Chapter 7, Problem 15P

1.

To determine

Determine the cost index for each year for each pool using a base of 100 for each index.

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. It is calculate using the formula given below:

$\text{Cost Index = }\frac{\text{Ending inventory at Current year cost}}{\text{Ending inventory at Base year cost}}\times \text{100}$

Determine the cost index for each year for each pool:

For 2016
Pool 1	Pool 2
$\begin{array}{c}\text{=}\frac{\left(30,000\times \$11\right)+\left(12,000\times \$24\right)}{\left(30,000\times \$10\right)+\left(12,000\times \$20\right)}\times \text{100}\\ =\frac{\$618,000}{\$540,000}\times \text{100}\\ =114.4444\end{array}$	$\begin{array}{c}\text{=}\frac{\left(50,000\times \$7\right)+\left(22,000\times \$9\right)}{\left(50,000\times \$5\right)+\left(22,000\times \$8\right)}\times \text{100}\\ =\frac{\$548,000}{\$426,000}\times \text{100}\\ =128.6385\end{array}$
For 2017
Pool 1	Pool 2
$\begin{array}{c}\text{=}\frac{\left(40,000\times \$12\right)+\left(14,000\times \$22\right)}{\left(40,000\times \$10\right)+\left(14,000\times \$20\right)}\times \text{100}\\ =\frac{\$788,000}{\$680,000}\times \text{100}\\ =115.8824\end{array}$	$\begin{array}{c}\text{=}\frac{\left(46,000\times \$6\right)+\left(20,000\times \$8\right)}{\left(46,000\times \$5\right)+\left(20,000\times \$8\right)}\times \text{100}\\ =\frac{\$436,000}{\$390,000}\times \text{100}\\ =111.7949\end{array}$
For 2018
Pool 1	Pool 2
$\begin{array}{c}\text{=}\frac{\left(45,000\times \$12\right)+\left(13,000\times \$25\right)}{\left(45,000\times \$10\right)+\left(13,000\times \$20\right)}\times \text{100}\\ =\frac{\$865,000}{\$710,000}\times \text{100}\\ =121.8310\end{array}$	$\begin{array}{c}\text{=}\frac{\left(60,000\times \$7\right)+\left(25,000\times \$8\right)}{\left(60,000\times \$5\right)+\left(25,000\times \$8\right)}\times \text{100}\\ =\frac{\$620,000}{\$500,000}\times \text{100}\\ =124\end{array}$

Table (1)

Thus, the cost index of Pool 1 for the years 2016, 2017 and 2018 are 114.4444, 115.8824, and 121.8310 respectively and the cost index of Pool 2 for the years 2016, 2017 and 2018 are 128.6385, 111.7949, and 124 respectively.

2.

To determine

Using the dollar value LIFO method compute the ending inventory for all the years.

Explanation of Solution

Dollar-value LIFO method: In this method, the valuation of inventory is calculated on the monetary value of units instead of quantity of units held. The dollar value LIFO method uses the cost indexes to convert the current cost of inventory to the base year cost.

Compute the total ending inventory costs for all the years:

Year	Pool 1	Pool 2	Total cost
2015	$400,000	$360,000	$760,000
2016	$560,222	$444,901	$1,005,123
2017	$722,457	$398,591	$1,121,048
2018	$759,006	$534,991	$1,293,997

Table (2)

Working note 1: Compute the ending inventory for all the years:

Date	Ending inventory at Current costs	$\frac{\text{Base year}}{\text{Current cost}}$	Inventory at Base year costs
Pool 1
01/01/2016		-	$ 400,000
12/31/2016	$618,000	$\frac{100}{144.4444}$	$ 540,000
12/31/2017	$788,000	$\frac{100}{115.8824}$	$ 680,000
12/31/2018	$865,000	$\frac{100}{121.8310}$	$ 710,000
Pool 2
01/01/2016		-	$ 360,000
12/31/2016	$548,000	$\frac{100}{128.6385}$	$ 426,000
12/31/2017	$436,000	$\frac{100}{128.6385}$	$ 390,000
12/31/2018	$620,000	$\frac{124}{100}$	$500,000

Table (3)

Date	Increase/ decrease at base year cost	$\frac{\text{Relevant cost}}{\text{Base year cost}}$	Increase/ decrease at relevant current cost	Ending inventory at LIFO
Pool 1	-	-
01/01/2016				$ 400,000
12/31/2016	$140,000	$\frac{144.4444}{100}$	$160,222	$ 560,222
12/31/2017	$140,000	$\frac{115.8824}{100}$	$162,235	$ 722,457
12/31/2018	$30,000	$\frac{121.8310}{100}$	$36,549	$ 759,056
Pool 2
01/01/2016				$360,000
12/31/2016	$66,000	$\frac{128.6385}{100}$	$84,901	$444,901
12/31/2017	($36,000)	$\frac{121.8310}{100}$	($46,310)	$398,591
12/31/2018	$110,000	$\frac{121.8310}{100}$	$136,400	$534,991

Table (4)