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LIFO double extension method is a specific internal price index that is derived by the company itself. As the name suggests, it is called double extension because the inventory value is extended at both base-year and current-year prices.

The formula to compute the Price index using the double extension method is-

$\mathrm{Price}\mathrm{Index}=\frac{\mathrm{Ending}\mathrm{inventory}\mathrm{at}\mathrm{current}\mathrm{cost}\mathrm{price}}{\mathrm{Ending}\mathrm{inventory}\mathrm{at}\mathrm{base}\mathrm{year}\mathrm{cost}}$

$\begin{array}{rcl}\mathrm{Inventory}\mathrm{value}\mathrm{at}\mathrm{base}\mathrm{year}\mathrm{price}& =& \left(\mathrm{Units}\mathrm{of}\mathrm{product}\mathrm{A}脳\mathrm{Cost}\right)+\left(\mathrm{Units}\mathrm{of}\mathrm{product}\mathrm{B}脳\mathrm{Cost}\right)\\ & =& \left(25,500脳\$10.20\right)+\left(10,350脳\$37\right)\\ & =& \$260,100+\$382,950\\ & =& \$643,050\end{array}$

$\begin{array}{rcl}\mathrm{Inventory}\mathrm{value}\mathrm{at}\mathrm{current}\mathrm{year}\mathrm{price}& =& \left(\mathrm{Units}\mathrm{of}\mathrm{product}\mathrm{A}脳\mathrm{Cost}\right)+\left(\mathrm{Units}\mathrm{of}\mathrm{product}\mathrm{B}脳\mathrm{Cost}\right)\\ & =& \left(25,500脳\$21\right)+\left(10,350脳\$45.60\right)\\ & =& \$535,500+\$471,960\\ & =& \$1,007,460\end{array}$

$\begin{array}{rcl}\mathrm{Price}\mathrm{Index}& =& \frac{\mathrm{Inventory}\mathrm{value}\mathrm{at}\mathrm{current}\mathrm{year}\mathrm{prices}}{\mathrm{Inventory}\mathrm{value}\mathrm{at}\mathrm{base}\mathrm{year}\mathrm{prices}}\\ & =& \frac{\$1007460}{\$643050}\\ & =& 1.567\mathrm{or}157\%\end{array}$