After-Tax Cash Flow and the Depreciation Tax Shield

Derive it from inflows minus outflows, writing project taxes as $\tau$ times operating profit minus $\tau$ times depreciation, with operating expenses taken without depreciation and capital expenditures neither taxed nor deducted.

State that the shield is a positive cash flow kept in the firm, equal to the tax rate times the depreciation deduction, and that equipment cost is deducted only through the depreciation schedule.

For the $1,000,000 machine with $300K revenue, $100K expenses, 10-year straight-line depreciation and 40% tax, compute $100K earnings and $160K after-tax cash flow, and tabulate both streams date by date.

State that shareholders want the NPV of the business maximized, and record how bankruptcy and financial-distress costs enter that same NPV calculation rather than a separate solvency test.