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I am doing personal investing stocks and know FCF is important figure to look at. From my understanding depreciation is added back when calculating FCF because has no bearing on cash inflow/outflow. However, I cannot understand why it is if we add it to capital expenditure: change in PPE + depreciation = capex.

Therefore, the depreciation income statement should be offset with depreciation in capex so no need to ad depreciation on top? Is this correct?

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It's not really "added back" to get cash flow - it's removed from net income to get the income that is cash-based. Since it was subtracted from revenue to get net income, it's added back to cancel it out. It's common for cash flow to be calculated by starting with net income (which includes depreciation) and "adding back" all non-cash expenses and subtracting non-cash revenue to cancel them out.

For capex, it's also added back to cancel it out from "change in PPE". Depreciation reduces PPE so it must be added back to determine how much PPE changed because of capital expenditures (e.g. buying more equipment)

For example, if your starting PPE was $500, you had depreciation of $20 and bought another $100, your new PPE would be 500 - 20 + 100 = 580 and your "change in PPE" would be 80. In order to calculate how much of that change was cash-based (capex), you'd "add back" the non-cash portion of 20.

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