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

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

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

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

Ending inventory is calculated as follows:

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

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

Ending inventory is calculated as follows:

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

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

Ending inventory is calculated as follows:

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

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

Ending inventory is calculated as follows:

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