Depreciation goes up by $10. Walk me through the three statements.

I'll assume a 25% tax rate. Starting with the income statement, depreciation is an expense, so pre-tax income goes down by $10. Taxes fall by $2.50, so net income is down by $7.50. On the cash flow statement, I start with the lower net income. Depreciation is a non-cash expense, so I add back the full $10 in cash flow from operations. Net income was down $7.50 and I added back $10, so cash flow from operations is up by $2.50. Nothing else changes, so cash is up by $2.50. On the balance sheet, PP&E is down by $10. Cash is up by $2.50, so total assets are down by $7.50. On the other side, retained earnings are down by $7.50 because of the lower net income, so both sides match and it balances.

I'll assume a 25% tax rate. Starting with the income statement, depreciation is an expense, so pre-tax income goes down by $10. Taxes fall by $2.50, so net income is down by $7.50. On the cash flow statement, I start with the lower net income. Depreciation is a non-cash expense, so I add back the full $10 in cash flow from operations. Net income was down $7.50 and I added back $10, so cash flow from operations is up by $2.50. Nothing else changes, so cash is up by $2.50. That increase is the tax saving. Depreciation didn't cost any cash, but it lowered the tax bill. On the balance sheet, PP&E is down by $10. Cash is up by $2.50, so total assets are down by $7.50. On the other side, retained earnings are down by $7.50 because of the lower net income, so both sides match and it balances. The intuition is that depreciation is a non-cash charge that reduces taxable income. Earnings go down, but cash goes up by the tax saved, which is $10 times the 25% rate. One caveat is that this assumes the extra depreciation is also deductible for tax. If book and tax depreciation differ, the difference would run through deferred taxes.