Chapter 6, Problem 13AP

(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	8	9,600
February 11	1,500	9	13,500				1,200	8	9,600
							1,500	9	13,500
									23,100
March 1				1,200	8	9,600	1,300	9	11,700
				200	9	1,800			11,700
May 18	1,400	10	14,000				1,300	9	11,700
							1,400	10	14,000
									25,700
July 1				1,300	9	11,700	1,300	10	13,000
				100	10	1,000
									13,000
October 23	1,100	14	15,400				1,300	10	13,000
							1,100	14	15,400
									28,400
October 29				1,200	10	12,000	100	10	1,000
							1,100	14	15,400
Total	4,000		42,900	4,000		$36,100	1,200		$16,400

Table (1)

Conclusion

Therefore, the cost of ending inventory and cost of goods sold are $16,400 and $36,100 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	8	9,600
February 11	1,500	9	13,500				1,200	8	9,600
							1,500	9	13,500
									23,100
March 1				1,400	9	12,600	1,200	8	9,600
							100	9	900
									10,500
May 18	1,400	10	14,000				1,200	8	9,600
							100	9	900
							1,400	10	14,000
									24,500
July 1				1,400	10	14,000	1,200	8	9,600
							100	9	900
									10,500
October 23	1,100	14	15,400				1,200	8	9,600
							100	9	900
							1,100	14	15,400
									25,900
October 29				1,100	14	15,400
				100	9	900
							1,200	8	9,600
Total	4,000		42,900	4,000		$42,900	1,200		$9,600

Table (2)

Conclusion

Therefore, the cost of ending inventory and cost of goods sold are $9,600 and $42,900 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	8	9,600
February 11	1,500	9	13,500				2,700	8.556	23,100
March 1				1,400	8.556	11,978	1,300	8.556	11,122
May 18	1,400	10	14,000				2,700	9.304	25,122
July 1				1,400	9.304	13,026	1,300	9.304	12,096
October 23	1,100	14	15,400				2,400	11.46	27,504
October 29				1,200	11.46	13,752	1,200	11.46	13,752
Total	4,000		42,900	4,000		$38,756	1,200		$41,256

Table (3)

Working Notes:

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

Details	Units	Cost ($)
Beginning Inventory	1,200	9,600
Purchase on February 11	1,500	13,500
Goods Available for Sale on February 11	2,700	23,100

Table (4)

$\begin{array}{c}\begin{array}{l}\text{Weighted-average }\\ \text{Cost }\end{array}\}=\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total number of units Available for Sale}}\\ =\frac{\$23,100}{\text{2,700 Units}}\\ =\text{ \$8}\text{.556}\end{array}$

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	11,122
Purchase on May 18	1,400	14,000
Goods Available for Sale on February 11	2,700	25,122

Table (5)

$\begin{array}{c}\begin{array}{l}\text{Weighted-average}\\ \text{ Cost}\end{array}\}=\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total number of units Available for Sale}}\\ =\frac{\$25,122}{\text{2,700 Units}}\\ =\text{\$9}\text{.304}\end{array}$

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	12,096
Purchase on October 23	1,100	15,400
Goods Available for Sale on February 11	2,400	27,496

Table (6)

$\begin{array}{c}\begin{array}{l}\text{Weighted-average}\\ \text{ Cost}\end{array}\}=\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total number of units Available for Sale}}\\ =\frac{\$27,496}{\text{2,400 Units}}\\ =\text{\$11}\text{.45}\end{array}$

Conclusion

Therefore, the cost of ending inventory and cost of goods sold are $41,256 and $38,756 respectively.

To determine

Determine the effect of cost of goods sold under each method, if the replacement cost of inventory at year-end is $13.

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	8	9,600
Add: Purchases
February 11	1,500	9	13,500
May 18	1,400	10	14,000
October 23	1,100	14	15,400
Total Goods available for Sale	5,200		$52,500

Table (7)

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

$\begin{array}{c}\begin{array}{l}\text{Cost of Goods Sold }\\ \text{at Replacement Cost }\end{array})\text{= }\left[\begin{array}{c}\left(\text{Goods Available for Sale}\right)\\ -\\ \left(\begin{array}{l}\text{ Ending Inventory Units }\\ \times \text{ Replacement Cost}\end{array}\right)\end{array}\right]\\ \text{=}\text{\$52,500 }-\left(1,200\times 15\right)\\ =\text{\$52,500}-18,000\\ =\$34,500\end{array}$

Step 3: Determine the effect of cost of goods sold under each method, if the replacement cost of inventory at year-end is $15.

Effect of Cost of Goods Sold (When the Replacement Cost of Ending inventory is $13)
Details	FIFO	LIFO	WA
Cost of Goods Sold at Acquisition Cost ($)	36,100	42,900	38,756
Less: Cost of Goods Sold at Replacement Cost ($)	34,500	34,500	34,500
Decrease in Cost of Goods Sold ($)	$1,600	$8,400	$4,256

Table (8)

Therefore, if the replacement cost of the inventory at year-end is $15, then the cost of goods sold will decrease by $\boxed{\$1,600,\$8,400,\text{ and \$4,256 }}$ in FIFO, LIFO, and Weighted average method respectively.

Justification:

• The replacement cost is $15 and the acquisition costs are less than $15.
• 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.