Chapter 7, Problem 7.1PA

Analyzing the Effects of Four Alternative Inventory Methods in a Periodic Inventory System

Gladstone Company tracks the number of units purchased and sold throughout each accounting period but applies its inventory costing method at the end of each period, as if it uses a periodic inventory system. Assume its accounting records provided the following information at the end of the annual accounting period, December 31.

Transactions	Units	Unit Cost
Beginning inventory, January 1 Transactions during the year:	1,800	$50
a. Purchase, January 30	2,500	62
b. Sale, March 14 ($100 each)	(1,450)
c. Purchase, May 1	1,200	80
d. Sale, August 31 ($100 each)	(1,900)

Required:

1. 1. Compute the amount of goods available for sale, ending inventory, and cost of goods sold at December 31 under each of the following inventory costing methods:
   1. a. Last-in, first-out.
   2. b. Weighted average cost.
   3. c. First-in, first-out.
   4. d. Specific identification, assuming that the March 14 sale was selected two-fifths from the beginning inventory and three-fifths from the purchase of January 30. Assume that the sale of August 31 was selected from the remainder of the beginning inventory, with the balance from the purchase of May 1.
2. 2. Of the four methods, which will result in the highest gross profit? Which will result in the lowest income taxes?

To determine

The cost of goods available for sale.

Explanation of Solution

Determine cost of goods available for sale.

Date	Particulars	Units ($)	Unit cost($)	Total cost($)
		(a)	(b)	(c = a × b)
January 1	Beginning inventory	1,800	50	90,000
January 30	Purchased	2,500	62	155,000
May 1	Purchased	1,200	80	96,000
	Total	5,500		$341,000
	Less: Goods sold	3,350
	Ending inventory	2,150

Table (1)

Conclusion

Therefore, the cost of goods sold available for sale for 2,150 units of inventory is $341,000.

To determine

The ending inventory and the cost of goods sold under LIFO.

Explanation of Solution

In Last-in-First-Out method, the cost of last purchased items is sold first. The value of the closing stock consists the initial purchased items.

Determine the amount of cost of goods sold.

Date	Particulars	Units	Unit cost($)	Total cost($)
		(a)	(b)	(c = a × b)
May 1	Purchased	1,200	80	96,000
January 30	Purchased	2,150	62	133,300
	Cost of goods sold	3,350		$229,300

Table (2)

Determine ending inventory under LIFO method.

Date	Particulars	Units	Unit cost($)	Total cost($)
		(a)	(b)	(c = a × b)
January 1	Beginning inventory	1,800	50	90,000
January 30	Purchased	350	62	21,700
	Ending inventory	2,150		$111,700

Table (3)

Conclusion

Hence, the cost of goods sold under LIFO is $229,300 and the value of ending inventory is $111,700.

To determine

The ending inventory and the cost of goods sold under weighted average-cost method.

Explanation of Solution

In Average Cost Method the cost of inventory is priced at the average rate of the goods available for sale. Following is the mathematical representation:

$\text{Weighted-average Cost}=\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total Number of Units Available For Sale}}$

Determine cost of ending inventory under average-cost method.

Date	Particulars	Units	Unit cost($)	Total cost($)
		(a)	(b)	(c = a × b)
January 1	Beginning inventory	1,800	50	90,000
January 30	Purchased	2,500	62	155,000
May 1	Purchased	1,200	80	96,000
	Cost of goods available for sale	5,500		341,000
	Less: Ending inventory	2,150	62	133,300
	Cost of goods sold	3,350		$207,700

Table (4)

Working note:

Determine weighted average unit cost.

$\begin{array}{c}\begin{array}{c}\text{Weighted}\\ \text{average}\text{unit}\text{cost}\end{array}\}=\frac{\left(\begin{array}{l}\text{Cost}\text{of}\text{goods}\\ \text{available}\text{for}\text{sale}\end{array}\right)}{\left(\begin{array}{l}\text{Total}\text{units}\\ \text{available}\text{for}\text{sales}\end{array}\right)}\\ =\frac{\$341,000}{5,500}\\ =\$62\text{per unit}\end{array}$

Conclusion

Hence, the cost of goods sold under weighted average-cost method is $207,700 and the value of ending inventory is $133,300.

To determine

The ending inventory and the cost of goods sold under FIFO.

Explanation of Solution

In First-in-First-Out method, the cost of initial purchased items is sold first. The value of the ending inventory consists the recent purchased items.

Determine the amount of cost of goods sold.

Date	Particulars	Units	Unit cost($)	Total cost($)
		(a)	(b)	(c = a × b)
January 1	Beginning inventory	1,800	50	90,000
January 30	Purchased	1,550	62	96,100
	Cost of goods sold	3,350		$186,100

Table (5)

Determine ending inventory under FIFO method.

Date	Particulars	Units	Unit cost($)	Total cost($)
		(a)	(b)	(c = a × b)
January 30	Purchased	950	62	58,900
May 1	Purchased	1,200	80	96,000
	Ending inventory	2,150		$154,900

Table (6)

Conclusion

Hence, the cost of goods sold under FIFO is $12,400 and the value of ending inventory is $12,200.

To determine

The ending inventory and the cost of goods sold under specific identification method.

Explanation of Solution

Specific identification method can be said as identifying the items precisely which are being sold and those which are being stored as closing inventory. The companies are required to keep perfect records of the original cost of each and every individual items of the inventory.

Determine the amount of cost of goods sold.

Date	Particulars	Units	Unit cost($)	Total cost($)
		(a)	(b)	(c = a × b)
January 1	Beginning inventory	580	50	29,000
January 1	Beginning inventory	1,220	50	61,000
January 30	Purchased	870	62	53,940
May 1	Purchased	680	80	54,400
	Cost of goods sold	3,350		$198,340

Table (7)

Determine ending inventory under FIFO method.

Date	Particulars	Units	Unit cost($)	Total cost($)
		(a)	(b)	(c = a × b)
May 1	Purchased	520	80	41,600
January 30	Purchased	1,630	62	101,060
	Ending inventory	2,150		$142,660

Table (8)

Conclusion

Hence, the cost of goods sold under specific identification method is $198,340 and the value of ending inventory is $142,660.

To determine

The method of inventory costing results highest in gross profit and minimizes income taxes.

Explanation of Solution

• FIFO method provides a lower cost of goods sold and a higher gross profit than in LIFO.
• By comparing the three inventory method, it is found that the use of LIFO method will minimizes the income taxes because it reports less taxable income as a result of using higher unit costs (in this case) to calculate cost of goods sold.
• A higher Cost of Goods Sold means less Income from Operations. Therefore it reduce tax amount.