\mathbf{Price}\mathbf{}\mathbf{Index}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{750}}{\mathbf{1}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{750} \end{gathered}$$

A layer is a difference between the ending base year price and the opening base year price.

Ending Inventory at base year prices	Layer at base year prices	X	Price Index	=	Ending Inventory at LIFO Cost
$19,750	$19,750	X	100	=	$19,750

Value of ending inventory at the end of 2016 using dollar-value LIFO amounts to $19,750.

Value of ending inventory for 2017 using dollar-value LIFO

$$\begin{gathered} \mathbf{Ending}\mathbf{}\mathbf{inventory}\mathbf{}\mathbf{at}\mathbf{}\mathbf{base}\mathbf{}\mathbf{yaer}\mathbf{}\mathbf{prices}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{Inventory}\mathbf{}\mathbf{at}\mathbf{}\mathbf{current}\mathbf{}\mathbf{cost}}{\mathbf{Price}\mathbf{}\mathbf{Index}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{22}\mathbf{,}\mathbf{140}}{\mathbf{1}\mathbf{.}\mathbf{08}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{20}\mathbf{,}\mathbf{500} \end{gathered}$$

Ending Inventory at base year prices	Layer at base year prices	X	Price Index	=	Ending Inventory at LIFO Cost
	2016, $19,750	X	100	=	$19,750
$20,500	2017, + $750	X	108	=	+ $810
	$20,500				$20,560

Value of ending inventory at the end of 2016 using dollar-value LIFO amounts to $20,560.

Value of ending inventory for 2018 using dollar-value LIFO

$$\begin{gathered} \mathbf{Ending}\mathbf{}\mathbf{inventory}\mathbf{}\mathbf{at}\mathbf{}\mathbf{base}\mathbf{}\mathbf{yaer}\mathbf{}\mathbf{prices}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{Inventory}\mathbf{}\mathbf{at}\mathbf{}\mathbf{current}\mathbf{}\mathbf{cost}}{\mathbf{Price}\mathbf{}\mathbf{Index}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{25}\mathbf{,}\mathbf{935}}{\mathbf{1}\mathbf{.}\mathbf{14}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{22}\mathbf{,}\mathbf{750} \end{gathered}$$

Ending Inventory at base year prices	Layer at base year prices	X	Price Index	=	Ending Inventory at LIFO Cost
	2016, $19,750	X	100	=	$19,750
$22,750	2017, + $750	X	108	=	+ $810
	2018, + $2,250	X	114	=	+ $2,565
	$22,750				$23,125

The value of ending inventory at the end of 2016 using dollar-value LIFO amounts to $23,125.