NPV and IRR Calculator

A rupee or a dollar received in five years is worth less than one received today, because today’s money can be invested, and because the future is uncertain. Net present value puts every cash flow of a project on the same footing by discounting it back to today, then adds them up. If the total is positive, the project returns more than the discount rate you chose. This page also finds the internal rate of return, the payback time and the profitability index.

How the numbers are built

Enter a discount rate for one period, usually a year, and the cash flows one per line, starting with today. Money out is negative. Each flow is multiplied by a discount factor of 1 ÷ (1 + rate)^period, and the page lists the factor, the present value and a running total. The sum is the NPV. The IRR is the rate at which that sum would be zero.

Why period 0 is not discounted

A spreadsheet NPV function treats its first value as arriving one period from now. Most project appraisals instead put the initial investment at the start, which is period 0, and discount only what follows. The page follows the second convention and says so in a note. If you compare with a spreadsheet, add the first flow separately, or the answers will differ by a whole period of discounting.

A worked example

The default is an equipment purchase: 100,000 out today, then 30,000, 35,000, 40,000, 45,000 and 25,000 in the next five years, at a 10% discount rate. The present values run from 27,272.73 in year 1 to 15,523.03 in year 5, and the running total ends at 32,509.58. That is the NPV. The IRR is 21.86%, well above 10%. Payback is 2.88 periods, because the undiscounted total turns positive in the third year, and discounted payback is 3.45 periods. The profitability index is 1.33, from 175,000 coming in against 100,000 going out. A second sample puts 50,000 into a project paying 8,000 for four years at 8%: the NPV is minus 23,502.99, the IRR is minus 15.74% and the payback is never reached.

When there are several IRRs

If the cash flows change sign more than once, for example a clean-up cost at the end of a mine’s life, the NPV can cross zero at more than one rate. The sample “Cash cost at the end” uses minus 1,000, plus 2,300 and minus 1,320, which has IRRs of 10% and 20%. The page shows the one nearest zero and lists both in a warning. In that case rely on the NPV at your own discount rate, which is unambiguous: at 15% it is a small positive 1.89.

Edge cases

At least two flows are needed, and at most 200. Brackets count as negative, so (100) is minus 100. A project with only inflows or only outflows has no IRR, and the page says “not defined”. A discount rate of zero gives the plain sum of the flows. Rates below minus 99% are rejected.

Limits

NPV and IRR assume that the cash flows are certain and arrive at the end of each period, and that money received can be reinvested at the discount rate. Real projects have risk, delays and taxes, none of which are modelled. Payback ignores everything after it, so it can favour a quick small win over a better long project. Use the page to compare options on equal terms, not to predict.

Related tools

• XIRR Calculator handles cash flows that arrive on irregular dates.
• ROI Calculator gives a plain percentage return without discounting.
• Compound Interest Calculator grows a sum forward, the reverse of discounting.
• Break-Even Point Calculator tests how much volume a project needs to pay for itself.