How and why the change in inventory is adjusted to the net income in the indirect method for cash flow from operations

Let us start with the net income of a company.

Net income = Total Revenue - Cost of Goods sold (COGS)- Other Costs of revenue - Other expenses 

Net income = Total Revenue - COGS- All other Expenses ( Equation 1)

Now we all know that 

COGS = Beginning Inventory + Purchases- Ending Inventory

From here onward we will always assume that there has been a decrease of inventory at the end of the year. 

Re Arranging the above equation

COGS = Purchases + Decrease in Inventory

COGS = Cash Purchases + Credit Purchases + Decrease in Inventory  (Equation 2)

If you look at Equation 1, we have arrived at net income from the following three figures. 

1. Total Revenue 

2. COGS

3. All other Expenses

All these three figures have non cash computations in them, due to the nature of accrual accounting. But in this topic, we have to be concerned only about COGS.

 Coming back to Equation 2, we can see that there are two components of COGS which are non cash.

1. Credit Purchases

2. Decrease in Inventory

These two needs to be re adjusted to the net income inorder to eliminate the non cash components of COGS. As we can see in Equation 1, COGS is subtracted from the Total Revenue to arrive at the net income figure. And from Equation two, we can see that, Credit purchases and Decrease inventory both needs to be added back to the net income, in order to eliminate the non cash components of COGS, which inturn is subtracted from Total Revenue to arrive at Net Income figure.

     Note that Cash purchases need not be adjusted at all to the net income figure.

If you are familiar with indirect method, all the increase in Accounts Payables, are already added back to net income to arrive at operating cash flow, inorder to eliminate the non cash expenses which are represented by the accounts payables. Along with this, the Purchase Payables are also automatically added back to net income, which represents the adjustment of credit purchases. This is done as a separate step in the indirect method. 

 Thus we don't need to adjust credit purchases again, separately, from the net income figure. 

This leaves us with the decrease in inventory figure. In order to eliminate this non cash expense component of the COGS ( as COGS is an expense which is subtracted from the Total Revenue),

we add it back to the net income figure to arrive at Operating Cash flow.

On the other hand if there is an increase in inventory, we intuitively subtract it from the net income figure. 

COGS, Calculation, Explanation, Formula all in a simple illustration.

The gross profit is simply Sales minus the Cost of the goods sold. It’s quite logical, if you think about it. So you need the Cost of Goods Sold figure (COGS), for a period, to find out the gross profit for that period. How to calculate the COGS if you don't have a computer to do it for you, is what we need to find out.

The first thing to come in mind is to take all the sales receipts and invoices for the period for which you need to find the COGS. Then, find out which all items were sold out. Find the cost of the individual items, from the purchase register. Then calculate the cost of all the items sold. This will be your COGS for that period. By now you can see that it's not that simple at all. But, fortunately, there is another way.

Imagine that you are an accountant recruit at a retail firm. On the first day of your employment, you are asked to calculate the stock (inventory) at the warehouse of the retail firm.  After a day of grueling work, you arrive at an inventory figure, which represents the inventory at the end of the day at the warehouse. Let’s say that it is I₁ (Inventory on day 1 at your job). You note it down and soon forget it. 

A few months go by. You are busy at your job. Suddenly your boss asks how much is the COGS for the sales done, from your beginning of your joining date. You scroll through the various registers and find out that there has been lots of purchase of goods, since your date of joining. An the firm has also had a good period, with a lot of sales.  You think of calculating the cost of each items sold, and after sometime, conclude, that it’s quite cumbersome. So you think that you need to find another way.

Then you remember the inventory value I₁ (Inventory on day 1 at your job), which you had jotted down on the first day at the firm. 

You know that the inventory values must have been quite changed from the beginning inventory figure I₁, due to purchases and sales of goods, that have happened after you started working in the firm.  So you wonder what changes must have happened to I₁ , to arrive at the present inventory. You spend almost a day to calculate the present inventory figure, which is  I₂ (inventory on the day you are asked to calculate COGS).

You know that purchases increase the  inventory, and sales (measured in COGS) decreases the inventory.  If there were no sales, then I₁ + Purchases would have been, the total goods available for sale from day 1 to the present day.  But the sales did happen, and the total goods available for sale must have got reduced by the sale of goods (measured in COGS).  So, the present inventory I_2, would be

                    I₁ + Purchases-COGS.

This whole story of inventory change can be represented in the equation

                    I₂= I₁ + Purchases-COGS

OR              COGS= I₁- I₂+ Purchases

Now you got an easy method to calculate COGS, and you don’t waste any time. So you immediately begin calculating the  the COGS for the period starting from the day of your joining to the day at which you were asked to find COGS.

When the boss asks you the next time, to calculate the COGS for the current financial year, you know that the formula for COGS, you arrived earlier can be used that time too. You can modify your formula and finally arrive at the general formula, which  used world over, for calculating COGS.

                   COGS= I_(Beginning)- I_(Ending)+ Purchases