Chapter 6, Problem 6.4E

To determine

Periodic Inventory System: It is a system in which the inventory is updated in the accounting records on a periodic basis such as at the end of each month, quarter or year. In other words, it is an accounting method which is used to determine the amount of inventory at the end of each accounting period.

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

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

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:

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

To Compute: The ending inventory at September 30, and cost of goods sold using the FIFO methods.

Explanation of Solution

Calculate the ending inventory and cost of goods sold using FIFO method.

Particulars	Amount ($)	Amount ($)
Beginning inventory		1,200
Add: Purchases on:
12th September	4,635
19th September	5,200
26th September	2,100	11,935
Cost of goods available for sale		13,135
Less: Ending inventory [Table (2)]		(2,620)
Cost of goods sold		$10,515

Table (1)

Working Notes:

Calculate the amount of ending inventory using FIFO method:

FIFO method	Units	Cost ($)	Total cost ($)
September 19	5	104	$520\left(5\times 104\right)$
September 26	20	105	$2,100\left(20\times 105\right)$
Value of ending inventory			$2,620

Table (2)

Therefore, the cost of goods sold using FIFO method is $10,515, and the ending inventory on September 30 is $2,620.

To determine

To Prove: The amount allocated to cost of goods sold under FIFO method.

Explanation of Solution

Proof of amount allocated to cost of goods sold under FIFO method.

Particulars	Units (a)	Unit cost ($) (b)	Total cost ($) $\left[(c)=(a)\times (b)\right]$
Beginning inventory	12	100	1200
Purchase on 12th September	45	103	4,635
Purchase on 19th September	45	104	4,680
Cost of goods sold	102		$10,515

Table (3)

Therefore, it is proved that the cost of goods sold under FIFO method is $10,515.

To determine

To Compute: The ending inventory at September 30, and cost of goods sold using the LIFO methods.

Explanation of Solution

Calculate the ending inventory and cost of goods sold using LIFO method

Particulars	Amount ($)	Amount ($)
Beginning inventory		1,200
Add: Purchases on:
12th September	4,635
19th September	5,200
26th September	2,100	11,935
Cost of goods available for sale		13,135
Less: Ending inventory [Table (5)]		(2,539)
Cost of goods sold		$10,596

Table (4)

Working Notes:

Calculate the amount of ending inventory using LIFO method:

LIFO method	Units	Cost ($)	Total cost ($)
September 12	13	103	$1,339\left(13\times 103\right)$
Beginning inventory on September 1	12	100	$1,200\left(12\times 100\right)$
Value of ending inventory			$2,539

Table (5)

Therefore, the cost of goods sold using LIFO method is $10,596, and the ending inventory on September 30 is $2,539.

To determine

To Prove: The amount allocated to cost of goods sold under LIFO method.

Explanation of Solution

Proof of amount allocated to cost of goods sold under LIFO method.

Particulars	Units (a)	Unit cost ($) (b)	Total cost ($)$\left[(c)=(a)\times (b)\right]$
Purchase on 26th September	20	105	2,100
Purchase on 19th September	50	104	5,200
Purchase on 12th September	32	103	3296
Beginning inventory
Cost of goods sold	121		$10,596

Table (6)

Therefore, it is proved that the cost of goods sold under LIFO method is $10,596.

To determine

To Compute: The ending inventory at September 30, and cost of goods sold using the average-cost methods.

Explanation of Solution

Calculate the ending inventory using average-cost method.

Weighted average unit cost = $103.425 (1)

Ending units in hand = 25

  $\begin{array}{c}\text{Cost}\text{of}\text{ending}\text{inventory}=\text{Weighted}\text{average}\text{unit}\text{cost}\times \text{Units}\text{in}\text{hand}\\ =\$103.425\times 25\\ =\$2,585.625\end{array}$

Calculate the cost of goods sold using average-cost method.

Weighted average unit cost = $103.425 (1)

Number of units = 102

  $\begin{array}{c}\text{Cost of goods sold =}\left(\text{ Weighted}\text{average}\text{unit}\text{cost}\times \text{Units}\text{sold}\right)\\ =\left(\$103.425\times 102\right)\\ =\$10,549.35\end{array}$

Working Notes:

Compute weighted average unit cost.

Total cost of goods available for sale = $13,135

Total units available for sale = 127

  $\begin{array}{c}\text{Weighted-average Cost}=\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total Number of Units Available For Sale}}\\ =\frac{\$13,135}{127}\\ =\$103.425\end{array}$ (1)

Therefore, the cost of goods sold using average-cost method is $10,549.35, and the ending inventory on September 30 is $2,585.625.

To determine

To Prove: The amount allocated to cost of goods sold under average-cost method.

Explanation of Solution

Proof of amount allocated to cost of goods sold under average-cost method.

Particulars	Units (a)	Unit cost ($) (b)	Total cost ($)$\left[(c)=(a)\times (b)\right]$
Cost of goods sold	121	103.425 (1)	$10,549.35

Table (6)

Conclusion

Therefore, it is proved that the cost of goods sold under average-cost method is $10,549.35.