NPV, IRR and payback calculator

Name: NPV and IRR calculator
Author: Richard Injante

Appraise a project with different cash flows each year: NPV, IRR, modified IRR, profitability index, payback and the NPV profile.

Content reviewed by Richard Injante Published by SolucionesAhora.com Updated on 2026-10-08 How we verify

Calculator inputs

Enter your figures, or press “See example” to watch it work.
If your case is unusual, open “Advanced options”.
Read the result and, below it, what it means and how it was worked out.

Initial investment

The period-0 outlay, written as a positive number. If there are later investments (a refurbishment, an expansion), put the negative flow in the matching period of the list.

What you pay today (as a positive number)

Cash flow of each period

What comes in (or goes out, as a negative) at the end of each period, starting with period 1. You can enter different flows each year, including loss-making years. All periods have the same length (years, quarters…), just like the discount rate.

One value per period, separated by spaces or commas

Discount rate %

The minimum return you demand from the project, that is, what you would earn from the best alternative of similar risk (the opportunity cost or cost of capital). A positive NPV means the project beats it.

Your required minimum return

Advanced options

Reinvestment rate (optional) (optional) %

The return at which you assume you reinvest the positive flows. The modified IRR uses it and avoids the unrealistic assumption of reinvesting at the IRR itself.

For the modified IRR; blank = the discount rate

See the result

Results

NPV (net present value)1,372.36

IRR (internal rate of return)15.24 %

Modified IRR12.87 %

Profitability index1.137

Payback period3.33

Discounted payback4.26

Decision by NPVViable project

Discounted and cumulative flows
Period	Cash flow	Discounted flow	Cumulative	Discounted cumulative
0	-10,000	-10,000	-10,000	-10,000
1	3,000	2,727.27	-7,000	-7,272.73
2	3,000	2,479.34	-4,000	-4,793.39
3	3,000	2,253.94	-1,000	-2,539.44
4	3,000	2,049.04	2,000	-490.4
5	3,000	1,862.76	5,000	1,372.36

Discounted cumulative flow
Period	Discounted cumulative
0	-10,000
1	-7,272.73
2	-4,793.39
3	-2,539.44
4	-490.4
5	1,372.36

NPV by discount rate
Discount rate (%)	NPV
0	5,000
1	4,560.29
2	4,140.38
3	3,739.12
4	3,355.47
5	2,988.43
6	2,637.09
7	2,300.59
8	1,978.13
9	1,668.95
10	1,372.36
11	1,087.69
12	814.33
13	551.69
14	299.24
15	56.47
16	-177.12
17	-401.96
18	-618.49
19	-827.1
20	-1,028.16
21	-1,222.05
22	-1,409.08
23	-1,589.58
24	-1,763.85
25	-1,932.16
26	-2,094.79
27	-2,251.98
28	-2,403.98
29	-2,551.01
30	-2,693.29

See the working step by step

NPV = 1,372.36; profitability index = 1.137
Modified IRR = 12.87 %

In short

What it calculates: Appraise a project with different cash flows each year: NPV, IRR, modified IRR, profitability index, payback and the NPV profile.
Formula used: NPV = −I + Σ CF_t / (1 + r)^t
Example: Example 1. A conventional project.

NPV and IRR calculator

Before investing in a business, a machine or a renovation, the question is whether what you will receive justifies what you pay today, bearing in mind that a pound five years from now is worth less than one today. NPV and IRR answer that, but each can mislead if used alone.

Enter the initial investment, the cash flow of each period (they can differ, or be negative) and your discount rate. You get the NPV, the IRR, the modified IRR, the profitability index and how long it takes to recover the investment, with and without discounting, plus a chart of the cumulative flow and of how NPV changes with the rate. Everything runs in your browser.

How it works

NPV brings every cash flow to the present by discounting it at your rate: each flow is divided by (1 + rate) raised to the period number. If the sum, minus the investment, is positive, the project returns more than your alternative and creates value.

IRR is the discount rate that makes NPV zero: the project’s own return. You compare it with your rate: if it is higher, the project is acceptable. When flows change sign more than once there can be several IRRs (the calculator warns you and gives the one closest to your rate), and then NPV is the reliable criterion.

The modified IRR assumes positive flows are reinvested at a realistic rate rather than at the IRR itself. Payback measures how long it takes to get the investment back; the discounted version does it with discounted flows.

Formula

NPV = −I + Σ CF_t / (1 + r)^t
IRR: the rate r that satisfies NPV(r) = 0 (all roots between −99% and 1,000% are searched)
Profitability index = present value of positive flows ÷ present value of outflows
Modified IRR = (FV of positive flows at the reinvestment rate ÷ PV of outflows at the discount rate)^(1/n) − 1
Payback = previous period + amount still to recover ÷ flow of the period when it is recovered (interpolated)
Discounted payback: the same, with discounted flows

Worked example

Example 1. A conventional project.
An investment of $10,000 and five flows of $3,000 at 10%: NPV $1,372.36, IRR 15.24%, profitability index 1.137 and modified IRR 12.87%. You recover the investment in 3.33 years undiscounted and in 4.26 years discounted. As the NPV is positive and the IRR exceeds 10%, the project is viable.

Example 2. A project that does not pay.
An investment of $20,000 and flows of 4,000, 4,500, 5,000 and 5,500 at 12%: the NPV is −$5,786.95 and the IRR −1.92%: the investment is not even recovered (the flows add up to $19,000). It is not viable, and never pays back.

Example 3. Several IRRs.
An investment of $1,000 and flows of 6,000, −11,000 and 6,000 (a big works project in year two). There are three different IRRs: 0%, 100% and 200%. At a 10% rate the NPV is −$128.47, so it does not pay; the IRR is useless as a criterion here, while NPV works.

Explanation

NPV: the main criterion

Net present value adds up the cash flows discounted at your rate and subtracts the investment. It answers the right question: how much value does this project add, in today’s money, over what you would earn from your best alternative? If positive, accept; if negative, reject. Between two mutually exclusive projects, the one with the higher NPV is better.

IRR: useful, but be careful

IRR is the project’s own return and is easy to communicate. But it has problems:

With **several sign changes** in the flows, there may be several IRRs or none.
It assumes positive flows are **reinvested at the IRR itself**, which is often optimistic.
It ignores **size**: a small project with a high IRR may add less value than a big one with a lower IRR.

Modified IRR and payback

The **modified IRR** fixes the reinvestment problem: you set the rate at which flows are reinvested. **Payback** measures liquidity and risk (how long it takes to get your money back) but ignores what happens afterwards. The **discounted** version at least accounts for the time value of money.

How to choose the discount rate

It is the return you demand for taking on the project’s risk. It can be your cost of financing, what you would earn from an alternative investment of similar risk, or a premium over the risk-free rate. The result is very sensitive to it: the NPV-profile chart shows how much it changes.

Common mistakes

Using IRR alone, without NPV.
Mixing periods of different length, or monthly flows with an annual rate.
Ignoring later negative flows (refurbishments, replacements).
Choosing a discount rate that is too low for the risk.
Forgetting residual value or the recovery of working capital at the end.

Limits of this calculator

Flows are treated as arriving at the end of each period, all periods the same length.
It does not include taxes, inflation or the project’s financing; the flows must be the net ones you worked out.
The IRR search covers rates from −99% to 1,000% per period.
It accepts up to 200 periods.

Notice

The result is an estimate and depends entirely on the assumptions you enter. It is not investment advice.

Frequently asked questions

What is NPV?

Net present value: the sum of future cash flows discounted at your rate, minus the initial investment. If positive, the project returns more than your alternative.

What is IRR?

The discount rate that makes NPV zero: the project’s own return. It is compared with your minimum required rate.

What discount rate should I use?

The return you demand for the project’s risk: your cost of financing, that of an alternative of similar risk, or the risk-free rate plus a premium.

Why can there be several IRRs?

Because if flows change sign more than once, the equation NPV = 0 can have several solutions. In that case, decide by NPV.

What is the difference between IRR and modified IRR?

IRR assumes flows are reinvested at the IRR itself; the modified one, at a rate you choose, and gives a more realistic result.

What is the profitability index?

The present value of positive flows divided by that of outflows. Above 1 the project creates value; it helps compare projects of different size.

What does payback measure?

How long it takes to recover the investment. It measures liquidity and risk but ignores what happens afterwards; the discounted version accounts for the time value of money.

Is my data sent to a server?

No. The calculation runs in your browser.

Sources and references

The formula behind this calculator is not ours. These are the sources it comes from, in APA 7 format, in case you want to go to the original or cite them in your own work.

Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of corporate finance (13.ª ed.). McGraw-Hill Education. NPV, IRR, the profitability index and payback, with their limits.
Kierulff, H. (2008). MIRR: A better measure. Business Horizons, 51(4), 321–329. https://doi.org/10.1016/j.bushor.2008.02.005 https://doi.org/10.1016/j.bushor.2008.02.005 The modified IRR compared with the IRR and the reinvestment assumption.
Hazen, G. B. (2003). A new perspective on multiple internal rates of return. The Engineering Economist, 48(1), 31–51. https://doi.org/10.1080/00137910308965050 https://doi.org/10.1080/00137910308965050 Why cash flows with several sign changes can have multiple IRRs.

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