Chapter 7, Problem 13P

Webster Company adopted do liar-value LIFO on January 1, 2019. Webster produces three products: X, Y, and Z. Webster’s beginning inventory consisted of the following:

During 2019, Webster had the following purchases and sales:

Required:

1. 1. Compute the LIFO cost of the ending inventory assuming Webster uses a single inventory pool. Round cost index to 4 decimal places.
2. 2. Compute the LIFO cost of the ending inventory assuming Webster uses three inventory pools. Round cost indexes to 4 decimal places.

To determine

Calculate the ending inventory for LIFO cost if single inventory pool is used.

Explanation of Solution

Cost index:

Cost index refer to the index which relates the inventory cost of current year with the base year. The cost index is usually prepared with a sample from the total inventory.

Double-extension method:

Under the double-extension method of cost index, the ending inventory of the current year are valued at the current year costs and related with the base year’s cost.

Calculate the ending inventory in units:

Particulars	Product X	Product Y	Product Z
Beginning inventory	30,000	10,000	25,000
Add: Net Purchases	110,000	100,000	75,000
Units available for sale	140,000	110,000	100,000
Less: Sales	(90,000)	(85,000)	(70,000)
Ending inventory	50,000	25,000	30,000

Table (1)

Calculate the cost index:

$\begin{array}{c}\text{Cost Index = }\frac{\text{Ending inventory at Current year cost}}{\text{Ending inventory at Base year cost}}\times \text{100}\\ \text{=}\frac{\left(50,000\times \$4.75\right)+\left(25,000\times \$3.75\right)+\left(30,000\times \$2.10\right)}{\left(50,000\times \$4.25\right)+\left(25,000\times \$3.50\right)+\left(30,000\times \$2.00\right)}\times \text{100}\\ =\frac{\$394,250}{\$360,000}\times \text{100}\\ =109.5139\end{array}$

Calculate the ending inventory at the Base year cost:

$\begin{array}{c}\begin{array}{l}\text{Ending inventory at}\\ \text{Base year cost}\end{array}\}\text{ = }\frac{\text{100}}{\text{Cost Index}}\times \text{Ending inventory at Current year cost}\\ \text{=}\frac{100}{109.5139}\times \$394,250\\ =\$360,000\text{ rounded}\end{array}$

Calculate the increase in inventory at the Base year cost:

$\begin{array}{c}\begin{array}{l}\text{Increase in inventory}\\ \text{at Base year cost}\end{array}\}\text{ = }\$360,000-\$212,500\\ =\$147,500\end{array}$

Calculate the layer increase in inventory at the Current year cost:

$\begin{array}{c}\begin{array}{l}\text{Layer increase at}\\ \text{current year cost}\end{array}\}\text{ = }\$147,500\times \frac{109.5139}{100}\\ =\$161,533\text{ rounded}\end{array}$

Calculate the LIFO ending inventory cost:

$\begin{array}{c}\begin{array}{l}\text{LIFO Ending}\\ \text{inventory cost}\end{array}\}\text{ = }\$212,500+\$161,533\\ =\$374,033\end{array}$

Thus, the ending inventory for LIFO cost if single inventory pool is used is $374,033.

To determine

Calculate the ending inventory for LIFO cost if three inventory pools are used.

Explanation of Solution

Calculate the cost index for Product X:

$\begin{array}{c}\text{Cost Index = }\frac{\text{Ending inventory at Current year cost}}{\text{Ending inventory at Base year cost}}\times \text{100}\\ \text{=}\frac{\left(50,000\times \$4.75\right)}{\left(50,000\times \$4.25\right)}\times \text{100}\\ =\frac{\$237,500}{\$212,500}\times \text{100}\\ =111.7647\end{array}$

Calculate the ending inventory at the Base year cost for Product X:

$\begin{array}{c}\begin{array}{l}\text{Ending inventory at}\\ \text{Base year cost}\end{array}\}\text{ = }\frac{\text{100}}{\text{Cost Index}}\times \text{Ending inventory at Current year cost}\\ \text{=}\frac{100}{111.7647}\times \$237,500\\ =\$212,500\text{ rounded}\end{array}$

Calculate the increase in inventory at the Base year cost for Product X:

$\begin{array}{c}\begin{array}{l}\text{Increase in inventory}\\ \text{at Base year cost}\end{array}\}\text{ = }\$212,500-\$127,500\\ =\$85,000\end{array}$

Calculate the layer increase in inventory at the Current year cost for Product X:

$\begin{array}{c}\begin{array}{l}\text{Layer increase at}\\ \text{current year cost}\end{array}\}\text{ = }\$85,000\times \frac{111.7647}{100}\\ =\$95,000\text{ rounded}\end{array}$

Calculate the LIFO ending inventory cost for Product X:

$\begin{array}{c}\begin{array}{l}\text{LIFO Ending}\\ \text{inventory cost}\end{array}\}\text{ = }\$127,500+\$95,000\\ =\$222,500\end{array}$

Thus, the ending inventory for LIFO cost for Product X if three inventory pools are used is $222,500.

Calculate the cost index for Product Y:

$\begin{array}{c}\text{Cost Index = }\frac{\text{Ending inventory at Current year cost}}{\text{Ending inventory at Base year cost}}\times \text{100}\\ \text{=}\frac{\left(25,000\times \$3.75\right)}{\left(25,000\times \$3.50\right)}\times \text{100}\\ =\frac{\$93,750}{\$87,500}\times \text{100}\\ =107.1429\end{array}$

Calculate the ending inventory at the Base year cost for Product Y:

$\begin{array}{c}\begin{array}{l}\text{Ending inventory at}\\ \text{Base year cost}\end{array}\}\text{ = }\frac{\text{100}}{\text{Cost Index}}\times \text{Ending inventory at Current year cost}\\ =\frac{100}{107.1429}\times \$93,750\\ =\$87,500\text{ rounded}\end{array}$

Calculate the increase in inventory at the Base year cost for Product Y:

$\begin{array}{c}\begin{array}{l}\text{Increase in inventory}\\ \text{at Base year cost}\end{array}\}\text{ = }\$87,500-\$35,000\\ =\$52,500\end{array}$

Calculate the layer increase in inventory at the Current year cost for Product Y:

$\begin{array}{c}\begin{array}{l}\text{Layer increase at}\\ \text{current year cost}\end{array}\}\text{ = }\$52,500\times \frac{107.1429}{100}\\ =\$56,252\text{ rounded}\end{array}$

Calculate the LIFO ending inventory cost for Product Y:

$\begin{array}{c}\begin{array}{l}\text{LIFO Ending}\\ \text{inventory cost}\end{array}\}\text{ = }\$35,000+\$56,252\\ =\$91,252\end{array}$

Thus, the ending inventory for LIFO cost for Product Y if three inventory pools are used is $91,252.

Calculate the cost index for Product Z:

$\begin{array}{c}\text{Cost Index = }\frac{\text{Ending inventory at Current year cost}}{\text{Ending inventory at Base year cost}}\times \text{100}\\ \text{=}\frac{\left(30,000\times \$2.10\right)}{\left(30,000\times \$2.00\right)}\times \text{100}\\ =\frac{\$63,000}{\$60,000}\times \text{100}\\ =105\end{array}$

Calculate the ending inventory at the Base year cost for Product Z:

$\begin{array}{c}\begin{array}{l}\text{Ending inventory at}\\ \text{Base year cost}\end{array}\}\text{ = }\frac{\text{100}}{\text{Cost Index}}\times \text{Ending inventory at Current year cost}\\ \text{=}\frac{100}{105}\times \$63,000\\ =\$60,000\text{ rounded}\end{array}$

Calculate the increase in inventory at the Base year cost for Product Z:

$\begin{array}{c}\begin{array}{l}\text{Increase in inventory}\\ \text{at Base year cost}\end{array}\}\text{ = }\$60,000-\$50,000\\ =\$10,000\end{array}$

Calculate the layer increase in inventory at the Current year cost for Product Z:

$\begin{array}{c}\begin{array}{l}\text{Layer increase at}\\ \text{current year cost}\end{array}\}\text{ = }\$10,000\times \frac{105}{100}\\ =\$10,500\end{array}$

Calculate the LIFO ending inventory cost for Product Z:

$\begin{array}{c}\begin{array}{l}\text{LIFO Ending}\\ \text{inventory cost}\end{array}\}\text{ = }\$50,000+\$10,500\\ =\$60,500\end{array}$

Thus, the ending inventory for LIFO cost for Product Z if three inventory pools are used is $60,500.

Calculate the LIFO ending inventory cost:

$\begin{array}{c}\text{Ending Inventory = Product X + Product Y+ Product Z}\\ \text{= }\$222,500+\$91,252+\$60,500\\ =\$374,252\end{array}$

Thus, the ending inventory for LIFO cost if three inventory pools are used is $374,252.