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why does depreciation and amortization affect a firm's cash balance on the balance sheet if it is a non-cash expense?

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Answer:

When you are preparing a statement of cash flows, you start with operating income. Operating income is basically net income + adjustments. The adjustments that always increase the cash flows are depreciation expense and amortization expense. Even though they are not actual cash expenses, they reduce taxable income and therefore, total taxes paid.