How to use the irr and npv calculator
- Enter the initial investment as a positive number. It is treated as money paid out at the start.
- Enter your discount rate per period, the return you need to justify the risk.
- List the cash flow for each period after the start, separated by commas, spaces or new lines. Use a minus sign for money paid out.
- Read the net present value, the internal rate of return, the payback period and the discounted cash flow table.
Formula
NPV = sum over t of cash flow t / (1 + r)^t, with the investment at t = 0 as a negative amount
IRR is the rate r that makes NPV equal zero
Profitability index = (NPV + investment) / investment
Payback = the period in which the running total of cash flows reaches zero, interpolated within the period
NPV tells you how much value the project adds in today's money at your required rate. IRR is the rate of return the cash flows themselves imply. If IRR is higher than your discount rate, NPV is positive.
Worked example
A project costs $10,000 and returns $3,000, $4,000, $4,500 and $3,500 over four years. At an 8% discount rate the present values of the four cash flows add up to $12,351.98, so NPV is 12,351.98 - 10,000 = $2,351.98.
The rate that makes NPV zero is 17.80%, well above 8%. The total received is $15,000, so the profitability index is 1.235. The running total reaches zero after 2 + 3,000 / 4,500 = 2.67 periods.
A $1,000 investment that returns $1,100 after one period has an IRR of exactly 10% and an NPV of $0 at a 10% discount rate.
NPV and IRR answer different questions
NPV says how many dollars of value the project creates after paying for the capital at your required rate. IRR gives a single percentage that can be compared with other options. NPV is the better guide when the two disagree, because it measures the amount of value, and IRR can favor small projects with high percentages.
A rate of return is not a guarantee. Cash flows are forecasts, and the further out they are, the less certain they are. Try the calculation with a few lower cash flow scenarios as well.
When IRR is unreliable
The method has some known problems, and the calculator tells you when they occur.
- If the cash flows change sign more than once, such as a late cleanup cost, there may be more than one IRR. The tool lists each one and shows a warning.
- If the cash flows never change sign, there is no IRR.
- Payback ignores everything after the break-even point and ignores the time value of money.
- The period can be a year, a quarter or a month. Use a discount rate for the same period.
Assumptions and limits
- Cash flows arrive at the end of each period, and the investment is paid at time zero.
- The discount rate is per period and must match the length of your periods.
- IRR is searched between minus 99% and 10,000% per period.
- Taxes, inflation and financing costs are not modeled unless you include them in your cash flows.
Frequently asked questions
How do I calculate NPV?
Divide each cash flow by one plus the discount rate raised to the power of its period, then add them up with the initial investment shown as a negative number. A positive total means the project earns more than the discount rate.
What does an IRR mean?
It is the rate of return that makes the present value of the future cash flows equal to the investment. A project is attractive if its IRR is higher than the return you could get elsewhere at similar risk.
Why do I get two IRRs?
When cash flows switch from negative to positive and back, the NPV curve can cross zero more than once. Each crossing is a valid rate, which is why the tool shows all of them with a warning and why NPV is the safer measure in that case.
Which discount rate should I use?
Use the return you need or could earn elsewhere at similar risk, such as the cost of borrowing or an expected return on other investments. Try a few rates to see how sensitive the result is.