Negative IRR indicates that the sum of post-investment cash flows is less than the initial investment; i.e. the non-discounted cash flows add up to a value which is less than the investment.

So yes, both in theory and practice negative IRR exists, and it means that an investment loses money at the rate of the negative IRR.

In such cases the net present value (NPV) will always be negative unless the cost of capital is also negative, which may not be practically possible.

However, note that a negative NPV doesn't always mean a negative IRR. It simply means that the cost of capital or discount rate is more than the project IRR.

#### In this post we will explore the concept of negative IRR and also touch upon the issue of multiple IRRs.

Let's consider the following cash flow stream:

You will notice that the sum of all the cash flows is negative.

We can calculate the IRR by using the Excel IRR function:

You will notice that the IRR is -2.6.

What does it mean? You are investing 600 and getting back 560, so you are losing 40 over the cash flow period. So the IRR -2.6 is the rate at which you are losing money.

Such scenario is very much possible in real life situations, and there is nothing wrong with your analysis if you get negative IRR.

IRR is often defined as the theoretical discount rate at which the NPV of a cash flow stream becomes zero. So, does it means we should use negative IRR as a discount rate to calculate the present value!

Certainly not. Negative discount rate would mean money available at the present time is worth less than the same amount in the future.

**Multiple IRRs**

With certain cash flow streams, it is possible to produce multiple IRRs. A net cash flow stream will have multiple IRRs when it Includes more than one sign change.

When the first cash flow is negative and the second cash flow is positive, that is one sign change and there will be one IRR for the stream. If another, later, net cash flow event is negative, that makes 2 sign changes. There will be one IRR for every sign change in the cash flow stream.

Now consider the following cash flow:

If we use the Excel IRR formula, we will get 6.6% as IRR. But we know that there will be two IRRs as the cash flow changes sign twice.

Now let's calculate the NPV at different discount rates:

You will notice that the NPV changes sigh at two discount rates, i.e. NPV is zero for two discount rates. This means there is another IRR possible. This will be more clear when plot a chart:

It is obvious that there is two IRRs. We can calculate both possible IRRs by inputting the 'guess' optional input in the Excel IRR function:

From the chart above, it is clear that one IRR is close to 6% and another one close to 36%. We need to calculate the IRR twice; first we need to put 6% as 'guess' option input and in second calculation 36%.

We will get both possible IRRs:

So what should we do in such situation? Which IRR should consider while evaluating projects with such cash flow streams?

In my opinion, it is rational to consider the IRR which is closest to the cost of capital as the "true" IRR.

Hope you enjoyed this post on negative IRR. If you have any questions, let me know through the comment section below.

You can also download the Negative IRR Workbook FREE!

**Further Reading:**

IRR Calculation in Excel: Formulae and Use

Project IRR and Equity IRR: A Curious Connection

Can Equity IRR be lower than Project IRR?

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this stuff is way too complicated! i’m in marketing—i’ll let finance geeks figure it out.

this stuff is way too complicated! i’m in marketing—i’ll let finance geeks figure it out.

Can there be more than 2 IRRs if there are multiple sign changes in the cash flows?

Can there be more than 2 IRRs if there are multiple sign changes in the cash flows?

Hello! Could you explain what an IRR of 0% means when the NPV is slightly positive?

An IRR of 0 means that NPV=0. It basically means than your future cash flows at present value are enough to cover your initial investment and not provide any additional return, i.e., profits on the project

Well understood. But I came across someone who gave me a formula for calculating IRR when the NPV is always negative and the IRR will still be positive. How real is this? Can you throw more light on it?

Hello! Could you explain what an IRR of 0% means when the NPV is slightly positive?

An IRR of 0 means that NPV=0. It basically means than your future cash flows at present value are enough to cover your initial investment and not provide any additional return, i.e., profits on the project

Well understood. But I came across someone who gave me a formula for calculating IRR when the NPV is always negative and the IRR will still be positive. How real is this? Can you throw more light on it?

What is the IRR if the cashflow only has a negative value at the end of the period??

In your second example, you’ve invested 3,200, but have only received 3,100 in distributions; this indicates that the return should be negative and not positive, don’t you agree? I think there should be a negative…

A smart question Dan! Two IRRS 6.6% AND 36.5% (This is the case discussed in A. Damodaran). I have published a paper in Australian Economic Papers in details about such issues and this specific case of IRR 6.6% and 35.5%. Please note the ACTUAL IRR IS -9%. The undiscounted NCF = -100 and that being the net loss of 10%. By discounting it works out to -9%.

Link to those papers are below:

https://onlinelibrary.wiley.com/doi/full/10.1111/1759-3441.12239

Non?monotonic NPV Function Leads to Spurious NPVs and Multiple IRR Problems: A New Method that Resolves these Problems? Kannapiran C. Arjunan Economic Papers, Volume38, Issue1 March 2019

Pages 56-69

Arjunan, Kannapiran, Non-monotonic NPV Function Leads to Spurious NPVs and Multiple IRR Problems: A Critical Analysis to Resolve These Problems (August 3, 2018). Forthcoming in the Australian Economic Papers Journal. Available at SSRN: https://ssrn.com/abstract=3225559 or http://dx.doi.org/10.2139/ssrn.3225559

Published in the Australian Economic Papers Journal

In your second example, you’ve invested 3,200, but have only received 3,100 in distributions; this indicates that the return should be negative and not positive, don’t you agree? I think there should be a negative…

A smart question Dan! Two IRRS 6.6% AND 36.5% (This is the case discussed in A. Damodaran). I have published a paper in Australian Economic Papers in details about such issues and this specific case of IRR 6.6% and 35.5%. Please note the ACTUAL IRR IS -9%. The undiscounted NCF = -100 and that being the net loss of 10%. By discounting it works out to -9%.

Link to those papers are below:

https://onlinelibrary.wiley.com/doi/full/10.1111/1759-3441.12239

Non?monotonic NPV Function Leads to Spurious NPVs and Multiple IRR Problems: A New Method that Resolves these Problems? Kannapiran C. Arjunan Economic Papers, Volume38, Issue1 March 2019

Pages 56-69

Arjunan, Kannapiran, Non-monotonic NPV Function Leads to Spurious NPVs and Multiple IRR Problems: A Critical Analysis to Resolve These Problems (August 3, 2018). Forthcoming in the Australian Economic Papers Journal. Available at SSRN: https://ssrn.com/abstract=3225559 or http://dx.doi.org/10.2139/ssrn.3225559

Published in the Australian Economic Papers Journal

If the Net-Present-Value of an investment is less than zero, the investment is:

1. Attractive on its financial merits.

2. Not attractive on its financial merits.

3. Only attractive if the IRR is also less than zero.

4. Not determinable from the information provided.

Which is the correct answer? (I don’t know the answer)

Not attractive on its financial merits.

Without knowing the discount rate and your desired rate of return (or WACC) its not sensible to reply to your query. When the NPV at your required rate of discount or return (or wacc) is zero the investment is in breakeven i.e just recover the cost with a return equivalent to your desired rate. If negative then reject the investment, If positive Accept the investment. But try to use IRR also.

Dr Kannan?Arjunan, PhD (Economics), MBA (Finance), CAIIB, B.Sc. Agri.

Brisbane, Australia?

View my research on my SSRN Author page:

https://ssrn.com/author=2637148https://rdcu.be/bidzh – Non-monotonic NPV Function Leads toSpurious NPVs and Multiple IRR

Thank you for sharing Dr. Kanna, I was scratching my head over a DCF analysis with multiple IRRs and stumbled upon your paper.

If the Net-Present-Value of an investment is less than zero, the investment is:

1. Attractive on its financial merits.

2. Not attractive on its financial merits.

3. Only attractive if the IRR is also less than zero.

4. Not determinable from the information provided.

Which is the correct answer? (I don’t know the answer)

Not attractive on its financial merits.

Without knowing the discount rate and your desired rate of return (or WACC) its not sensible to reply to your query. When the NPV at your required rate of discount or return (or wacc) is zero the investment is in breakeven i.e just recover the cost with a return equivalent to your desired rate. If negative then reject the investment, If positive Accept the investment. But try to use IRR also.

Dr Kannan?Arjunan, PhD (Economics), MBA (Finance), CAIIB, B.Sc. Agri.

Brisbane, Australia?

View my research on my SSRN Author page:

https://ssrn.com/author=2637148https://rdcu.be/bidzh – Non-monotonic NPV Function Leads toSpurious NPVs and Multiple IRR

Thank you for sharing Dr. Kanna, I was scratching my head over a DCF analysis with multiple IRRs and stumbled upon your paper.

Excellent article on feasibility study. Keep it up.

Excellent article on feasibility study. Keep it up.

Do you have any example for some project that has negative IRR?

Do you have any example for some project that has negative IRR?

Will it be effective to calculate MIRR in case of cash flows have more than one sign change?

MIRR is a spurious rate, pls never use it.

See below: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2942456

Arjunan, Kannapiran, Modified IRR (MIRR) Is a Spurious Criterion and Should Not Be Used in Cost-Benefit Analysis (CBA) and Investment Analysis (March 28, 2017). Forthcoming in the Journal of Economic and Finance Education . Available at SSRN: https://ssrn.com/abstract=2942456 or http://dx.doi.org/10.2139/ssrn.2942456

Dr Kannan?Arjunan, PhD (Economics), MBA (Finance), CAIIB, B.Sc. Agri.

Brisbane, Australia?

View my research on my SSRN Author page:

https://ssrn.com/author=2637148https://rdcu.be/bidzh – Non-monotonic NPV Function Leads toSpurious NPVs and Multiple IRR

What about in the event of a total loss? IE Recovery of 0% is your IRR then -100%? Or is it 0?

What about in the event of a total loss? IE Recovery of 0% is your IRR then -100%? Or is it 0?

If sum of NCF is zero then IRR is zero. However if the sum of NCF is negative and the negative value is matching with the capital investment amount, then yes you get -100% IRR

An intelligent argument on Zero and negative IRR. Most texts miss this point.

Dr Kannan?Arjunan, PhD (Economics), MBA (Finance), CAIIB, B.Sc. Agri.

Brisbane, Australia?

View my research on my SSRN Author page:

https://ssrn.com/author=2637148https://rdcu.be/bidzh – Non-monotonic NPV Function Leads to Spurious NPVs and Multiple IRR

Hello Naiyer: I quote your statement above “In my opinion, it is rational to consider the IRR which is closest to the cost of capital as the ?true? IRR”. Two IRRS 6.6% AND 36.5% (This is the case discussed in A. Damodaran). I have published a paper in Australian Economic Papers in details about such issues and this specific case of IRR 6.6% and 35.5%. Please note the ACTUAL IRR IS -9%. The undiscounted NCF = -100 and that being the net loss of 10%. By discounting it works out to -9%.

Link to those papers are below:

Arjunan, Kannapiran, Non-monotonic NPV Function Leads to Spurious NPVs and Multiple IRR Problems: A Critical Analysis to Resolve These Problems (August 3, 2018). Forthcoming in the Australian Economic Papers Journal. Available at SSRN: https://ssrn.com/abstract=3225559 or http://dx.doi.org/10.2139/ssrn.3225559

Published in the Australian Economic Papers Journal

An intelligent argument on Zero and negative IRR. Most texts miss this point.

Dr Kannan?Arjunan, PhD (Economics), MBA (Finance), CAIIB, B.Sc. Agri.

Brisbane, Australia?

View my research on my SSRN Author page:

https://ssrn.com/author=2637148https://rdcu.be/bidzh – Non-monotonic NPV Function Leads to Spurious NPVs and Multiple IRR

I’m trying to understand why I get a negative IRR when I have zero initial investment, positive cash flows until the final cash flow, which is negative. This can be the case when refinancing costs are financed and the new mortgage payment is lower, resulting in payment savings to the borrower, but a negative outflow because the mortgage balance is higher if the mortgage is paid off early. Is it simply mathematics where there’s 3 sign changes?

First, DCF can estimate when there is an investment i.e. negative cashflow in year zero (investment year). If not you can onl;y calculate NPV. If you get negative IRR due to intermittent negative cashflow, then the sum of NCF must be below zero or negative.

I’m trying to understand why I get a negative IRR when I have zero initial investment, positive cash flows until the final cash flow, which is negative. This can be the case when refinancing costs are financed and the new mortgage payment is lower, resulting in payment savings to the borrower, but a negative outflow because the mortgage balance is higher if the mortgage is paid off early. Is it simply mathematics where there’s 3 sign changes?

First, DCF can estimate when there is an investment i.e. negative cashflow in year zero (investment year). If not you can onl;y calculate NPV. If you get negative IRR due to intermittent negative cashflow, then the sum of NCF must be below zero or negative.

whats your sum of NCF? If negative then IRR will be negative!

whats your sum of NCF? If negative then IRR will be negative!

Here is the samole example. Can anyone sol this examole with error and trail method. And use interpolitation.

A strip-mining project requires an initial investment of $60. The cash flow in the first year is $155. In the second year, the mine is depleted, but the firm has to spend $100 to restore the land.

Here is the samole example. Can anyone sol this examole with error and trail method. And use interpolitation.

A strip-mining project requires an initial investment of $60. The cash flow in the first year is $155. In the second year, the mine is depleted, but the firm has to spend $100 to restore the land.