Net Present Value

NPV is only as good as the cash flow stream fed into it. The inputs are incremental, after-tax operating cash flows: revenue less cash costs less taxes, with depreciation added back because it is a non-cash charge that matters only through its tax shield. Changes in net working capital are outflows when working capital builds and inflows when it is released, typically at project end. Terminal-year items include after-tax salvage proceeds. Sunk costs are excluded, opportunity costs of assets already owned are included at market value, and financing costs are excluded because they are captured in the discount rate.

Each year's cash flow is divided by one plus the required return raised to the power of the number of periods, the discounted amounts are summed, and the initial outlay is subtracted. The result is expressed in today's currency units and represents value created for existing owners.

NPV measures value in currency terms rather than as a rate, which makes it consistent with the objective of maximising shareholder wealth. Two properties matter. First, value additivity: the NPV of a set of independent projects equals the sum of their individual NPVs, so a firm can evaluate a capital budget project by project without distortion. Percentage measures such as IRR do not add up this way.

Second, NPV embeds the correct opportunity cost. Cash flows are discounted at the return available on alternatives of equal risk, so a positive NPV means the project beats what capital markets offer for that risk class. IRR, by contrast, solves for the rate that sets NPV to zero and can produce multiple solutions when cash flow signs alternate, no solution in some cases, and misleading rankings when projects differ in scale or in the timing of cash flows.

In corporate practice NPV underpins capital expenditure approval, bid pricing for concessions and licences, lease-versus-buy analysis, and the evaluation of acquisitions, where the purchase price plays the role of the initial outlay and projected free cash flows plus a terminal value form the inflows. Discounted cash flow equity valuation is the same arithmetic applied to an entire firm.

The concept also appears in reporting. Impairment testing compares carrying amounts with recoverable amounts built from discounted cash flows, so a collapse in expected prices or a rise in required returns can force write-downs on assets that were approved when NPV was positive. In efficient markets, announcement of a clearly positive-NPV investment should be reflected in the share price, which is why management commentary on project economics and hurdle rates attracts analyst attention.

Expect to compute NPV on a financial calculator using the cash flow register, entering the outlay as a negative period-zero figure and the remaining flows in order, then solving with the required return. Be able to state the accept-reject rule for an independent project and the highest-NPV rule for mutually exclusive projects, and to explain why the two can diverge from IRR rankings because of scale and cash flow timing, with the crossover rate marking where the NPV profiles intersect.

Also practise reading an NPV profile, identifying the vertical intercept as the undiscounted sum of cash flows and the horizontal intercept as the IRR. Recognise adjustments for unequal project lives, for capital rationing, and for real versus nominal treatment: real cash flows must be paired with a real discount rate, nominal with nominal.