Chapter 6, Problem 13BP

 (a)

To determine

Calculate the value of ending inventory and cost of goods sold at year-end using FIFO method - Perpetual inventory system.

Explanation of Solution

Perpetual Inventory System refers to the inventory system that maintains the detailed records of every inventory transactions related to purchases and sales on a continuous basis. It shows the exact on-hand-inventory at any point of time.

First-in-First-Out: In First-in-First-Out method, the costs of the initially purchased items are considered as cost of goods sold, for the items which are sold first. The value of the ending inventory consists of the recent purchased items.

Prepare a perpetual inventory schedule using FIFO method of inventory costing.

Perpetual Inventory Costing Method (FIFO)
Date	Purchases			Cost of Goods Sold			Inventory on Hand
	Quantity (Units)	Unit Cost ($)	Total Cost ($)	Quantity (Units)	Unit Cost ($)	Total Cost ($)	Quantity (Units)	Unit Cost ($)	Total Cost ($)
January 1							1,200	18	21,600
February 11	1,500	19	28,500				1,200	18	21,600
							1,500	19	28,500
									50,100
March 1				1,200	18	21,600	1,300	19	24,700
				200	19	3,800			24,700
May 18	1,400	21	29,400				1,300	19	24,700
							1,400	21	29,400
									54,100
July 1				1,300	19	24,700	1,300	21	27,300
				100	21	2,100
									27,300
October 23	1,100	23	25,300				1,300	21	27,300
							1,100	23	25,300
									52,600
October 29				1,000	21	21,000	300	21	6,300
							1,100	23	25,300
Total	4,000		83,200	3,800		$73,200	1,400		$31,600

Table (1)

Conclusion

Therefore, the cost of ending inventory and cost of goods sold are $31,600 and $73,200 respectively.

b.

To determine

Calculate the value of ending inventory and cost of goods sold at year-end using LIFO method - Perpetual inventory system.

Explanation of Solution

Last-in-Last-Out: In Last-in-First-Out method, the costs of last purchased items are considered as the cost of goods sold, for the items which are sold first. The value of the closing stock consists of the initial purchased items.

Prepare a perpetual inventory schedule using LIFO method of inventory costing.

Perpetual Inventory Costing Method (LIFO)
Date	Purchases			Cost of Goods Sold			Inventory on Hand
	Quantity (Units)	Unit Cost ($)	Total Cost ($)	Quantity (Units)	Unit Cost ($)	Total Cost ($)	Quantity (Units)	Unit Cost ($)	Total Cost ($)
January 1							1,200	18	21,600
February 11	1,500	19	28,500				1,200	18	21,600
							1,500	19	28,500
									50,100
March 1				1,400	19	26,600	1,200	18	21,600
							100	19	1,900
									23,500
May 18	1,400	21	29,400				1,200	18	21,600
							100	19	1,900
							1,400	21	29,400
									52,900
July 1				1,400	21	29,400	1,200	18	21,600
							100	19	1,900
									23,500
October 23	1,100	23	25,300				1,200	18	21,600
							100	19	1,900
							1,100	23	25,300
									48,800
October 29				1,000	23	23,000	1,200	18	21,600
							100	19	1,900
							100	23	2,300
Total	4,000		83,200	3,800		$79,000	1,400		$25,800

Table (2)

Conclusion

Therefore, the cost of ending inventory and cost of goods sold are $25,800 and $79,000 respectively.

(c)

To determine

Calculate the value of ending inventory and cost of goods sold at year-end using weighted-average inventory costing method - Perpetual inventory system.

Explanation of Solution

Weighted-average cost method: In moving-average Cost Method, the cost of inventory is priced at the average rate of the goods available for sale. Following is the mathematical representation:

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

Prepare a perpetual inventory schedule using weighted-average method of inventory costing.

Perpetual Inventory Costing Method (Weighted-Average)
Date	Purchases			Cost of Goods Sold			Inventory on Hand
	Quantity (Units)	Unit Cost ($)	Total Cost ($)	Quantity (Units)	Unit Cost ($)	Total Cost ($)	Quantity (Units)	Unit Cost ($)	Total Cost ($)
January 1							1,200	18	21,600
February 11	1,500	19	28,500				2,700	18.556	50,100
March 1				1,400	18.556	25,978	1,300	18.556	24,122
May 18	1,400	21	29,400				2,700	19.823	53,522
July 1				1,400	19. 823	27,752	1,300	19.823	25,770
October 23	1,100	23	25,300				2,400	21.28	51,072
October 29				1,000	21.28	21,280	1,400	21.28	29,792
Total	4,000		83,200	3,800		$75,010	1,400		$29,792

Table (3)

Working Notes:

Calculate the average cost of inventory balance after the purchase on February 11.

Details	Units	Cost ($)
Beginning Inventory	1,200	21,600
Purchase on February 11	1,500	28,500
Goods Available for Sale on February 11	2,700	50,100

Table (4)

$\begin{array}{c}\begin{array}{l}\text{Weighted-average}\\ \text{ Cost}\end{array}\}=\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total number of units Available for Sale}}\\ =\frac{\$50,100}{\text{2,700 Units}}\\ =\text{\$18}\text{.556}\end{array}$

Calculate the average cost of inventory balance after the purchase on May 18.

Details	Units	Cost ($)
Inventory after the Sale on March 1	1,300	24,122
Purchase on May 18	1,400	29,400
Goods Available for Sale on February 11	2,700	53,522

Table (5)

$\begin{array}{c}\begin{array}{l}\text{Weighted-average}\\ \text{ Cost}\end{array}\}\text{ = }\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total number of units Available for Sale}}\\ =\frac{\$53,522}{\text{2,700 Units}}\\ =\text{ \$19}\text{.823}\end{array}$

Calculate the average cost of inventory balance after the purchase on October 23.

Details	Units	Cost ($)
Inventory after the Sale on July 1	1,300	25,770
Purchase on October 23	1,100	25,300
Goods Available for Sale on February 11	2,400	51,070

Table (6)

$\begin{array}{c}\begin{array}{l}\text{Weighted-average}\\ \text{ Cost}\end{array}\}\text{ = }\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total number of units Available for Sale}}\\ =\frac{\$51,070}{\text{2,400 Units}}\\ =\text{ \$21}\text{.28}\end{array}$

Conclusion

Therefore, the cost of ending inventory and cost of goods sold are $29,792 and $75,010 respectively.

To determine

Determine the effect of cost of goods sold under each method, if the replacement cost of inventory at year-end is $25.

Explanation of Solution

Step 1: Calculate the Total Cost and units of Goods Available for Sales.

Calculation of Goods Available for Sales
Details	Number of Units	Rate per unit ($)	Total Cost ($)
Beginning balance, January 1	1,200	18	21,600
Add: Purchases
February 11	1,500	19	28,500
May 18	1,400	21	29,400
October 23	1,100	23	25,300
Total Goods available for Sale	5,200		$104,800

Step 2: Compute the Cost of goods sold at replacement cost.

$\begin{array}{c}\begin{array}{l}\text{Cost of Goods Sold }\\ \text{at Replacement Cost }\end{array})\text{= }\left[\begin{array}{c}\left(\text{Goods Available for Sale}\right)\\ -\\ \left(\begin{array}{l}\text{ Ending Inventory Units }\\ \times \text{ Replacement Cost}\end{array}\right)\end{array}\right]\\ =\$104,800-\left(1,400\times \$25\right)\\ =\$104,800-35,000\\ =\$69,800\end{array}$

Step 3: Determine the effect of cost of goods sold under each method, if the replacement cost of inventory at year-end is $25.

Effect of Cost of Goods Sold (When the Replacement Cost of Ending inventory is $13)
Details	FIFO	LIFO	WA
Cost of Goods Sold at Acquisition Cost ($)	73,200	79,000	75,010
Less: Cost of Goods Sold at Replacement Cost ($)	69,800	69,800	69,800
Decrease in Cost of Goods Sold ($)	$3,400	$9,200	$5,210

Therefore, if the replacement cost of the inventory at year-end is $23, then the cost of goods sold will decrease by $\boxed{\$3,400,\$9,200,\text{ and \$5,210 }}$ in FIFO, LIFO, and Weighted average method respectively.

Justification:

• The replacement cost is $25 and the acquisition costs are less than $25.
• Hence, the ending inventory at replacement cost will be higher than ending inventory at acquisition cost.
• As the ending inventory cost is higher at replacement cost, the cost of goods sold will be lower at replacement cost as compared to the acquisition cost