Formula and conventions
Net present value discounts each cash flow back to time 0 and adds them up: NPV = Σ CFt ÷ (1 + r)^t. The internal rate of return is the r that makes that sum zero. Payback is the time until cumulative cash flow turns positive, interpolated within the period; discounted payback does the same with discounted flows. The profitability index is the present value of future flows divided by the initial outlay, shown when the first flow is an outflow. These are the standard corporate finance definitions.
When to use it
Use it to recompute a client's capital project analysis, to test whether a discounted cash flow model behind an impairment or valuation estimate is arithmetically sound, and to compare financing choices. Under ASC 360 the recoverability step of an impairment test uses undiscounted cash flows, while measuring fair value uses discounted ones, so the same flow list can be run at a rate of zero and at the valuation rate. For loan payments and schedules see the loan amortization calculator.
Limits
Periods are assumed equally spaced. Flows on irregular dates need an XIRR-style date-weighted calculation, which this tool does not do. The reinvestment assumption behind IRR (that interim flows earn the IRR itself) is often unrealistic, one reason NPV is preferred for ranking projects. Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
What is the NPV formula?
NPV = Σ CFt ÷ (1 + r)^t, summed over t = 0 to n, where CFt is the cash flow in period t and r is the discount rate per period. A positive NPV means the flows earn more than the discount rate. This calculator treats the first value as occurring at time 0 and does not discount it.
Why does Excel NPV() give a different answer?
The spreadsheet NPV function assumes the first value in its range arrives one period from now. If you pass it the whole list including the time 0 outflow, it discounts that outflow by one period and the result is understated by a factor of (1 + r). The usual fix is =NPV(rate, flows after time 0) + the time 0 flow. This tool shows the spreadsheet figure next to the correct one.
What is IRR and how is it found?
IRR is the discount rate at which NPV equals zero. There is no closed form, so the tool scans rates from −99% to 1,000% for sign changes in NPV and bisects each one to high precision.
Can a project have more than one IRR?
Yes. When the cash flows change sign more than once, for example an outflow, inflows and then a clean-up outflow, NPV can cross zero at several rates, and the IRR is not a reliable decision measure. The tool lists every root it finds and warns when the signs change more than once. If all flows have the same sign there is no IRR at all.
What discount rate should I use?
The rate must match the risk of the cash flows and the length of the period. A cost of capital for a capital budgeting decision, a market-based rate for a fair value measurement, or the rate a contract specifies are different choices with different supporting evidence. When the discount rate is part of an accounting estimate, evaluating it is part of auditing that estimate under AU-C 540.
Runs in your browser. The figures you type are not sent to CORAA or stored. Check the result against your firm's methodology before relying on it.