Chapter 6, Problem 16AE

To determine

Ascertain the cost of goods sold and the ending inventory cost under (a) first-in first-out, (b) last-in first-out, and (c) weighted average cost method.

Explanation of Solution

Perpetual inventory system: The method or system of maintaining, recording, and adjusting the inventory perpetually throughout the year, is referred to as perpetual inventory system.

First-in-First-Out (FIFO): In this method, items purchased initially are sold first. So, the value of the ending inventory consist the recent cost for the remaining unsold items.

Last-in-First-Out (LIFO): In this method, items purchased recently are sold first. So, the value of the ending inventory consist the initial cost for the remaining unsold items.

Weighted-average Cost Method: In this method, the inventories are priced at the average rate of goods available for sales.

Ascertain the cost of goods sold and the ending inventory cost under (a) first-in first-out, (b) last-in first-out, and (c) weighted average cost method as follows:

(a) first-in first-out method:

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							200	10	2,000
February 11	500	14	7,000				200	10	2,000
							500	14	7,000
									9,000
March 1				200	10	2,000	300	14	4,200
				200	14	2,800			4,200
May 18	400	16	6,400				300	14	4,200
							400	16	6,400
									10,600
July 1				300	14	4,200	320	16	5,120
				80	16	1,280
									5,120
October 23	100	18	1,800				320	16	5,120
							100	18	1,800
Total	1,000		15,200	780		10,280	420		6,920

Table (1)

Therefore, the cost of ending merchandised inventory and cost of goods sold under FIFO are $6,920 and $10,280 respectively.

(b) Last-in first-out method:

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							200	10	2,000
February 11	500	14	7,000				200	10	2,000
							500	14	7,000
									9,000
March 1				400	14	5,600	200	10	2,000
							100	14	1,400
									3,400
May 18	400	16	6,400				200	10	2,000
							100	14	1,400
							400	16	6,400
									9,800
July 1				380	16	6,400	200	10	2,000
							100	14	1,400
							20	16	320
									3,620
October 23	100	18	1,800				200	10	2,000
							100	14	1,400
							20	16	320
							100	18	1,800
Total	1,000		15,200	800		12,000	420		5,520

Table (2)

Therefore, the cost of ending merchandised inventory and cost of goods sold under LIFO are $5,520 and $12,000 respectively.

(c) Weighted average cost method:

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							200	10	2,000
February 11	500	14	7,000				700	12.86 (1)	9,000
March 1				400	12.86	5,144	300	12.86	3,856
May 18	400	16	6,400				700	14.65 (2)	10,256
July 1				380	14.65	5,567	320	14.65	4,688
October 23	100	18	1,800				420	15.35 (3)	6,447
Total	1,000		15,400	800		10,711	420		6,447

Table (3)

Therefore, the cost of ending merchandised inventory and cost of goods sold under weighted average method are $6,447 and $10,711 respectively.

Working note:

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

Here,

Details	Units	Cost ($)
Beginning Inventory	200	2,000
Purchase on February 11	500	7,000
Goods Available for Sale on February 11	700	9,000

Table (4)

$\begin{array}{c}\begin{array}{l}\text{Weighted-average}\\ \text{ Cost}\end{array}\}=\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total number of units Available for Sale}}\\ =\frac{\$9,000}{\text{700 Units}}\\ =\text{\$12}\text{.86}\end{array}$ (1)

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

Here,

Details	Units	Cost ($)
Inventory after the Sale on March 1	300	3,856
Purchase on May 18	400	6,400
Goods Available for Sale on February 11	700	10,256

Table (5)

$\begin{array}{c}\begin{array}{l}\text{Weighted-average}\\ \text{ Cost}\end{array}\}=\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total number of units Available for Sale}}\\ =\frac{\$10,256}{\text{700 Units}}\\ =\text{\$16}\text{.65}\end{array}$ (2)

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

Here,

Details	Units	Cost ($)
Inventory after the Sale on July 1	380	5,567
Purchase on October 23	100	1,800
Goods Available for Sale on February 11	480	7,367

Table (5)

$\begin{array}{c}\begin{array}{l}\text{Weighted-average}\\ \text{ Cost}\end{array}\}=\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total number of units Available for Sale}}\\ =\frac{\$7,367}{\text{480 Units}}\\ =\text{\$15}\text{.35}\end{array}$ (3)