Chapter 6, Problem 9BP

 (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	20	28,000				1,300	19	24,700
							1,400	20	28,000
									52,700
July 1				1,300	19	24,700	1,300	20	26,000
				100	20	2,000
									26,000
October 23	1,100	22	24,200				1,300	20	26,000
							1,100	22	24,200
									50,200
October 29				1,000	20	20,000	300	20	6,000
							1,100	22	24,200
Total	4,000		80,700	3,800		$72,100	1,400		$30,200

Table (1)

Conclusion

Therefore, the cost of ending inventory and cost of goods sold are $30,200 and $72,100 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	8	21,600
							100	19	1,900
									23,500
May 18	1,400	20	28,000				1,200	8	21,600
							100	19	1,900
							1,400	20	28,000
									51,500
July 1				1,400	20	28,000	1,200	8	21,600
							100	19	1,900
									23,500
October 23	1,100	22	24,200				1,200	8	21,600
							100	19	1,900
							1,100	22	24,200
									47,700
October 29				1,000	22	22,000	1,200	8	21,600
							100	19	1,900
							100	22	2,200
Total	4,000		80,700	3,800		$76,600	1,400		$25,700

Table (2)

Conclusion

Therefore, the cost of ending inventory and cost of goods sold are $25,700 and $76,600 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	20	28,000				2,700	19.304	52,122
July 1				1,400	19.304	27,026	1,300	19.304	25,096
October 23	1,100	22	24,200				2,400	20.54	49,296
October 29				1,000	20.54	20,540	1,400	20.54	28,756
Total	4,000		80,700	3,800		$73,544	1,400		$28,756

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	28,000
Goods Available for Sale on February 11	2,700	52,122

Table (5)

$\begin{array}{c}\begin{array}{l}\text{Weighted-average}\\ \text{ Cost}\end{array}\}\text{ = }\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total number of units Available for Sale}}\\ =\frac{\$52,122}{\text{2,700 Units}}\\ =\text{ \$19}\text{.304}\end{array}$

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	25,096
Purchase on October 23	1,100	24,200
Goods Available for Sale on February 11	2,400	49,296

Table (6)

$\begin{array}{c}\begin{array}{l}\text{Weighted-average}\\ \text{ Cost}\end{array}\}\text{ = }\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total number of units Available for Sale}}\\ =\frac{\$49,296}{\text{2,400 Units}}\\ =\text{ \$20}\text{.54}\end{array}$

Conclusion

Therefore, the cost of ending inventory and cost of goods sold are $28,756 and $73,544 respectively.

To determine

Determine the effect of cost of goods sold under each method, if the replacement cost of inventory at year-end is $23.

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	20	28,000
October 23	1,100	22	24,200
Total Goods available for Sale	5,200		102,300

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

$\begin{array}{c}\begin{array}{l}\text{Cost of Goods Sold }\\ \text{at Replacement Cost }\end{array})\text{= }\left[\begin{array}{c}\left(\text{Goods Available for Sale}\right)\\ -\\ \left(\begin{array}{l}\text{ Ending Inventory Units }\\ \times \text{ Replacement Cost}\end{array}\right)\end{array}\right]\\ =\$102,300-\left(1,400\times 23\right)\\ =\$102,300-32,200\\ =\$70,100\end{array}$

Step 3: Determine the effect of cost of goods sold under each method, if the replacement cost of inventory at year-end is $23.

Effect of Cost of Goods Sold (When the Replacement Cost of Ending inventory is $13)
Details	FIFO	LIFO	WA
Cost of Goods Sold at Acquisition Cost ($)	72,100	76,600	73,544
Less: Cost of Goods Sold at Replacement Cost ($)	70,100	70,100	70,100
Decrease in Cost of Goods Sold ($)	2,000	6,500	3,444

Therefore, if the replacement cost of the inventory at year-end is $23, then the cost of goods sold will decrease by $\boxed{\$2,000,\$6,500,\text{ and \$3,444 }}$ in FIFO, LIFO, and Weighted average method respectively.

Justification:

• The replacement cost is $23 and the acquisition costs are less than $23.
• 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