Chapter 9, Problem 9.19E

To determine

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.

To Determine: the cost-to-retail percentage for the inventory on hand at 1/1/2016.

Explanation of Solution

Determine the cost-to-retail percentage for the inventory on hand at 1/1/2016.

$\begin{array}{c}\begin{array}{l}\text{Cost-to}\\ \text{ retail percentage}\end{array}\}\text{ = }\left(\frac{\text{Beginning inventory at cost}}{\text{Beginning inventory at retail}}\times 100\right)\\ =\left(\frac{\$21,000}{\$28,000}\times 100\right)\\ =75\%\end{array}$ (1)

Conclusion

Therefore, the cost-to-retail percentage for the inventory on hand at 1/1/2016 is 75%.

To determine

the cost-to-retail percentage for the inventory on hand at 12/31/2016.

Explanation of Solution

Determine the cost-to-retail percentage for the inventory on hand at 12/31/2016.

$\begin{array}{c}\begin{array}{l}\text{Cost-to}\\ \text{ retail percentage}\end{array}\}\text{ = }\left(\frac{\text{LIFO}\text{layer}\text{added}\text{at}\text{current}\text{year}\text{cost}}{\text{LIFO}\text{layer}\text{added}\text{at}\text{current}\text{year}\text{retail}}\right)\\ =\frac{\$1,792\left(7\right)}{\$2,240\left(6\right)}\\ =80\%\end{array}$ (2)

Working notes:

Calculate the amount of ending inventory at base year retail prices.

$\begin{array}{c}\begin{array}{l}\text{Ending inventory }\\ \text{at base year retail prices (2016) }\end{array}\}\text{= }\left(\frac{\text{Estimated ending inventory at retail}}{\text{Retail price index}}\right)\\ =\left(\frac{\$33,600}{1.12}\right)\\ =\$30,000\end{array}$ (2)

Calculate the amount of inventory layers at base year retail prices.

$\begin{array}{c}\begin{array}{l}\text{Inventory layers}\text{added at}\\ \text{ base year retail prices }\end{array}\}\text{= Beginning inventory at retail}\\ \text{=\$28,000 (Base)}\end{array}$ (3)

Calculate the amount of inventory layers at current year retail prices.

$\begin{array}{c}\begin{array}{l}\text{Inventory layers at}\\ \text{ current year retail prices (2016) }\end{array}\}\text{= }\left(\begin{array}{l}\text{Ending inventory at base}\\ \text{ year retail prices (2016)}\\ -\text{Beginning inventory at retail (2016)}\end{array}\right)\\ =\$30,000-\$28,000\\ =\$2,000\end{array}$ (4)

Calculate the amount of inventory layers converted to cost (Base).

$\begin{array}{c}\text{Inventory layers converted to cost =}\left(\begin{array}{l}\text{Beginning inventory at retail (Base)}\times \\ \text{Base price index}\times \\ \text{Base layer cost-to retail percentage}\end{array}\right)\\ =\left(\$18,750\times 1.00\times 80\%\right)\\ =\$15,000\\ \end{array}$ (5)

Calculate the amount of inventory layers added at current year retail (2016).

$\begin{array}{c}\begin{array}{l}\text{Inventory layers}\text{added}\\ \text{at}\text{current}\text{year}\text{retail (2016) }\end{array}\}\text{=}\left(\begin{array}{l}\text{Inventory layers at current year retail}\\ \text{ prices (2016)}\times \\ \text{Retail price index (2016)}\end{array}\right)\\ =\left(\$2,000\times 1.12\right)\\ =\$2,240\end{array}$ (6)

Calculate the amount of inventory layers added at current year cost (2016).

$\begin{array}{c}\begin{array}{l}\text{Inventory layers}\text{added}\\ \text{at}\text{current}\text{year}\text{cost (2016) }\end{array}\}\text{=}\left(\begin{array}{l}\text{Ending}\text{Inventory at current}\\ \text{ year cost(2016)}-\\ \text{ Beginning}\text{Inventory at current}\\ \text{ year cost(2016)}\end{array}\right)\\ =\$22,792-\$21,000\\ =\$1,792\end{array}$ (7)

Conclusion

Therefore, the cost-to-retail percentage for the inventory on hand at 12/31/2016 is 80%.

To determine

the ending inventory for 2017.

Explanation of Solution

Calculate the amount of estimated ending inventory for 2017.

Details	Cost ($)	Retail ($)
Beginning inventory	22,792	33,600
Add:  Net purchases	60,000	88,400
Goods available for sale – Including beginning inventory	82,792	122,000
Less:  Net sales		(80,000)
Estimated ending inventory at current year retail prices		42,000
Estimated ending inventory at cost	26,864

Table (1)

Working notes:

Calculate current year layer (2016) cost-to retail percentage.

$\begin{array}{c}\begin{array}{l}\text{Current year cost-to }\\ \text{retail percentage (2016)}\end{array}\}\text{ =}\left\{\frac{\left[\begin{array}{l}\text{Goods available for sale at cost}\\ \text{ (including beginning inventory)}\end{array}\right]}{\left[\begin{array}{l}\text{Goods available for sale at retail}\\ \text{(including beginning inventory)}\end{array}\right]}\times 100\right\}\\ =\left(\frac{\$82,792}{\$122,000}\times 100\right)\\ =67.87\%\end{array}$ (8)

Calculate the amount of estimated ending inventory at cost.

Ending inventory at dollar-value LIFO retail cost
	Step 1	Step 2	Step 3
Ending inventory at year-end retail prices ($)	Ending inventory at base year retail prices ($)	Inventory layers at base year retail prices ($)	Inventory layers converted to cost ($)
42,000 (refer Table 1)	35,000 (9)	28,000 (Base) (3)	21,000 (11)
		2,000 (2016) (4)	1,792 (7)
		5,000 (2017) (10)	4,072 (12)
Total ending inventory at dollar-value LIFO retail cost			$26,864

Table (2)

Calculate the amount of ending inventory at base year retail prices.

$\begin{array}{c}\begin{array}{l}\text{Ending inventory }\\ \text{at base year retail prices (2016) }\end{array}\}\text{= }\left(\frac{\text{Estimated ending inventory at retail}}{\text{Retail price index}}\right)\\ =\left(\frac{\$42,000}{1.20}\right)\\ =\$35,000\end{array}$ (9)

Calculate the amount of inventory layers at current year retail prices.

$\begin{array}{c}\begin{array}{l}\text{Inventory layers at}\\ \text{ current year retail prices (2017) }\end{array}\}\text{= }\left(\begin{array}{l}\text{Ending inventory at base }\\ \text{year retail prices (2017)}-\\ -\text{Beginning inventory at retail (2016)}-\\ \text{Inventory layers at current year}\\ \text{ retail prices (2016)}\end{array}\right)\\ =\$35,000-\$28,000-\$2,000\\ =\$5,000\end{array}$ (10)

Calculate the amount of inventory layers converted to cost (Base).

$\begin{array}{c}\text{Inventory layers converted to cost =}\left(\begin{array}{l}\text{Beginning inventory at retail (Base)}\times \\ \text{Base price index}\times \\ \text{Base layer cost-to retail percentage}\end{array}\right)\\ =\left(\$28,000\times 1.00\times 75\%\right)\\ =\$21,000\end{array}$ (11)

Calculate the amount of inventory layers converted to cost (2017).

$\begin{array}{c}\begin{array}{l}\text{Inventory layers }\\ \text{converted to cost (2017)}\end{array}\}\text{ =}\left(\begin{array}{l}\left(\begin{array}{l}\text{Inventory layers at current }\\ \text{year retail prices }\left(\text{2017}\right)\end{array}\right)\times \\ \text{Retail price index (2017)}\times \\ \text{Current year cost-to retail percentage (2017)}\end{array}\right)\\ =\left(\$5,000\times 1.20\times 67.87\%\right)\\ =\$4,072\end{array}$ (12)