Chapter 7, Problem 20E

Inventory Pools Stone Shoe Company adopted dollar-value LIFO on January 1, 2019. The company produces four products and uses a single inventory pool. The company’s beginning inventory consists of the following:

During 2019, the company has the following purchases and sales:

Required:

1. 1. Compute the dollar-value LIFO cost of the ending inventory. Round the cost index to 4 decimal places and all other amounts to the nearest dollar.
2. 2. Next Level By how much would the company’s gross profit differ if it had used four pools instead of a single pool?

To determine

Calculate the dollar value LIFO cost of the ending inventory.

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.

Calculate the dollar value of LIFO ending inventory:

$\begin{array}{c}\begin{array}{l}\text{Dollar-value LIFO }\\ \text{ending inventory}\end{array}\}=\left(\begin{array}{l}\text{Cost of base-year }\\ \text{ inventory}\end{array}\right)+\left(\begin{array}{l}\text{Increase at }\\ \text{current costs}\end{array}\right)\\ =\$3,250,000+\$449,209\\ =\$3,699,209\end{array}$

Therefore, the dollar value LIFO cost of ending inventory is $3,699,209.

Working note 1: Determine the ending inventory costs for previous year (2018) and current year (2019):

Particulars	Product R	Product T	Product B	Product S
Beginning inventory (in units)	80,000	30,000	60,000	40,000
Add: Purchases (in units)	150,000	130,000	100,000	120,000
	230,000	160,000	160,000	160,000
Less: Quantity sold (in units)	(140,000)	(100,000)	(90,000)	(140,000)
Ending inventory (in units) (a)	90,000	60,000	70,000	20,000
Cost per unit for Year 2018 (b)	$16	$15	$14	$17
Ending inventory for previous year costs $\left(\text{c}\right)=\left(\text{a}\right)\times \left(\text{b}\right)$	$1,440,000	$900,000	$980,000	$340,000
Cost per unit for Year 2019 (d)	$19	$16	$14	$18
Ending inventory for current year costs $\left(\text{e}\right)=\left(\text{a}\right)\times \left(\text{d}\right)$	$1,710,000	$960,000	$980,000	$360,000

Table (1)

Working note 2: Determine the cost index:

$\begin{array}{c}\text{Cost index}=\frac{\text{Ending inventory at current year costs}}{\text{Ending inventory at previous year costs}}\times 100\\ =\frac{\$1,710,000 +\$960,000 +\$980,000+\$360,000}{\$1,440,000 +\$900,000 +\$980,000 +\$340,000}\times 100\\ =\frac{\$4,010,000}{\$3,660,000}\times 100\\ =109.5628\end{array}$

Working note 3: Calculate the costs of inventory at base year:

Given: The current cost of inventory of 2019 is $4,010,000 and the cost index for 2018 is 100. The cost index for 2019 is 109.5628.

$\begin{array}{c}\begin{array}{l}\text{Ending inventory}\\ \text{ at base year costs}\end{array}\}=\left(\begin{array}{l}\text{Ending inventory}\\ \text{ at current costs}\end{array}\right)\times \frac{\text{Base-year cost index}}{\text{Current cost index}}\\ =\$4,010,000\times \frac{100}{109.5628}\\ =\$3,660,001\end{array}$

Working note 4: Calculate the increase in relevant current costs:

The total cost at the beginning of year is $3,250,000. The change in base costs is determined by deducting ending inventory at base year cost from total cost at the beginning of year.

$\begin{array}{c}\begin{array}{l}\text{Increase at relevant }\\ \text{current costs}\end{array}\}=\left(\begin{array}{l}\text{Changes at}\\ \text{ base costs}\end{array}\right)\times \frac{\text{Relevant cost index}}{\text{Base-year cost}}\\ =\left(\$3,660,001-\$3,250,000\right)\times \frac{109.5628}{100}\\ =\$410,001\times \frac{109.5628}{100}\\ =\$449,209\end{array}$

To determine

Compute the difference in amount of company’s gross profit if it had used four pools rather than single pool.

Explanation of Solution

If the company had used four cost pools rather than one, there would have been a LIFO liquidation profit on the Product S of $20,000$\left[\left(140,000\text{ units}–120,000\text{ units}\right)\times \left(\$18–\$17\right)\right]$ . Thus, the usage of one pool rather than four pools decreased the gross profit by $20,000.