Chapter 6, Problem 6.5E

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 May 31, and cost of goods sold using the FIFO methods.

Explanation of Solution

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

FIFO Method
Particulars	Amount ($)	Amount ($)
Beginning inventory		270
Add: Purchases on:
May 15	250
May 24	418	668
Cost of goods available for sale		938
Less: Ending inventory		(209) (1)
Cost of goods sold		$729

Table (1)

Working Notes:

Calculate the amount of ending inventory using FIFO method:

Total number of units = 93

Units sold in the month of May = 74

Unit cost = $11

$\begin{array}{c}\text{Ending inventory}=\left[\left(\text{Total units}-\text{Unit sold in the month of May}\right)\times \$11\right]\\ =\left(93-74\right)\times \$11\\ =19\times \$11\\ =\$209\end{array}$ (1)

Therefore, the cost of goods sold using FIFO method is $729, and the ending inventory on May 31 is $209.

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	30	9	270
Purchase on 15th May	25	10	250
Purchase on 24th May	19	11	209
Total	74		729

Table (2)

Therefore, it is proved that the cost of goods sold under FIFO method is $729.

To determine

To Compute: The ending inventory at May 31, and cost of goods sold using the LIFO methods.

Explanation of Solution

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

LIFO Method
Particulars	Amount ($)	Amount ($)
Beginning inventory		270
Add: Purchases on:
May 15	250
May 24	418	668
Cost of goods available for sale		938
Less: Ending inventory		(171) (2)
Cost of goods sold		$767

Table (3)

Working Notes:

Calculate the amount of ending inventory using LIFO method:

Total number of units = 93

Units sold in the month of May = 74

Ending unit cost = $9

$\begin{array}{c}\text{Ending inventory}=\left[\left(\text{Total units}-\text{Unit sold in the month of May}\right)\times \$11\right]\\ =\left(93-74\right)\times \$9\\ =19\times \$9\\ =\$171\end{array}$ (2)

Therefore, the cost of goods sold using LIFO method is $767, and the ending inventory on May 31 is $171.

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 24th May	38	11	418
Purchase on 15th May	25	10	250
Beginning inventory	11	9	99
Total	74		$767

Table (4)

Therefore, it is proved that the cost of goods sold under LIFO method is $767.

To determine

To Compute: The ending inventory at May 31, 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 = $10.086 (3)

Ending units in hand = 19

  $\begin{array}{c}\text{Cost}\text{of}\text{ending}\text{inventory}=\text{Weighted}\text{average}\text{unit}\text{cost}\times \text{Units}\text{in}\text{hand}\\ =\$10.086\times 19\\ =\$191.634\end{array}$

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

Weighted average unit cost = $10.086 (3)

Number of units sold = 74

  $\begin{array}{c}\text{Cost of goods sold =}\left(\text{ Weighted}\text{average}\text{unit}\text{cost}\times \text{Units}\text{sold}\right)\\ =\left(\$10.086\times 74\right)\\ =\$746.364\end{array}$

Working Notes:

Compute weighted average unit cost.

Total cost of goods available for sale = $938

Total units available for sale = 93

  $\begin{array}{c}\text{Weighted-average Cost}=\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total Number of Units Available For Sale}}\\ =\frac{\$938}{93}\\ =\$10.086\end{array}$ (3)

Therefore, the cost of goods sold using average-cost method is $746.364, and the ending inventory on May 31 is $191.634.

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	74	10.086 (3)	$746.364

Table (5)

Therefore, it is proved that the cost of goods sold under average-cost method is $746.364.