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.