Describe the LIFO double-extension method. Using the following information, compute the index at December 31, 2017, applying the double-extension method to a LIFO pool consisting of 25,500 units of product A and 10,350 units of product B. The base-year cost of product A is \(10.20 and of product B is \)37.00. The price at December 31, 2017, for product A is \(21.00 and for product B is \)45.60. (Round to two decimal places.)

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-

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

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

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

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