Chapter 6, Problem 6.4APR

(1)

To determine

Periodic Inventory System:

Periodic inventory system 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.

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.

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.

Weighted-average cost method:

Under Weighted average cost method, the company calculates a new average cost after every purchase is made. It is determined by dividing the cost of goods available for sale by the units on hand.

To determine: value of inventory on March 31, 2016 and cost of merchandise sold using first in first out method under periodic inventory system.

Explanation of Solution

The value of ending inventory on March 31, 2016 is calculated as follows:

$\begin{array}{c}\text{Ending Inventory}\left(\text{FIFO}\right)\text{ =}\left(2,500\text{ units}\times \$72\right)+\left(1,250\text{ units}\times \$71.60\right)\\ =\$180,000+\$89,500\\ =\$269,500\end{array}$

Calculate the cost of merchandise sold is as follows:

	Amount ($)
Beginning inventory, January 1, 2016	150,000
Add: Purchases                               Table (3)	3,024,000
Merchandise available for sale	3,174,000
Less: Ending inventory, March 31, 2016	269,500
Cost of merchandise sold	2,904,500

Table (1)

Working notes:

Calculate the units in ending inventory as follows:

	Units
Units  in beginning inventory and purchased	45,500
Less: Units sold	41,750
Units in ending inventory	3,750

Table (2)

Calculate the merchandise purchases as follows:

Purchases
Date	Quantity	Unit cost	Total
10-Jan	7,500	$68	$510,000
10-Feb	18,000	$70	$1,260,000
5-Mar	15,000	$71.60	$1,074,000
25-Mar	2,500	$72	$180,000
			$3,024,000

Table (3)

Conclusion

Hence, the ending inventory on March 31, 2016 under First in First out Method is $269,500 and cost of merchandise sold is $2,904,500.

(2)

To determine

value of inventory on March 31, 2016 and cost of merchandise sold using last in first out method under periodic inventory system.

Explanation of Solution

The value of ending inventory is calculated as follows:

$\begin{array}{c}\text{Ending Inventory}\left(\text{LIFO}\right)\text{ =}\left(2,500\text{ units}\times \$60\right)+\left(1,250\text{ units}\times \$68\right)\\ =\$150,000+\$85,000\\ =\$235,000\end{array}$

Calculate the cost of merchandise sold is as follows:

	Amount ($)
Beginning inventory, January 1, 2016	150,000
Add: Purchases                               Table (3)	3,024,000
Merchandise available for sale	3,174,000
Less: Ending inventory, March 31, 2016	235,000
Cost of merchandise sold	2,939,000

Table (4)

Conclusion

Hence, the ending inventory on March 31, 2016 under Last in First out Method is $235,000 and cost of merchandise sold is $2,939,000.

(3)

To determine

value of inventory on March 31, 2016 and cost of merchandise sold using weighted average method under periodic inventory system.

Explanation of Solution

The value of ending inventory is calculated by multiplying ending inventory with weighted average cost per unit.

$\begin{array}{c}\text{Ending Inventory}\left(\text{Weighted average}\right)\text{ =}\left[3,750\text{ units}\times \$69.76\left(1\right)\right]\\ =\$261,600\end{array}$

Calculate the cost of merchandise sold is as follows:

	Amount ($)
Beginning inventory, January 1, 2016	150,000
Add: Purchases                               Table (3)	3,024,000
Merchandise available for sale	3,174,000
Less: Ending inventory, March 31, 2016	261,600
Cost of merchandise sold	2,912,400

Table (5)

Working note:

The weighted average unit cost is calculated as follows:

$\begin{array}{c}\text{Weighted average unit cost = }\frac{\text{Total cost of inventory available for sale}}{Total\text{ units available for sale}}\\ =\frac{\$3,174,000}{45,500}\\ =\$69.76\end{array}$ (1)

Conclusion

Hence, the ending inventory on March 31, 2016 under weighted average cost Method is $261,600 and cost of merchandise sold is $2,912,400.

(4)

To determine

To compare: The gross profit and inventories on March 31, 2016 of all the three methods.

Explanation of Solution

The table showing all the three methods of inventory is as follows:

	FIFO ($)	LIFO ($)	Weighted average ($)
Sales	$ 5,191,250	$ 5,191,250	$ 5,191,250
Less: Cost of merchandise sold	$ 2,904,500	$ 2,939,000	$ 2,912,400
Gross Profit	$ 2,286,750	$ 2,252,250	$ 2,278,850
Ending Inventory, March 31, 2016	$ 269,500	$ 235,000	$ 261,600

Table (6)

Working notes:

Calculate the total sales for the three-month period:

Sales
Date	Quantity	Unit cost	Total
28-Jan	3,750	$120	$450,000
30-Jan	1,250	$120	$150,000
5-Feb	500	$120	$60,000
16-Feb	9,000	$125	$1,125,000
28-Feb	8,500	$125	$1,062,500
14-Mar	10,000	$125	$1,250,000
30-Mar	8,750	$125	$1,093,750
Total			$5,191,250

Table (7)