Chapter 8, Problem 10P

To determine

Calculate the cost of ending inventory for 2016, 2017, and 2018 using the dollar-value LIFO retail inventory method.

Explanation of Solution

Dollar-Value-LIFO: This method shows all the inventory figures at dollar price rather than units. Under this inventory method, the units that are purchased last are sold first. Thus, it starts from the selling of the units recently purchased and ending with the beginning inventory.

Calculate the cost of ending inventory for 2016, 2017, and 2018 using the dollar-value LIFO retail inventory method:

For the year 2016:

Step 1: Calculate the amount of estimated ending inventory at retail.

B Company
Ending Inventory Under DVL Retail Method
For the Year 2016
Details	Cost ($)	Retail ($)
Beginning inventory	50,000	100,000
Add:  Net purchase	200,000	420,000
Net additional markups		20,000
Less:  Net markdowns	0	(10,000)
Goods available for sale – Excluding beginning inventory	200,000	430,000
Goods available for sale – Including beginning inventory	250,000	530,000
Less:  Net sales		(400,000)
Estimated ending inventory at retail for 2016		$130,000

Table (1)

Step 2:  Calculate ending inventory at retail at base-year prices.

$\begin{array}{c}\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices }\end{array}\}\text{=}\left[\begin{array}{l}\text{ Ending inventory at retail}\times \\ \left(\frac{\text{Price index on 1/1/16}}{\text{Price index on 31/12/16}}\right)\end{array}\right]\\ =\left[\text{ \$130,000}\times \left(\frac{\text{100}}{\text{108}}\right)\right]\\ =\$120,370\end{array}$

Step 3: Calculate inventory change at retail at base year prices.

$\begin{array}{c}\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\end{array}\}\text{= }\left(\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices}\\ -\text{Beginning inventory at retail}\end{array}\right)\\ =\left(\$120,370-\$100,000\right)\\ =\$20,370\end{array}$

Step 4: Calculate the change at relevant current costs.

$\begin{array}{c}\text{Change at relevant current costs =}\left[\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\times \\ \left(\frac{\text{Price index on 31/12/16}}{\text{Price index on 1/1/16}}\right)\\ \times \text{Cost-to-retail ratio}\end{array}\right]\\ \text{=}\left[\$20,370\times \left(\frac{\text{108}}{\text{100}}\right)\times .465\right]\\ =\$10,230\end{array}$

Step 5: Calculate ending inventory at cost.

$\begin{array}{c}\text{Ending inventory at cost = }\left(\begin{array}{l}\text{Base-year layer + }\\ \text{2016 layer}\end{array}\right)\\ \text{=}\left[\begin{array}{l}\text{\$}50,000\left(\text{Beginning inventory for 2016}\right)\\ +\$10,230\left(\text{Change at current cost}\right)\end{array}\right]\\ =\$60,230\end{array}$

Hence, the ending inventory at cost for 2016is $60,230.

Working note 1:

Calculate cost-to-retail ratio.

$\begin{array}{c}\text{Cost-to-retail ratio= }\left(\frac{\text{Beginning inventory for cost}}{\text{Beginning inventory for retail}}\right)\\ =\left(\frac{\text{\$50,000}}{\$100,000}\right)\\ =.5\end{array}$

Working note 2:

Calculate cost-to-retail ratio.

$\begin{array}{c}\text{Cost-to-retail ratio= }\left(\frac{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}\right)\\ =\left(\frac{\text{\$200,000}}{\$430,000}\right)\\ =.465\end{array}$

For the year 2017:

Step 1: Calculate the amount of estimated ending inventory at retail.

B Company
Ending Inventory Under DVL Retail Method
For the Year 2017
Details	Cost ($)	Retail ($)
Beginning inventory	60,230	130,000
Add:  Net purchase	250,000	550,000
Net additional markups		30,000
Less:  Net markdowns	0	(40,000)
Goods available for sale – Excluding beginning inventory	250,000	540,000
Goods available for sale – Including beginning inventory	310,230	670,000
Less:  Net sales		(600,000)
Estimated ending inventory at retail for 2017		$70,000

Table (2)

Step 2:  Calculate ending inventory at retail at base-year prices.

$\begin{array}{c}\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices }\end{array}\}\text{=}\left[\begin{array}{l}\text{ Ending inventory at retail}\times \\ \left(\frac{\text{Price index on 1/1/16}}{\text{Price index on 31/12/17}}\right)\end{array}\right]\\ =\left[\text{ \$70,000}\times \left(\frac{\text{100}}{\text{115}}\right)\right]\\ =\$60,870\end{array}$

Step 3: Calculate inventory change at retail at base year prices.

$\begin{array}{c}\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\end{array}\}\text{= }\left(\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices for 2017}\\ -\text{Ending inventory at retail }\\ \text{at base-year prices for 2016}\end{array}\right)\\ =\left(\$60,870-\$120,370\right)\\ =-\$59,500\end{array}$

Step 4: Calculate the total change at relevant current costs.

(i)

Calculate the change at relevant current costs for 2016 (2016 layer):

$\begin{array}{c}\text{Change at relevant current costs =}\left[\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\times \\ \left(\frac{\text{Price index on 31/12/16}}{\text{Price index on 1/1/16}}\right)\\ \times \text{Cost-to-retail ratio}\end{array}\right]\\ \text{=}\left[-\$20,370\times \left(\frac{\text{108}}{\text{100}}\right)\times .465\right]\\ =-\$10,230\end{array}$

(ii)

Calculate the change at relevant current costs for 2017(base-year layer):

$\begin{array}{c}\text{Change at relevant current costs =}\left[\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\times \\ \left(\frac{\text{Price index on 1/1/16}}{\text{Price index on 1/1/16}}\right)\\ \times \text{Cost-to-retail ratio}\end{array}\right]\\ \text{=}\left[\begin{array}{l}-\$39,130\left(\$59,500-\$20,370\right)\\ \times \left(\frac{\text{100}}{\text{100}}\right)\times .50\end{array}\right]\\ =-\$19,565\end{array}$

(iii)

Calculate the total change at relevant current costs.

$\begin{array}{c}\text{Total change at relevant current costs =}\left(\begin{array}{l}\text{ Change at relevant current}\\ \text{ costs for 2016 +}\\ \text{Change at relevant current }\\ \text{costs for 2017}\end{array}\right)\\ =\left(-\$10,230-\$19,565\right)\\ =-\$29,795\end{array}$

Step 5: Calculate ending inventory at cost.

$\begin{array}{c}\text{Ending inventory at cost =}\left(\begin{array}{l}\text{ Ending inventory cost for 2016}-\\ \text{Total change at relevant current costs}\end{array}\right)\\ \text{=}\left(\$60,230-\$29,795\right)\\ =\$30,435\end{array}$

Hence, the ending inventory at cost for 2017 is $30,435.

Working note 1:

Calculate cost-to-retail ratio for 2016.

$\begin{array}{c}\text{Cost-to-retail ratio= }\left(\frac{\text{Beginning inventory for cost}}{\text{Beginning inventory for retail}}\right)\\ =\left(\frac{\text{\$50,000}}{\$100,000}\right)\\ =.5\end{array}$

Working note 2:

Calculate cost-to-retail ratio.

$\begin{array}{c}\text{Cost-to-retail ratio= }\left(\frac{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}\right)\\ =\left(\frac{\text{\$250,000}}{\$540,000}\right)\\ =.463\end{array}$

For the year 2018:

Step 1: Calculate the amount of estimated ending inventory at retail.

B Company
Ending Inventory Under DVL Retail Method
For the Year 2018
Details	Cost ($)	Retail ($)
Beginning inventory	30,435	70,000
Add:  Net purchase	240,000	500,000
Net additional markups		10,000
Less:  Net markdowns	0	(20,000)
Goods available for sale – Excluding beginning inventory	240,000	490,000
Goods available for sale – Including beginning inventory	270,435	560,000
Less:  Net sales		(450,000)
Estimated ending inventory at retail for 2018		$110,000

Table (3)

Step 2:  Calculate ending inventory at retail at base-year prices.

$\begin{array}{c}\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices }\end{array}\}\text{=}\left[\begin{array}{l}\text{ Ending inventory at retail}\times \\ \left(\frac{\text{Price index on 1/1/16}}{\text{Price index on 31/12/18}}\right)\end{array}\right]\\ =\left[\text{ \$110,000}\times \left(\frac{\text{100}}{\text{120}}\right)\right]\\ =\$91,667\end{array}$

Step 3: Calculate inventory change at retail at base year prices.

$\begin{array}{c}\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\end{array}\}\text{= }\left(\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices for 2018}\\ -\text{Ending inventory at retail }\\ \text{at base-year prices for 2017}\end{array}\right)\\ =\left(\$91,667-\$60,870\right)\\ =\$30,797\end{array}$

Step 4: Calculate the change at relevant current costs.

$\begin{array}{c}\text{Change at relevant current costs =}\left[\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\times \\ \left(\frac{\text{Price index on 31/12/18}}{\text{Price index on 1/1/16}}\right)\\ \times \text{Cost-to-retail ratio}\end{array}\right]\\ \text{=}\left[\$30,797\times \left(\frac{\text{120}}{\text{100}}\right)\times .49\right]\\ =\$18,109\end{array}$

Step 5: Calculate ending inventory at cost.

$\begin{array}{c}\text{Ending inventory at cost = }\left(\begin{array}{l}\text{Base-year layer + }\\ \text{2018 layer}\end{array}\right)\\ \text{=}\left[\begin{array}{l}\text{\$}30,435\left(\text{Beginning inventory for 2018}\right)\\ +\$18,109\left(\text{Change at current cost}\right)\end{array}\right]\\ =\$48,544\end{array}$

Hence, the ending inventory at cost for 2018 is$48,544.

Working note 1:

Calculate cost-to-retail ratio.

$\begin{array}{c}\text{Cost-to-retail ratio= }\left(\frac{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}\right)\\ =\left(\frac{\text{\$240,000}}{\$490,000}\right)\\ =.49\end{array}$