NPV Calculator

About the NPV Calculator

Money received later is worth less than money today, because today’s money could be earning a return in the meantime. Net present value (NPV) discounts every future cash flow of a project back to today at your discount rate — the return you could earn elsewhere on an investment of similar risk — and adds them up, investment included. A positive NPV means the project earns more than that rate; a negative NPV means it earns less.

Enter the cash flows one per year, half-year, quarter or month (period 0 is today), or on exact dates for XNPV. Use one discount rate, or a different rate for each period. The calculator shows the NPV, the present value of the money coming in and going out, the profitability index, the simple and discounted payback, a chart of the running total and the Excel formula that gives the same answer — including the common mistake with Excel’s NPV, which discounts the first value as well. Nothing you enter leaves your browser.

Common uses

• Decide whether a machine, a new outlet or a software project is worth its cost at your cost of capital.
• Compare projects of different sizes by NPV and by profitability index.
• Check a spreadsheet NPV — and catch the first-value-discounted mistake.
• Value irregular cash flows on real dates, such as staged payments for a property or milestone payments in a contract.

The NPV formula and the NPV rule

NPV = CF₀ + CF₁ ÷ (1 + r) + CF₂ ÷ (1 + r)² + … + CFₙ ÷ (1 + r)ⁿ

• CFₜ is the net cash flow of period t (CF₀, today, is usually the investment and is not discounted).
• r is the discount rate per period: the opportunity cost of capital, the return investors give up by putting money into this project rather than into an investment of similar risk.

The NPV rule in Brealey, Myers & Allen’s Principles of Corporate Finance is to accept projects with a positive NPV, because they are worth more than they cost. NPV is in money, so the NPVs of separate projects can be added up — unlike rates of return.

Excel’s NPV and XNPV: what they assume

• NPV(rate, value1, …) assumes value1 arrives one period from now (Microsoft: “the NPV investment begins one period before the date of the value1 cash flow”). An investment made today must be added outside the function: =NPV(rate, year 1 … year n) + today’s amount. Including it inside discounts it by one period, and the result is the true NPV ÷ (1 + rate).
• NPV skips empty cells, so a blank year moves every later cash flow one period earlier. Type 0 for a period with no cash flow; this calculator counts a blank between two amounts as 0 and says so.
• XNPV(rate, values, dates) discounts each amount to the first date in the list with (1 + rate)^((dᵢ − d₁) ÷ 365). The other dates may be in any order, but XNPV returns #NUM! if any of them is earlier than the first, so put the earliest date first. The rate is always a yearly rate.

Google Sheets and LibreOffice Calc use the same definitions. Function behaviour as documented on Microsoft’s NPV and XNPV help pages.

Profitability index and payback

• Profitability index (PI) = present value of the cash flows after today ÷ the initial investment. A PI above 1 is the same as a positive NPV. Brealey, Myers & Allen define it as NPV ÷ investment (above 0 = positive NPV); both versions are shown and rank projects the same way. It is useful when capital is limited, to rank projects by value per rupee invested.
• Simple payback is how long the undiscounted cash flows take to repay the investment; discounted payback uses the present values, so it is always at least as long. Within the period in which the total turns positive, the cash flow is assumed to arrive evenly.
• Payback ignores everything after the payback point, so a project with a quick payback can still have a lower NPV. Use it as a measure of risk and liquidity alongside NPV, not instead of it.

A different rate for each period

Choose A rate for each period and type a rate on each row (a blank row uses the main rate):

• Chained period rates: each rate applies to its own period and compounds on the earlier ones — DFₜ = DFₜ₋₁ ÷ (1 + rₜ). Use this when the required return changes over time, for example a higher rate in a riskier early phase.
• Spot rates: each rate is the rate for money received at that date, as read from a yield curve — DFₜ = 1 ÷ (1 + rₜ)^t. This is how Brealey, Myers & Allen value cash flows when interest rates differ by maturity.

Excel’s NPV takes a single rate; the table’s discount-factor column lets you rebuild the result with SUMPRODUCT.

Monthly, quarterly and half-yearly periods

With periods shorter than a year, a yearly rate R becomes a rate per period in one of two ways:

• Compounded yearly (effective): (1 + R)^(1/k) − 1, where k is the number of periods in a year. 10% a year is 2.4114% a quarter. Use this when R is an effective annual rate, as a cost of capital usually is.
• Nominal: R ÷ k. 12% a year is 1% a month — the convention behind loan and deposit rates.

Or type the rate per period directly. The page shows the per-period rate it used.

Limitations

• Each periodic cash flow is treated as arriving at the end of its period (period 0 = today). Cash that arrives through the year is not modelled as mid-period.
• The result is only as good as the forecasts: taxes, inflation and financing costs count only if they are in the cash flows. Keep the rate consistent with the cash flows — nominal rates with nominal (inflated) cash flows.
• XNPV counts days on a 365-day year from the first date, as Excel does; a leap day counts as 1/365 of a year.
• Up to 1,200 periods or dated cash flows at a time.

Privacy

Everything is calculated in your browser. The cash flows, rates and results are never uploaded or stored on a server.