Chapter 8, Problem 12P

To determine

Calculate the cost of inventory destroyed in the fire 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 inventory destroyed in the fire using dollar-value LIFO retail method.

For the year 2019:

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

G Company
Ending Inventory Under DVL Retail Method
For the Year 2019
Details	Cost ($)	Retail ($)
Beginning inventory	40,000	90,000
Add:  Net purchase	100,000	210,000
Net additional markups		20,000
Less:  Net markdowns	0	(40,000)
Goods available for sale – Excluding beginning inventory	100,000	190,000
Goods available for sale – Including beginning inventory	140,000	280,000
Less:  Net sales		(200,000)
Estimated ending inventory at retail for 2019		$80,000

Table (1)

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

$\begin{array}{c}\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices }\end{array}\}\text{=}\left[\begin{array}{l}\text{ Ending inventory at retail}\times \\ \left(\frac{\text{Price index on 1/1/19}}{\text{Price index on 31/12/19}}\right)\end{array}\right]\\ =\left[\text{ \$80,000}\times \left(\frac{\text{100}}{\text{106}}\right)\right]\\ =\$75,472\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\end{array}\}\text{= }\left(\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices}\\ -\text{Beginning inventory at retail}\end{array}\right)\\ =\left(\$75,472-\$90,000\right)\\ =-\$14,528\end{array}$

Step 4: Calculate the change at relevant current costs.

$\begin{array}{c}\text{Change at relevant current costs =}\left[\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\times \\ \left(\frac{\text{Price index on 1/1/19}}{\text{Price index on 1/1/19}}\right)\\ \times \text{Cost-to-retail ratio}\end{array}\right]\\ \text{=}\left[-\$14,528\times \left(\frac{\text{100}}{\text{100}}\right)\times .444\right]\\ =-\$6,450\end{array}$

Step 5: Calculate ending inventory at cost.

$\begin{array}{c}\text{Ending inventory at cost =}\left(\begin{array}{l}\text{Beginning inventory for 2019}\\ -\text{Change at current cost}\end{array}\right)\\ \text{=}\left[\text{\$4}0,000-\$6,450\right]\\ =\$33,550\end{array}$

Hence, the ending inventory at cost for 2019 is $33,550.

Working note 1:

Calculate cost-to-retail ratio.

$\begin{array}{c}\text{Cost-to-retail ratio= }\left(\frac{\text{Beginning inventory for cost}}{\text{Beginning inventory for retail}}\right)\\ =\left(\frac{\text{\$40,000}}{\$90,000}\right)\\ =.444\end{array}$

Working note 2:

Calculate cost-to-retail ratio.

$\begin{array}{c}\text{Cost-to-retail ratio= }\left(\frac{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}\right)\\ =\left(\frac{\text{\$100,000}}{\$190,000}\right)\\ =.526\end{array}$

For the year 2020:

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

G Company
Ending Inventory Under DVL Retail Method
For the Year 2020
Details	Cost ($)	Retail ($)
Beginning inventory	33,550	80,000
Add:  Net purchase	160,000	350,000
Net additional markups		40,000
Less:  Net markdowns		(70,000)
Goods available for sale – Excluding beginning inventory	160,000	320,000
Goods available for sale – Including beginning inventory	193,550	400,000
Less:  Net sales		(280,000)
Estimated ending inventory at retail for 2020		$120,000

Table (2)

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

$\begin{array}{c}\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices }\end{array}\}\text{=}\left[\begin{array}{l}\text{ Ending inventory at retail}\times \\ \left(\frac{\text{Price index on 1/1/17}}{\text{Price index on 30/9/20}}\right)\end{array}\right]\\ =\left[\text{ \$120,000}\times \left(\frac{\text{100}}{\text{110}}\right)\right]\\ =\$109,091\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\end{array}\}\text{= }\left(\begin{array}{l}\text{Ending inventory at retail }\\ \text{at base-year prices for 2020}\\ -\text{Ending inventory at retail }\\ \text{at base-year prices for 2019}\end{array}\right)\\ =\left(\$109,091-\$75,472\right)\\ =\$33,619\end{array}$

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

$\begin{array}{c}\text{Change at relevant current costs =}\left[\begin{array}{l}\text{Inventory change at retail }\\ \text{at base-year prices}\times \\ \left(\frac{\text{Price index on 30/9/20}}{\text{Price index on 1/1/19}}\right)\\ \times \text{Cost-to-retail ratio}\end{array}\right]\\ \text{=}\left[\$33,619\times \left(\frac{\text{110}}{\text{100}}\right)\times .50\right]\\ =\$18,490\end{array}$

Step 5: Calculate ending inventory at cost.

$\begin{array}{c}\text{Ending inventory at cost =}\left(\begin{array}{l}\text{ Ending inventory cost for 2019+}\\ \text{Change at relevant current costs for 2020}\end{array}\right)\\ \text{=}\left(\$33,550+\$18,490\right)\\ =\$52,040\end{array}$

Hence, the ending inventory at cost for 2020 is $52,040.

Working note 1:

Calculate cost-to-retail ratio.

$\begin{array}{c}\text{Cost-to-retail ratio= }\left(\frac{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}{\begin{array}{l}\text{Goods available for sale at retail }\\ \text{excluding beginning inventory}\end{array}}\right)\\ =\left(\frac{\text{\$160,000}}{\$320,000}\right)\\ =.5\end{array}$

Calculate inventory lost in the fire.

Inventory Lost in the Fire
Particulars	Amount ($)
Purchases in transit	8,000
Undamaged goods salvaged	5,000
Inventory after the fire	13,000
Less: Inventory before the fire	(52,040)
Inventory lost	$(39,040)

Table (3)

Working note 1:

Calculate undamaged goods salvaged.

$\begin{array}{c}\text{Undamaged goods salvaged}\text{=}\left(\begin{array}{l}\text{Undamaged goods salvaged}\times \\ \text{Cost-to-retail ratio}\end{array}\right)\\ =\$10,000\times .5\\ =\$5,000\end{array}$

Conclusion

Therefore, the cost of inventory destroyed in the fire is $39,040.