Question

(Dollar-Value LIFO Retail) You assemble the following information for Seneca Department Store, which computes its inventory under the dollar-value LIFO method. Cost Retail Inventory on January 1, 2017 \(216,000 \)300,000 Purchases 364,800 480,000 Increase in price level for year 9% Instructions Compute the cost of the inventory on December 31, 2017, assuming that the inventory at retail is (a) \(294,300 and (b) \)365,150.

Short answer

The ending inventory for year 2016-2019 equals $61,250.40, $69,908.40, $59,437.80 and $74,662.80, respectively.

Step-by-step solution

Calculation of cost to retail ratio of beginning inventory

The cost-to-retail ratio of beginning inventory is calculated as follows:

$$\begin{gathered} \mathrm{Cost}‐\mathrm{to}‐\mathrm{Retail}\mathrm{Ratio}\mathrm{of}\mathrm{Beginning}\mathrm{Inventory}=\frac{\mathrm{Beginning}\mathrm{Inventory}\mathrm{at}\mathrm{Cost}}{\mathrm{Beginning}\mathrm{Inventory}\mathrm{at}\mathrm{Retail}} \\ =\frac{\$54,000}{\$100,000} \\ =54\% \end{gathered}$$

Calculation of ending inventory at base year retail prices

The cost of ending inventory at base year retail price for 2016 is calculated as follows:

$$\begin{gathered} \mathrm{Ending}\mathrm{Inventory}\mathrm{at}\mathrm{Base}\mathrm{Year}\mathrm{Retail}\mathrm{Price}=\frac{\mathrm{Ending}\mathrm{Inventory}\mathrm{at}\mathrm{Retail}}{\mathrm{Price}\mathrm{Index}} \\ =\frac{\$118,720}{106\%} \\ =\$112,000 \end{gathered}$$

Calculation of ending inventory under dollar-value-LIFO retail method in 2016

Ending inventory is calculated as follows:

Ending Inventory at Base Year Retail Prices	Layers at Base Year Retail Prices			Price Index (Percentage)		Cost-to-Retail (Percentage)		Ending Inventory at LIFO Cost
$112,000	2015	$100,000	x	100%	x	54%	=	$54,000
	2016	12,000	x	106%	x	57%	=	7,250.40
								$61,250.40

Calculation of ending inventory at base year retail prices for the year 2017

The cost of ending inventory at base year retail price for 2017 is calculated as follows:

$$\begin{gathered} \mathrm{Ending}\mathrm{Inventory}\mathrm{at}\mathrm{Base}\mathrm{Year}\mathrm{Retail}\hspace{0.17em}\mathrm{Price}=\frac{\mathrm{Ending}\mathrm{Inventory}\mathrm{at}\mathrm{Retail}}{\mathrm{Price}\mathrm{Index}} \\ =\frac{\$138,750}{111\%} \\ =\$125,000 \end{gathered}$$

Calculation of ending inventory under dollar-value-LIFO retail method in 2017

Ending inventory is calculated as follows:

Ending Inventory at Base Year Retail Prices	Layers at Base Year Retail Prices			Price Index (Percentage)		Cost-to-Retail (Percentage)		Ending Inventory at LIFO Cost
$125,000	2015	$100,000	x	100%	x	54%	=	$54,000
	2016	12,000	x	106%	x	57%	=	7,250.40
	2017	13,000	x	111%	x	60%	=	8,658
								$69,908.40

Calculation of ending inventory at base year retail prices for the year 2018

The cost of ending inventory at base year retail price for 2018 is calculated as follows:

$$\begin{gathered} \mathrm{Ending}\mathrm{Inventory}\mathrm{at}\mathrm{Base}\mathrm{Year}\mathrm{Retail}\mathrm{Price}=\frac{\mathrm{Ending}\mathrm{Inventory}\mathrm{at}\mathrm{Retail}}{\mathrm{Price}\mathrm{Index}} \\ =\frac{\$125,350}{115\%} \\ =\$109,000 \end{gathered}$$

Calculation of ending inventory under dollar-value-LIFO retail method in 2018

Ending inventory is calculated as follows:

Ending Inventory at Base Year Retail Prices	Layers at Base Year Retail Prices			Price Index (Percentage)		Cost-to-Retail (Percentage)		Ending Inventory at LIFO Cost
$125,000	2015	$100,000	x	100%	x	54%	=	$54,000
	2016	9,000	x	106%	x	57%	=	5,437.80
								$59,437.80

Calculation of ending inventory at base year retail prices for the year 2019

The cost of ending inventory at base year retail price for 2019 is calculated as follows:

$$\begin{gathered} \mathrm{Ending}\mathrm{Inventory}\mathrm{at}\mathrm{Base}\mathrm{Year}\mathrm{Retail}\mathrm{Price}=\frac{\mathrm{Ending}\mathrm{Inventory}\mathrm{at}\mathrm{Retail}}{\mathrm{Price}\mathrm{Index}} \\ =\frac{\$162,500}{125\%} \\ \$130,000 \end{gathered}$$

Calculation of ending inventory under dollar-value-LIFO retail method in 2019

Ending inventory is calculated as follows:

Ending Inventory at Base Year Retail Prices	Layers at Base Year Retail Prices		Price Index (Percentage)		Cost-to-Retail (Percentage)		Ending Inventory at LIFO Cost
$125,000	2015	$100,000	x	100%	x	54%	=	$54,000
	2016	9,000	x	106%	x	57%	=	5,437.80
	2017	21,000	x	125%	x	58%	=	15,225
								$74,662.80

Thus, inventory for year 2016, 2017, 2018, and 2019 equals $61,250.40, $69,908.40, $59,437.80, and $74,662.80, respectively.