NPV Calculator: Net Present Value, IRR and Payback

How to calculate NPV

Net present value discounts every cash flow back to time 0 and adds the results. Because the first value in this calculator is the time-0 cash flow, it is not discounted:

NPV = CF₀ + CF₁/(1+r) + CF₂/(1+r)² + … + CF_n/(1+r)ⁿ

Here, CF is the cash flow, r is the discount rate per period and n is the period number. A positive NPV means the discounted inflows exceed the discounted outflows at the selected rate; it is not a guarantee that an investment will perform as forecast.

IRR and payback

The internal rate of return is the rate that makes NPV equal to zero. This tool reports IRR only when the sequence contains exactly one change between positive and negative signs. Multiple sign changes can produce multiple IRRs, so a single result could be misleading.

Simple payback uses undiscounted cash flows. Discounted payback uses present values at the selected discount rate. Both show the first period in which cumulative value recovers the initial outflow, including a linear fraction of the crossing period.

Worked example

For cash flows of -10,000, 3,000, 3,500, 4,000, 2,500 and a discount rate of 8% per year, the calculator discounts periods 1 through 4 while leaving the initial investment at time 0. The result is an NPV of approximately $791.37, an IRR of approximately 11.54% per year, simple payback of 2.88 periods and discounted payback of approximately 3.57 periods.

Assumptions and limits

• Cash flows must be equally spaced and entered in chronological order.
• The discount rate stays constant for all periods.
• The currency selector changes formatting only; it does not convert exchange rates.
• The annualized IRR compounds the per-period IRR using 1, 4 or 12 periods per year.
• Forecasts, taxes, inflation, financing terms and reinvestment assumptions are not inferred.

Related calculators

Use the time value of money calculator for a single present value, future value or constant payment. Use the ROI calculator for a simple gain-versus-cost comparison without a cash-flow schedule.

Formula references

Microsoft’s documentation explains that NPV uses a discount rate per period and equally spaced future cash flows, while a time-0 cash flow is added separately. Its IRR documentation defines IRR as the rate that makes NPV zero and requires at least one positive and one negative cash flow: NPV function and IRR function.