NPV, IRR and what they tell you
Net present value answers one question: after paying for the money you tie up, does this project create value? Each future cash flow is discounted back to today at your required rate — a dollar in year 3 at 10% is worth 1 ÷ 1.1³ = $0.751 now — and the discounted inflows are summed against the initial outlay. Invest $1,000 and receive $300, $400, $500 and $600 over four years at a 10% discount rate and the NPV is 272.73 + 330.58 + 375.66 + 409.81 − 1,000 = $388.77. Positive NPV means the project earns more than your hurdle rate; negative means it destroys value even if it "makes money" in nominal terms.
Internal rate of return is the discount rate at which NPV is exactly zero — the project's own annualised return. For the example it is about 24.9%. There is no closed-form formula; the calculator solves it numerically by bisection, which is robust for conventional projects (an outflow followed by inflows). Compare IRR with your cost of capital: an IRR above the hurdle rate agrees with a positive NPV. Where they disagree, for mutually exclusive projects of different sizes, trust NPV — it measures dollars created, not a rate.
Profitability index is present value of inflows ÷ investment; anything above 1.0 is value-creating and the ratio helps rank projects when capital is limited. Payback period is how many years until cumulative cash flow turns positive — simple to explain, but it ignores the time value of money and everything after the payback point, so it is a liquidity check, not a decision rule. Discounted payback fixes the first flaw by using present values instead.
Choosing a discount rate. Use your weighted average cost of capital for typical corporate projects, a higher rate for riskier ventures, or the return on your next-best alternative. Small changes matter: the example's NPV falls from $389 at 10% to $235 at 15%. If cash flows change sign more than once (an outflow in the middle, for instance) the IRR can have multiple solutions — the calculator reports the one nearest a sensible range and NPV remains the reliable guide.