NPV vs IRR: What They Measure and When They Disagree

• NPV is a dollar amount. IRR is a percentage.
• Accept a project when NPV is above zero, or when IRR is above the required rate.
• The two can rank projects differently when size or timing differs.
• When they conflict, NPV is usually the more reliable measure.

What NPV measures

Money received in the future is worth less than money in hand today, because today's money can be invested. Discounting is the process of converting a future amount into its value today. The rate used is called the discount rate. It represents the return you require, often the cost of funding the project.

Net present value adds up all of a project's cash flows after discounting them, including the initial cost as a negative number.

The present value of one cash flow is: amount / (1 + rate)^years.

Example: invest $1,000 today and receive $600 at the end of year 1 and $600 at the end of year 2, with a 10% discount rate.

• Year 1: $600 / 1.10 = $545.45
• Year 2: $600 / 1.21 = $495.87
• Total present value: $1,041.32
• NPV: $1,041.32 - $1,000 = $41.32

The project returns the required 10% and adds $41.32 of value on top. The NPV calculator handles any number of cash flows.

What IRR measures

The internal rate of return is the discount rate that makes NPV exactly zero. In plain words, it is the yearly return the project itself earns on the money tied up in it.

For a single payoff after one year, IRR is easy to see. Invest $1,000 and receive $1,200 a year later. The gain is $200 on $1,000, so the IRR is 20%. Check: $1,200 / 1.20 = $1,000, which gives an NPV of zero.

With several cash flows there is no direct formula. IRR is found by trial and error: try a rate, compute NPV, and adjust until NPV reaches zero. Spreadsheets and the IRR calculator do this search automatically.

IRR is popular because a percentage is easy to compare with a loan rate or a target return.

The decision rules

Each measure has a simple rule for a single project:

• NPV rule: accept if NPV is greater than zero at your required rate. Reject if it is below zero.
• IRR rule: accept if IRR is higher than your required rate, sometimes called the hurdle rate. Reject if it is lower.

For a normal project, with one outlay followed by inflows, the two rules give the same answer. If IRR is above the required rate, NPV at that rate is positive.

The required rate matters a great deal. Many businesses base it on their weighted average cost of capital, explained in what is WACC.

Problems start when you must choose between projects, or when cash flows follow an unusual pattern.

Where they disagree: scale and timing

Scale

IRR ignores project size. Compare two one-year projects at a 10% required rate.

A has the higher IRR. B adds five times as much value. If you can only choose one and have the funds for either, B leaves you better off.

Timing

IRR also favors quick paybacks. Take two projects that each cost $1,000:

• C pays $1,300 after one year. IRR is 30%. NPV at 10% is $1,300 / 1.10 - $1,000 = $181.82.
• D pays $1,728 after three years. IRR is 20%. NPV at 10% is $1,728 / 1.331 - $1,000 = $298.27.

C wins on IRR and D wins on NPV. A high rate earned for a short time can be worth less than a lower rate earned for longer.

Unusual cash flows and the reinvestment assumption

More than one IRR

Some projects have a cost at the end as well as the start, such as cleanup or removal costs. When the cash flows change sign more than once, there can be more than one IRR, or none at all.

Example: pay $1,000 today, receive $2,300 in year 1, then pay $1,320 in year 2. NPV is zero at both 10% and 20%. Neither figure is a useful answer on its own. NPV at your required rate still gives one clear number.

Reinvestment

IRR is often read as if cash received along the way can be reinvested at the IRR itself. For a project with a very high IRR, that is rarely realistic. NPV assumes those cash flows earn the discount rate, which is usually a more modest and more defensible assumption.

A variation called modified IRR lets you set the reinvestment rate yourself, which removes this problem and always gives a single answer.

Which to trust and when

Both measures are useful. They answer different questions.

1. Single, normal project: either works. They will agree on accept or reject.
2. Choosing between projects: rank by NPV. It measures the value added in dollars, which is the thing you are trying to increase.
3. Cash flows that change sign more than once: use NPV, or modified IRR.
4. Communicating a result: IRR is a handy summary, as long as NPV supports the same choice.
5. Limited budget: compare NPV per dollar invested to see which mix of projects adds the most value.

A practical habit is to report both. Lead with NPV to show how much value is created, and give IRR alongside it to show how much room there is before the project stops paying its way. If the two point in different directions, find out why before deciding.

Neither figure is better than the forecasts behind it. Test the result with lower and higher cash flow estimates and with different discount rates. Simpler checks such as the payback period and return on investment can sit alongside them as a sanity check.

Try it with your own numbers

• NPV CalculatorA project's value in today's money.
• IRR CalculatorThe yearly return a project really earns.
• Payback Period CalculatorYears until an investment pays for itself.
• WACC CalculatorBlended cost of equity and debt.

Frequently asked questions

This guide is general education, not financial advice. Rules of thumb vary by lender, industry and country.