## Related questions with answers

Under the last-in first-out (LIFO) inventory valuation method, a price index for inventory must be established for tax purposes. The quantity weights are based on year-ending inventory levels. Use the beginning-of-the-year price per unit as the base-period price and develop a weighted aggregate index for the total inventory value at the end of the year. What type of weighted aggregate price index must be developed for the LIFO inventory valuation?

$\begin{matrix} \text{ } & \text{Ending} & \text{Unit} & \text{Price (\$)}\\ \hline \text{Product} & \text{Inventory} & \text{Beginning} & \text{Ending}\\ \hline \text{A} & \text{500} & \text{.15} & \text{.19}\\ \text{B} & \text{50} & \text{1.60} & \text{1.80}\\ \text{C} & \text{100} & \text{4.50} & \text{4.20}\\ \text{D} & \text{40} & \text{12.00} & \text{13.20}\\ \end{matrix}$

Solutions

Verified$\color{#4257b2}{\text{Paasche index}}$ must be developed for the LIFO inventory valuation. The weighted aggregate index in period $t$ is calculated by the following formula:

$\boxed{\color{#4257b2}{I_t=\dfrac{\sum{P_{it}Q_{it}}}{\sum{P_{i0}Q_{it}}}(100)}}$

Therefore,

$\begin{align*} I_t &=\dfrac{\sum{P_{it}Q_{it}}}{\sum{P_{i0}Q_{it}}}(100)\\ &=\dfrac{0.19(500)+1.80(50)+4.20(100)+13.20(40)}{0.15(500)+1.60(50)+4.50(100)+12.00(40)}(100)\\ &\approx\boxed{104} \end{align*}$

Let $Q_{i0}, P_{i0}$ and $P_{it}$ be, in order, the quantity, the base (earlier) years price and the current price for items $i=A, B, C, D$. **Especially when the quantities come in a wide range, use weighted index.** Its formula is:

$I_t=\dfrac{\sum Q_{i0}P_{it}}{\sum Q_{i0}P_{i0}}\cdot 100$

All the values $Q_{i0},\ P_{i0},\ P_{it}$ are given, substitute them to obtain:

$I_t=\dfrac{1085}{1133}\cdot 100=104$

So, the current cost is 104% of the earlier years cost, a 4% increase.

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