Viceroy

I would think a simpler explanation is that you depreciate an asset before taxes. So when it comes to adjusting things to determine you CF, you add the amount that was originally depreciated (which was before taxes).

When it comes to finding out the true cash flow of the firm, you adhere to the law of equilibrium: if you take out $50 before taxes, you add $50 for the adjustment, so that things are "equal."

As Pope pointed out above, depreciation, being a non-cash expense, is added back to represent the proper cash on hand for the firm.