CFA CFA Level 1 Financial Statement Analysis Q

# Financial Statement Analysis Q

Topic Resolution: Resolved
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For a firm using FIFO, gross profit is the same whether the firm uses a periodic or perpetual inventory system. For a firm using LIFO or average cost, gross profit can be different depending on the choice of inventory system.

Can someone explain why this is the case? Thank you!

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Consider the following string of orders:

 Month Number of Units bought Cost per unit Number of units sold Selling price per unit Jan 100 2 Feb 50 1 Mar 200 3 Apr 20 4

What is perpetual inventory system? Its nothing but accounting for cost of goods sold as you go along the period.
What is periodic inventory system? It is nothing but accounting for cost of goods sold at the very end.

First lets calculate average cost,
At the end of Feb, the average cost per unit = 2*100/100 = 2
At the end of Apr the average cost per unit = (2*100+3*200)/(100+200) = 2.67

In a periodic inventory system (at the very end of April),
FIFO COGS = 50*2 + 20*2 = 140

LIFO COGS = 50*3 + 20*3 = 210

Average cost COGS = (50 + 20)*2.67 =  186.9 (Use Average cost per unit for the end of April)

In a perpetual inventory system (As we go along selling the inventory),
FIFO COGS = 50*2 + 20*2 = 140

LIFO COGS = 50*2 + 20*3 = 160

Average Cost COGS = 50*(Average cost per unit at the end of Feb) + 20*(Average cost per unit at the end of April)
= 50*2 + 20*2.67
= 153.4

Notice, the FIFO COGS didn’t change but the COGS for LIFO and Average cost method changed. This is the reason for change in gross profit.