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How do taxes and depreciation (capital allowances) affect project cash flows?

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Answer

Taxes reduce operating cash inflows (tax on profits) but depreciation/capital allowances create a tax shield: although depreciation isn't a cash flow, it reduces taxable profit, saving tax (tax shield = depreciation x tax rate). Capital budgeting uses after-tax cash flows, adding back the depreciation tax saving, to reflect the true cash impact.
Tax shield = Depreciation x Tax rate (a cash saving).
Real-world example Capital allowances on new plant reduce the tax bill, improving the project's after-tax cash flows and NPV.

Common follow-ups: Why is depreciation relevant despite being non-cash? | What are after-tax cash flows?