Chapter 6, Problem 6.5AP

(a)

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:

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

Gross profit rate is the financial ratio that shows the relationship between the gross profit and net sales. Gross profit is the difference between the total revenues and cost of goods sold. It is calculated by using the following formula:

$\text{Gross profit rate}=\frac{\text{Gross profit}}{\text{Net sales}}\times 100$

To Calculate: The ending inventory, cost of goods sold, gross profit, and gross profit rate under LIFO, FIFO, and Average-cost method.

Explanation of Solution

Step 1: Calculate the Total Cost and units of Goods Available for Sales.

Date	Particulars	Units ($)	Unit cost ($)	Total cost ($)
		(a)	(b)	(c = a × b)
October 1	Beginning inventory	60	24	1,440
October 9	Purchase	120	26	3,120
October 17	Purchase	100	27	2,700
October 25	Purchase	70	29	2,303
	Total	350		9,290

Table (1)

Step 2: Calculate total sales.

Date	Units	Unit cost ($)	Total cost ($)
	(a)	(b)	(c = a × b)
October 11	100	35	3,500
October 22	60	40	2,400
October 29	110	40	4,400
Total sales	270		10,300

Table (2)

Step 3: Calculate ending inventory.

$\begin{array}{c}\text{Ending inventory = }\left(\begin{array}{l}\text{Total units of purchases}-\\ \text{Total units of sales}\end{array}\right)\\ =\left(350-270\right)\\ =80\end{array}$

(1)

To determine

To Calculate: The ending inventory, cost of goods sold, gross profit, and gross profit rate under LIFO method.

Explanation of Solution

(i)

Calculate the Cost of Ending Inventory.

LIFO Method
Date	Units	Unit cost ($)	Total cost ($)
	(a)	(b)	(c = a × b)
October 9	20	26	520
October 1	60	24	1,440
Total	80		1,960

Table (3)

 (ii)

Calculate cost of goods sold.

Cost of Goods Sold
Details	Amount ($)
Total goods available for sale	9,290
Less: Ending inventory	(1,960)
Cost of goods sold	7,330

Table (4)

 (iii)

Calculate gross profit.

Gross Profit - LIFO
Details	Amount ($)
Sales	10,300
Less: Cost of goods sold	(7,330)
Gross profit	2,970

Table (5)

(iv)

Calculate gross profit percentage.

$\begin{array}{c}\text{Gross profit percentage}=\frac{\text{Gross profit}}{\text{Net sales}}\times 100\\ =\frac{\$2,970}{\$10,300}\times 100\\ =29\%\end{array}$

(2)

To determine

To Calculate: The ending inventory, cost of goods sold, gross profit, and gross profit rate under FIFO method.

Explanation of Solution

(i)

Calculate the Cost of Ending Inventory.

FIFO Method
Date	Units	Unit cost ($)	Total cost ($)
	(a)	(b)	(c = a × b)
October 17	10	27	270
October 25	70	29	2,030
Total	80		2,300

Table (6)

(ii)

Calculate cost of goods sold.

Cost of Goods Sold
Details	Amount ($)
Total goods available for sale	9,290
Less: Ending inventory	(2,300)
Cost of goods sold	$6,990

Table (7)

 (iii)

Calculate gross profit.

Gross Profit - FIFO
Details	Amount ($)
Sales	10,300
Less: Cost of goods sold	(6,990)
Gross profit	$3,310

Table (8)

(iv)

Calculate gross profit percentage:

$\begin{array}{c}\text{Gross profit percentage = }\frac{\text{Gross profit}}{\text{Net sales}}\times 100\\ =\frac{\$6,990}{\$10,300}\times 100\\ =\$68\%\end{array}$

(2)

To determine

To Calculate: The ending inventory, cost of goods sold, gross profit, and gross profit rate under Average-cost method.

Explanation of Solution

(i)

Calculate the Cost of Ending Inventory.

Step 1: Calculate the Weighted-average cost.

$\begin{array}{c}\text{Weighted-average Cost}=\frac{\text{Total Cost of Goods Available For Sale}}{\text{Total number of units Available for Sale}}\\ =\frac{\$9,290}{\text{350 Units}}\\ =\$26.54\end{array}$

Step 2: Calculate the amount of Ending Inventory.

$\begin{array}{c}\text{Cost of Ending inventory}=\left(\begin{array}{l}\text{Number of units in Ending inventory }\\ \times \text{Weighted-average cost per unit}\end{array}\right)\\ =80\text{units}\times \$26.54\\ \text{=}\text{\$2,123}\text{.2}\end{array}$

(ii)

Calculate the Cost of Goods Sold.

$\begin{array}{c}\text{Cost of goods sold}=\text{Goods available for sale}-\text{Ending inventory}\\ =\$9,290.00-\$2,123.20\\ =\$7,166.8\end{array}$

(iii)

Calculate the gross profit.

Gross Profit - FIFO
Details	Amount ($)
Sales	10,300.00
Less: Cost of goods sold	(7,166.80)
Gross profit	$3,133.20

Table (9)

(iv)

Calculate gross profit percentage:

$\begin{array}{c}\text{Gross profit percentage}=\frac{\text{Gross profit}}{\text{Net sales}}\times 100\\ =\frac{\$3,133.20}{\$10,300.00}\times 100\\ =\$30\%\end{array}$

(b)

To determine

To Compare: The results for the above three cost flow assumptions.

Answer to Problem 6.5AP

Compare results of the three methods.

Method/Results	Cost of Goods Sold	Gross Profit	Gross Profit Percentage
LIFO	$7,330 (Highest)	$2,970	29%
FIFO	$6,990	$3,310 (Highest)	68% (Highest)
Average-cost	$7,166.80	$3,133.20	30%

Table (10)

Explanation of Solution

As it is a case if rising prices, the cost of goods sold is the highest in LIFO and Gross profit is the highest in FIFO method