Chapter 8, Problem 11P

To determine

Calculate the cost of ending inventory for 2015, 2016, 2017, and 2018 years by using dollar-value LIFO retail 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 2015, 2016, 2017, and 2018 years by using dollar-value LIFO retail method:

For the year 2015:

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

I Incorporation
Ending Inventory Under DVL Retail Method
For the Year 2015
Details	Cost ($)	Retail ($)
Beginning inventory	40,000	80,000
Add:  Net purchase	85,500	190,000
Goods available for sale – Excluding beginning inventory	85,500	190,000
Goods available for sale – Including beginning inventory	125,500	270,000
Less:  Net sales		(200,000)
Estimated ending inventory at retail for 2015		$70,000

Table (1)

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

$\begin{array}{c}\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices }\end{array}\}\text{=}\left[\begin{array}{l}\text{ Ending inventory at retail}\times \\ \left(\frac{\text{Price index on 1/1/15}}{\text{Price index on 31/12/15}}\right)\end{array}\right]\\ =\left[\text{ \$70,000}\times \left(\frac{\text{100}}{\text{105}}\right)\right]\\ =\$66,667\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\end{array}\}\text{= }\left(\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices}\\ -\text{Beginning inventory at retail}\end{array}\right)\\ =\left(\$66,667-\$80,000\right)\\ =-\$13,333\end{array}$

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

$\begin{array}{c}\text{Change at retail at relevant current costs =}\left[\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\times \\ \left(\frac{\text{Price index on 1/1/15}}{\text{Price index on 1/1/15}}\right)\end{array}\right]\\ \text{=}\left[-\$13,333\times \left(\frac{\text{100}}{\text{100}}\right)\right]\\ =-\$13,333\end{array}$

Step 5: Calculate the change at relevant current costs.

$\begin{array}{c}\text{Change at relevant current costs =}\left[\begin{array}{l}\text{Change at retail at relevant}\\ \text{ current costs}\times \times \text{Cost-to-retail ratio}\end{array}\right]\\ \text{=}\left[-\$13,333\times .50\right]\\ =-\$6,667\end{array}$

Step 6: Calculate ending inventory at cost.

$\begin{array}{c}\text{Ending inventory at cost = }\left(\begin{array}{l}\text{Beginning inventory for 2015 }-\\ \text{Change at relevant current costs}\end{array}\right)\\ \text{=}\left[\$40,000-\$6,667\right]\\ =\$33,333\end{array}$

Hence, the ending inventory at cost for 2018 is $33,333.

Working note 1:

Calculate cost-to-retail ratio.

$\begin{array}{c}\text{Cost-to-retail ratio= }\left(\frac{\text{Beginning inventory for cost}}{\text{Beginning inventory for retail}}\right)\\ =\left(\frac{\text{\$40,000}}{\$80,000}\right)\\ =.5\end{array}$

Working note 2:

Calculate cost-to-retail ratio.

$\begin{array}{c}\text{Cost-to-retail ratio= }\left(\frac{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}\right)\\ =\left(\frac{\text{\$85,500}}{\$190,000}\right)\\ =.45\end{array}$

For the year 2016:

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

I Incorporation
Ending Inventory Under DVL Retail Method
For the Year 2016
Details	Cost ($)	Retail ($)
Beginning inventory	33,333	70,000
Add:  Net purchase	92,000	230,000
Goods available for sale – Excluding beginning inventory	92,000	230,000
Goods available for sale – Including beginning inventory	125,333	300,000
Less:  Net sales		(210,000)
Estimated ending inventory at retail for 2016		$90,000

Table (1)

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

$\begin{array}{c}\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices }\end{array}\}\text{=}\left[\begin{array}{l}\text{ Ending inventory at retail}\times \\ \left(\frac{\text{Price index on 1/1/15}}{\text{Price index on 31/12/16}}\right)\end{array}\right]\\ =\left[\text{ \$90,000}\times \left(\frac{\text{100}}{\text{110}}\right)\right]\\ =\$81,818\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\end{array}\}\text{= }\left(\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices for 2016}\\ -\text{Ending inventory at retail }\\ \text{at base-year prices for 2015}\end{array}\right)\\ =\left(\$81,818-\$66,667\right)\\ =\$15,151\end{array}$

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

$\begin{array}{c}\text{Change at retail at relevant current costs =}\left[\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\times \\ \left(\frac{\text{Price index on 31/12/16}}{\text{Price index on 1/1/15}}\right)\end{array}\right]\\ \text{=}\left[\$15,151\times \left(\frac{\text{110}}{\text{100}}\right)\right]\\ =\$16,666\end{array}$

Step 5: Calculate the change at relevant current costs.

$\begin{array}{c}\text{Change at relevant current costs =}\left[\begin{array}{l}\text{Change at retail at relevant}\\ \text{ current costs}\times \times \text{Cost-to-retail ratio}\end{array}\right]\\ \text{=}\left[16,666\times .40\right]\\ =\$6,666\end{array}$

Step 6: Calculate ending inventory at cost.

$\begin{array}{c}\text{Ending inventory at cost = }\left(\begin{array}{l}\text{Beginning inventory for 2016 +}\\ \text{Change at relevant current costs}\end{array}\right)\\ \text{=}\left[\$33,333+\$6,666\right]\\ =\$39,999\end{array}$

Hence, the ending inventory at cost for 2016 is $39,999.

Working note 1:

Calculate cost-to-retail ratio.

$\begin{array}{c}\text{Cost-to-retail ratio= }\left(\frac{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}\right)\\ =\left(\frac{\text{\$92,000}}{\$230,000}\right)\\ =.4\end{array}$

For the year 2017:

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

I Incorporation
Ending Inventory Under DVL Retail Method
For the Year 2017
Details	Cost ($)	Retail ($)
Beginning inventory	39,999	90,000
Add:  Net purchase	117,600	280,000
Goods available for sale – Excluding beginning inventory	117,600	280,000
Goods available for sale – Including beginning inventory	157,599	370,000
Less:  Net sales		(260,000)
Estimated ending inventory at retail for 2017		$110,000

Table (3)

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

$\begin{array}{c}\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices }\end{array}\}\text{=}\left[\begin{array}{l}\text{ Ending inventory at retail}\times \\ \left(\frac{\text{Price index on 1/1/15}}{\text{Price index on 31/12/17}}\right)\end{array}\right]\\ =\left[\text{ \$110,000}\times \left(\frac{\text{100}}{\text{120}}\right)\right]\\ =\$91,667\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\end{array}\}\text{= }\left(\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices for 2017}\\ -\text{Ending inventory at retail }\\ \text{at base-year prices for 2016}\end{array}\right)\\ =\left(\$91,667-\$81,818\right)\\ =\$9,849\end{array}$

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

$\begin{array}{c}\text{Change at retail at relevant current costs =}\left[\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\times \\ \left(\frac{\text{Price index on 31/12/17}}{\text{Price index on 1/1/15}}\right)\end{array}\right]\\ \text{=}\left[\$9,849\times \left(\frac{\text{120}}{\text{100}}\right)\right]\\ =\$11,818\end{array}$

Step 5: Calculate the change at relevant current costs.

$\begin{array}{c}\text{Change at relevant current costs =}\left[\begin{array}{l}\text{Change at retail at relevant}\\ \text{ current costs}\times \times \text{Cost-to-retail ratio}\end{array}\right]\\ \text{=}\left[11,819\times .42\right]\\ =\$4,964\end{array}$

Step 6: Calculate ending inventory at cost.

$\begin{array}{c}\text{Ending inventory at cost = }\left(\begin{array}{l}\text{Beginning inventory for 2017 +}\\ \text{Change at relevant current costs}\end{array}\right)\\ \text{=}\left[\$39,999+\$4,964\right]\\ =\$44,963\end{array}$

Hence, the ending inventory at cost for 2017 is$44,963.

Working note 1:

Calculate cost-to-retail ratio.

$\begin{array}{c}\text{Cost-to-retail ratio= }\left(\frac{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}\right)\\ =\left(\frac{\text{\$117,600}}{\$280,000}\right)\\ =.42\end{array}$

For the year 2018:

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

I Incorporation
Ending Inventory Under DVL Retail Method
For the Year 2018
Details	Cost ($)	Retail ($)
Beginning inventory	44,963	110,000
Add:  Net purchase	147,200	320,000
Goods available for sale – Excluding beginning inventory	147,200	320,000
Goods available for sale – Including beginning inventory	192,163	430,000
Less:  Net sales		(300,000)
Estimated ending inventory at retail for 2018		$130,000

Table (4)

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

$\begin{array}{c}\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices }\end{array}\}\text{=}\left[\begin{array}{l}\text{ Ending inventory at retail}\times \\ \left(\frac{\text{Price index on 1/1/15}}{\text{Price index on 31/12/18}}\right)\end{array}\right]\\ =\left[\text{ \$130,000}\times \left(\frac{\text{100}}{\text{125}}\right)\right]\\ =\$104,000\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\end{array}\}\text{= }\left(\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices for 2018}\\ -\text{Ending inventory at retail }\\ \text{at base-year prices for 2017}\end{array}\right)\\ =\left(\$104,000-\$91,667\right)\\ =\$12,333\end{array}$

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

$\begin{array}{c}\text{Change at retail at relevant current costs =}\left[\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\times \\ \left(\frac{\text{Price index on 31/12/17}}{\text{Price index on 1/1/15}}\right)\end{array}\right]\\ \text{=}\left[\$12,333\times \left(\frac{\text{125}}{\text{100}}\right)\right]\\ =\$15,416\end{array}$

Step 5: Calculate the change at relevant current costs.

$\begin{array}{c}\text{Change at relevant current costs =}\left[\begin{array}{l}\text{Change at retail at relevant}\\ \text{ current costs}\times \times \text{Cost-to-retail ratio}\end{array}\right]\\ \text{=}\left[15,416\times .46\right]\\ =\$7,091\end{array}$

Step 6: Calculate ending inventory at cost.

$\begin{array}{c}\text{Ending inventory at cost = }\left(\begin{array}{l}\text{Beginning inventory for 2018 +}\\ \text{Change at relevant current costs}\end{array}\right)\\ \text{=}\left[\$44,963+\$7,091\right]\\ =\$52,054\end{array}$

Hence, the ending inventory at cost for 2018 is$52,054.

Working note 1:

Calculate cost-to-retail ratio.

$\begin{array}{c}\text{Cost-to-retail ratio= }\left(\frac{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}\right)\\ =\left(\frac{\text{\$147,200}}{\$320,000}\right)\\ =.46\end{array}$