Why do we add back the entire non-cash expense (Depreciation or Amortization, for example) on the cash flow statement, instead of adding back only the after-tax expense?
First thing first, the cash flow statement shows the changes in cash with the net income as the starting line item, so if an expense item is noncash and it has been deducted from net income it must be added back. Non-cash expenses are tax-deductible so an increase in an item such as depreciation will reduce the amount of taxes we pay, which helps to increase our cash balance.
Now the reason as to why we add back the entire non cash expense rather than simply adding back the after-tax expense is because we want to reflect that the savings on taxes as created by the non-cash expense.
For example, lets assume we have a non-cash expense item of $100 and a tax rate of 40%. The net income would decrease by $60 as a result as compared to having no such non-cash expense. But then we would add back the entire non-cash expense of $100 on the cash flow statement so that the cash would goes up by $40.
That increase of $40 reflects the tax savings from the non-cash expense. If we were to only add back the after-tax expense of $60, it would have been equivalent to saying, “The non-cash expense had generated no tax benefits for us and therefore had no impact on our taxes or cash balance”