## Introduction

Whenever prices change, the allocation of total inventory costs between cost of sales on the income statement and inventory on the balance sheet will vary depending on a company’s choice of inventory valuation method.

## Calculation of Cost of Sales, Gross Profit, and Ending Inventory

The following illustration can assist in explaining how the calculation of the cost of sales, gross profit, and ending inventory will differ under the four inventory valuation methods.

## Example 1

In one year, a company received 3 shipments of 1,000 sewing machines at $110 each, then 2,500 sewing machines at$100 each, and finally 3,200 sewing machines at $95 each. During the year, the company sold 5,600 sewing machines at$200 each. The company is able to readily identify each shipment received. As a result, the company determines that the entire first shipment (1,000 sewing machines), 1,800 sewing machines from the second shipment, and 2,800 sewing machines from the third shipment were sold to customers during the year. The sales, cost of sales, gross profit, and ending inventory amounts under each inventory valuation method is as follows:

### Under the LIFO Method

Sales: 5,600 * $200 =$1,120,000

COGS: (2,400 * $100) + (3,200 * 95) =$544,000

Gross Profit: $1,120,000 –$544,000 = $576,000 Ending Inventory: (1,000 *$110) + (100 * $100) =$120,000

### Under the FIFO Method

Sales: 5,600 * $200 =$1,120,000

COGS: (1,000 * $110) + (2,500 *$100) + (2,100 * $95) =$559,500

Ending Inventory: (700 * $100) + (400 *$95) = $108,000 ### Under the Weighted Average Cost Method Sales: 5,600 *$200 = $1,120,000 Weighted Average Cost: [(1,000 *$110) + (2,500 * $100) + (3,200 *$95)] / 6,700 = $99.10 COGS: 5,600 *$99,10 = $554,960 Gross Profit:$1,120,000 – $554,960 =$565,040

Ending Inventory: 1,100 * $99.10 =$109,010

### Interpretation

The calculation demonstrates how each valuation method provides similar sales figures but provides different figures for the cost of sales, gross profit, and ending inventory. This arises from the fact that:

• The physical flow of the specific inventory items sold is matched to their actual costs, under the specific identification method;
• Under the weighted average cost method, the costs are allocated to cost of sales and ending inventory by using a weighted average of the actual costs incurred;
• The oldest inventory units that are acquired are assumed to be the first units that are sold under the FIFO method; and

Under the LIFO method, the newest inventory acquired are assumed to be the first sold.

## Periodic versus Perpetual Inventory Systems

Changes to inventory are usually recorded using either a periodic inventory system or a perpetual inventory system.

Under a periodic inventory system, inventory values and costs of sales are determined at the end of an accounting period, and a number of goods in ending inventory is typically obtained or verified through a physical count of the units in inventory.  The amount of cost of goods available for sale allocated to cost of sales and ending inventory may be quite different using the FIFO method compared to the weighted average cost method.

Under a perpetual inventory system, the inventory values and cost of sales are continuously updated to reflect purchases and sales.

Under either system, the allocation of goods available for sale to cost of sales and ending inventory is the same if the inventory valuation method used is either specific identification or FIFO. Both systems will also typically result in different allocations to cost of sales and ending inventory using the LIFO method.

## Example 2

### Under the Specific Identification Method

The cost of each item sold is separately added to the cost of sales. The rest of the steps would be the same as any other method. As the items in the example (LCD screens) are interchangeable, and it was not clearly disclosed which batch was sold first, we would assume that the company followed a first in first out basis. Under this assumption, the ending inventory and gross profit would be the same as they are under FIFO.

### Under the Weighted Average Cost Method

First, we need to find the average cost of each unit.

Average cost per unit on April 8th = $500 Average cost per unit on April 20th = [(200*500) + (1,200 * 650)] / 1400 = 629 Average cost per unit on April 30th = [(400*650) + (1,100*600)] / 1500 = 613 Total cost of all units sold within the period = (800*500) + (1,000 * 629) + (1,200* 613) = 1,764,600 Ending inventory =Beginning inventory + Purchases – COGS =$0 + $1,940,000 –$1,764,600= $175,400 Gross profit = Revenue – COGS = 2,100,000–$1,764,600= $336,000 ### Under the LIFO Method The cost of sales would be determined according to the price of the last purchased items. Cost of sales = (800 units *$500) + (1,000 units * $650) + [(1100 units *$600) + (100 units * $650)] =$1,775,000

Ending inventory = Beginning inventory + Purchases – COGS

= $0 +$1,940,000 – $1,775,000 =$165,000

Gross profit = Revenue – Cost of sales = $2,100,000–$1,775,000 = $325,000 ## 2. Calculations using the Periodic Method ### Under the FIFO Method The results would be the same as with the perpetual system. ### Under the Specific Identification Method The results would be the same as with the perpetual system. ### Under the Weighted Average Cost Method First, we need to find the average of the total cost of units. Average cost/Unit = Total amount of purchase cost/Total number of units purchased =$1,940,000/$3,300 =$587.88

COGS = [Average cost/Unit] * Number of units sold = $587.88 *$3,000 = $1,763,636 Ending inventory =Beginning inventory + Purchases – COGS =$0 + $1,940,000 –$1,763,636 = $176,364 Gross profit = Revenue – COGS =$2,100,000 – $1,763,636 =$336,364

As we can see, the difference between the periodic and the perpetual systems under the weighted average cost method is only $364. ### Under the LIFO Method COGS = (800 units *$600) + [(300 units * $600) + (700 units *$650)] + [(500 units *$650) + (700 units *$500)] = $1,790,000 Ending inventory =Beginning inventory + Purchases – COGS =$0 + $1,940,000 –$1,790,000 = 150,000

Gross profit = Revenue – COGS = $2,100,000 –$1,790,000 = $310,000 Comparing the LIFO method under the periodic system with the same method under the perpetual system, we notice that under the periodic system, the value of gross profit and the value of ending inventory is$15,000 higher under the periodic system.

## Question 1

Which of the following inventory valuation methods is most likely to yield different amounts of gross profit under the periodic inventory system and the perpetual inventory system?

A. FIFO

B. Specific identification method

C. LIFO

Solution

The correct answer is C.

LIFO is likely to yield a different gross profit under each inventory system, as the cost of goods sold varies under each inventory system using LIFO. Under the periodic system, the COGS varies because the cost of items purchased at the end of the period is added first to the cost of sales, while under the perpetual system, the cost of items last purchased before making a sale is added first to the cost of goods sold.

## Question 2

During the year 2006, company XYZ sells 380 folding chairs at $45 each. Given the following information on purchases made by the company during the year, what is the cost of sales and gross profit under the FIFO method. A. Cost of Sales:$15,000; Gross Profit: $3,800 B. Cost of Sales:$22,340; Gross Profit: $12,000 C. Cost of Sales:$10,640; Gross Profit: $6,460 Solution The correct answer is C. Cost of sales = (100*$23) + (150*$27) + (130*$33) = $10,640. Since sales = 380*$45 = $17,100, then gross profit =$17,100 – $10,640 =$6,460.

Reading 27 LOS 27c:

Calculate and compare cost of sales, gross profit, and ending inventory using different inventory valuation methods and using perpetual and periodic inventory systems

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