Calculating the internal rate of return (or IRR) of a project is one of the most popular methods that companies and managers use to determine whether a project is worth investing in. Now that I’ve covered a bit about NPVs and DCFs, it makes sense to go through what IRR is, how to use it, and why it’s not an ideal measurement.

When using NPV to determine whether or not to invest in a project, the general rule is to accept the project if NPV > 0 and reject if NPV is negative (or zero).

But since NPV results in a dollar figure, some managers have a hard time conceptualizing what that number (the present value of future cash flows) really represents. Instead, they prefer to look at percentages, and that’s where IRR comes in.

**IRR is the rate at which the project NPV equals 0. It also provides the expected return rate of the project, assuming certain conditions are met. **In other words, if C(n) is the cash flow for each period, then

**NPV = C(0) + C(1)/(1+r) + C(2)/(1+r)**

^{2}+ … + C(n)/(1+r)^{n}and you’d find IRR by setting NPV = 0 and solving for “r” above. (Excel’s IRR function makes this all a cinch by running an iterations.)

Let’s look back at Experiment in Finance’s NPV calculation as an example.

I noted in my previous entry that this site’s NPV through July was $89.93. Here are the cash flows again:

Using Excel’s IRR function, I put in the series of cash flows and find that my internal rate of return is 38.2%. But since my cash flows are monthly, 38.2% must be the monthly rate. This is equivalent to an annual IRR of 4,751.8%! This means that I must set an annual discount rate of 4,751.8% before my NPV calculation will equal 0; alternatively, it means I’m getting a seriously ridiculous return for my investment in my blog.

What’s the catch here? Well, recall that I don’t include labor costs in my NPV calculation, and that if I do, the NPV is resoundly negative. In fact, all my monthly cash flows are negative. In this case, IRR is undefined: there’s no discount rate small enough that makes NPV = 0. (A similar situation would happen if all my cash flows were positive.)

(Wow…I feel like a dot-com company. “NPV and IRR are great if I ignore labor costs…” doesn’t that just sound a little too much like the positive news on proforma and EBITDA earnings of yesteryear?)

Anyway, back to IRR. Managers like IRR because in theory, it gives them an idea of how much return they’ll be getting on a project. And if the IRR is higher than the discount rate used in the NPV calculation (which in companies is usually a fixed figure dictated by Treasury or some other internal group), then the project obviously is worth investing in.

You can see yourself how IRR is appealing. Suppose I told you I have an investment whose NPV is $15,682. Should you invest? How about if I told you the IRR (or rate of return) on the investment is 15%? Then you could easily compare it to what you’re getting on your savings account, CDs, or stocks. Intuitively it makes more sense, because we’re used to comparing investments using percentage rates.

Ah, but it’s a little too good to be true because, you see, IRR has serious flaws:

**1) Any time a project is forecasted to have negative cash outflows after having cash inflows, IRR is probably not the best method to use.**

Let’s say I told you I had a project with an IRR of 50%. Would you be interested in it? On the surface, a rate of 50% sounds pretty good. But the following two examples both give an IRR of 50%, and as an investor, you’d clearly be more interested in one than the other:

Opportunity 1: You put $1,000 into the project in Year 1, and in Year 2, you get $1,500 in return. IRR = 50%, NPV = $360 @ 8% discount rate.

Opportunity 2: You get $1,000 in year 1, and in Year 2, you put in $1,500 into the project. IRR = 50%, NPV = -$360 @ 8% discount rate.

Here, IRR doesn’t give an unambiguous answer, but NPV does. Using NPV, you’d reject Opportunity 2. Imagine if the situation were more complicated, and you received money in some periods and had to outlay money in others. IRR won’t give you the right answer in these situations, but NPV will. (Notice that in my example earlier, all my cash outflows came before I started getting positive returns!)

Similarly, you can have a situation where NPV = 0 at two different IRRs. This can happen when you have a large initial investment (outflow), followed by a series of returns (inflows), followed by another outflow of money.

Why can you end up with two IRRs? If you remember back to finding zeroes in pre-algebra, you’ll recall that when solving equations, you can have more than one “root” as an answer. The same thing is happening here. In these situations, NPV isn’t constantly increasing or decreasing with discount rates. Yet using NPV instead of IRR will give you the right answer in each case.

**2) When two projects are mutually exclusive, IRR may give the wrong answer.**

Let’s say you have a situation where you need to upgade a machine. You could either invest $10,000 up front and get a benefit of $25,000 the next year through an upgrade, or you could invest $25,000 up front to buy a new machine that will give you benefits of $50,000 the next year. Which would you choose? If you use IRR, you’ll find that the first option gives an IRR of 150%, and the second 100%. Using NPV and an 8% discount rate, you’ll find the first situation is worth $12,174 and the second, $19,719. In reality, you’ll be richer in the second scenario.

Think of it this way. I’m feeling awfully generous and let you choose one of two options. Option 1: if you give me $0.25, I’m willing to pay you a dollar. That’s a 300% return. Not bad. Or you can give me $100, and I’ll give you $300. Which would you choose, assuming you could find $100 to use for the transaction? Sure, your return would be worse in the second situation at 200%, but wouldn’t you rather get $300 for $100 instead of $1 for $0.25?

There are plenty more pitfalls and scenarios where IRR should be used with caution. But, this little intro should give you an idea of what IRR is all about. As usual, if you have any comments, corrections, or requests, feel free to leave them below!

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## Stewart Park

I am trying to calculate a complex IRR on a potential project. Our group always decides based on IRR. This project has a large investment going in at two separate dates and pays out a portion of the profit and the investment roughly annually. I have found a web program that gives me a number significantly higher than the Excel program I am using. I have a feeling neither are right. Can you send me in the right direction or tell me how to calculate it.

I can give you the specifics for calcualtion purposes or in a separate e-mail I could attach the programs I am using.

I truly appreciate any help you could give me.

Stewart Park

## Sheri Balthrop

Very helpful. I’m taking Business Finance this semester. This explanation of IRR was much clearer.

## Sandra Miranda

The information is useful and helped me in making my decision

## Amanuel Gebremichael.

please take different financial statements whicha are related with calculation of internal rate of return to show that the project is viable or not.

## Greg Feirman

Great post here. I’m an Investment Advisor and I’m trying to figure out the best way to measure my performance. Because I have inflows and outflows does that mean I can’t use IRR?

What is the best way for an investment professional like me to calculate returns?

Thanks!

## Praveen

Hello,

This article was very helpful. It helped me to calculate IRR for the cost/benefit analysis I was doing for a project.

thanks,

Praveen.

## exempli gratia » How to calculate an internal rate of return (IRR), and when not to use it | Experiments in Finance

[...] How to calculate an internal rate of return (IRR), and when not to use it | Experiments in Finance [...]

## Savings Account That Provides

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## christina kumar

this page has been very helpful in completing my business finance assignment.

## shier

4. Consider the following projects (figures are in $A):

Year 0 1 2 3 4 5

Project A -1,000 1,000

Project B -6,000 1,000 1,000 4,000 1,000 1,000

Project C -10,000 1,000 2,000 3,000 4,000 5,000

(a) If the cost of capital is 8%, which of the projects have a positive NPV?

(b) Calculate Discount payback?

(d) What is the internal rate of return on Project A? What is it on Project B?

## Md. mostafizur Rahman

fantastic. It really an excellent peace of example for any one to grab the concept of IRR and superiority of NPV

## Niels

Thanx! Been a great help!

Niels

## mohamed refaat

thank you .

## Dave the rave

unbelieveable, this website is going in as the best out there, i nearly failed an hnc but you saved me!!!!

## Betty

Thanks! You helped me understand this much better!

## Cem Inc?

Thanks for the articles. The examples are great as to understand the differences. It is now more logical to use the NPV in projects.

## Muhammad Faisal Khan

Thanx and i m greatful for your help as this help me to have better understanding of IRR.

## zainab

very interesting article n very helpful too.

## Praise Anya

I’ve been trying to solve this problem for sometime with no success. I have tried using your solution methods,still did not get to the answer.

Pls can u help?

FGM plc, a motor manufacturer, is considering the launch of a new range of custom-built sports cars, incorporating a revolutionary design of automatic gearbox, which is claimed to be ultra fuel-efficient. The project is code-named project X.

The new key features of the gearbox have been patented by the inventor but he has approached FGM with a view to selling the patent rights. However he requires an early response before he offers the patent to competitors. The patent would cost £5 million.

Profit estimates have been prepared based on market research and these are detailed below. The time-scale to launch the new range on the market would be 2 years from any go-ahead date, with the required manufacturing investment decision having to be made 1 year from now.

If the project goes ahead, a new factory needs to be built, costing £2million plus £6 million for manufacturing equipment. In addition the land site for the factory is expected to cost £3 million.

The company’s depreciation policy is to use the straight-line method with residual values assumed to be zero. Land costs are not depreciated. Patent costs are amortised over the expected useful life of the patent, which in this case is 10 years.

The new range has an expected market life of 10 years. The useful life of both the factory and the equipment is also 10 years.

The project will be financed by a bank loan, which will incur interest of £300,000 per annum, payable in arrears at the end of each year, with the loan being repaid after 10 years.

The working capital for the project is estimated to be £1.2 million starting from the year of the product launch.

Profit Estimates

The profits shown below are after charging depreciation, interest on the bank loan.

Year Profit/(Loss) £m

1 (2.3)

2 1.5

3 6.0

4 8.0

5 10.0

6 10.0

7 8.0

8 6.0

9 4.0

10 2.0

The project detailed above is code-named Project X.

There is also an alternative proposal, code-named Project Y.

This project involves using gear-box technology, already created internally, from the company’s own engineering laboratory. This technology is estimated to have cost £3 million. However this technology is less advanced and therefore production could take place in the existing factory by putting on a night shift. Also only £4 million would need to be spent on equipment, the bank loan would be unnecessary and the working capital requirement would reduce to £0.8 million.

As for Project X, the time-scale to launch the new range on the market under Project Y would also be 2 years from any go-ahead date, with the required manufacturing investment decision having to be made 1 year from now.

The profit estimates for Project Y after charging depreciation on the new equipment, are estimated as follows:

Year Profit/(Loss) £m

1 2.1

2 3.6

3 3.6

4 3.6

5 2.6

6 2.6

7 2.6

8 1.6

9 1.6

10 0.6

The company’s money cost of capital is 15% p.a. Of this cost, 3% comprises allowance for inflation.

All cash figures are expressed in today’s money i.e. exclusive of inflation.

Required:

Using the information presented above, prepare a Report for the Directors.

The Report should include:

- Recommendation as to which (if any) of the projects should be implemented. The recommendation must be logically argued and supported with both quantitative and qualitative factors

- Identification of any areas where further work or information is required and clear explanation of why such work or information is necessary.

- Explanation of how risk has been taken into account in arriving at your recommendation.

- Identification and critical evaluation of any of the techniques you have used or have recommended using

- Explanation and justification of all adjustments made to profit estimates to arrive at cash flow estimates

- How “real options” have been taken into account

- How inflation has been taken into account

(60% weighting)

-Quantitative analysis in support of the Report and recommendations

(40% weighting)

## diya

I’ve been trying to solve this problem for sometime with no success. I have tried using your solution methods,still did not get to the answer.

Pls can u help?

FGM plc, a motor manufacturer, is considering the launch of a new range of custom-built sports cars, incorporating a revolutionary design of automatic gearbox, which is claimed to be ultra fuel-efficient. The project is code-named project X.

The new key features of the gearbox have been patented by the inventor but he has approached FGM with a view to selling the patent rights. However he requires an early response before he offers the patent to competitors. The patent would cost £5 million.

Profit estimates have been prepared based on market research and these are detailed below. The time-scale to launch the new range on the market would be 2 years from any go-ahead date, with the required manufacturing investment decision having to be made 1 year from now.

If the project goes ahead, a new factory needs to be built, costing £2million plus £6 million for manufacturing equipment. In addition the land site for the factory is expected to cost £3 million.

The company’s depreciation policy is to use the straight-line method with residual values assumed to be zero. Land costs are not depreciated. Patent costs are amortised over the expected useful life of the patent, which in this case is 10 years.

The new range has an expected market life of 10 years. The useful life of both the factory and the equipment is also 10 years.

The project will be financed by a bank loan, which will incur interest of £300,000 per annum, payable in arrears at the end of each year, with the loan being repaid after 10 years.

The working capital for the project is estimated to be £1.2 million starting from the year of the product launch.

Profit Estimates

The profits shown below are after charging depreciation, interest on the bank loan.

Year Profit/(Loss) £m

1 (2.3)

2 1.5

3 6.0

4 8.0

5 10.0

6 10.0

7 8.0

8 6.0

9 4.0

10 2.0

The project detailed above is code-named Project X.

There is also an alternative proposal, code-named Project Y.

This project involves using gear-box technology, already created internally, from the company’s own engineering laboratory. This technology is estimated to have cost £3 million. However this technology is less advanced and therefore production could take place in the existing factory by putting on a night shift. Also only £4 million would need to be spent on equipment, the bank loan would be unnecessary and the working capital requirement would reduce to £0.8 million.

As for Project X, the time-scale to launch the new range on the market under Project Y would also be 2 years from any go-ahead date, with the required manufacturing investment decision having to be made 1 year from now.

The profit estimates for Project Y after charging depreciation on the new equipment, are estimated as follows:

Year Profit/(Loss) £m

1 2.1

2 3.6

3 3.6

4 3.6

5 2.6

6 2.6

7 2.6

8 1.6

9 1.6

10 0.6

The company’s money cost of capital is 15% p.a. Of this cost, 3% comprises allowance for inflation.

All cash figures are expressed in today’s money i.e. exclusive of inflation.

Required:

Using the information presented above, prepare a Report for the Directors.

The Report should include:

- Recommendation as to which (if any) of the projects should be implemented. The recommendation must be logically argued and supported with both quantitative and qualitative factors

- Identification of any areas where further work or information is required and clear explanation of why such work or information is necessary.

- Explanation of how risk has been taken into account in arriving at your recommendation.

- Identification and critical evaluation of any of the techniques you have used or have recommended using

- Explanation and justification of all adjustments made to profit estimates to arrive at cash flow estimates

- How “real options” have been taken into account

- How inflation has been taken into account

(60% weighting)

-Quantitative analysis in support of the Report and recommendations

(40% weighting)

pls send me the solution urgently

## J Castellano

Thanks for your helpful information.

I need to develop a methology for determinig which projects to undertake for my company and am unclear how to make IRR and cost of capital work in my situation.

We develop new products and although I know what the investment will be upfront, I don’t know what the returns will be until the products actually sell. I do have help with sales forecasting, but the forecasts may not be very accurate.

Can you shed some light?

## Rowen

how to calculate IRR of the project if net cash flow= R12000 p/y

on 10yrs,cost of capital is 8%, and initial investment=R50000

## Rowen

Purchase of a machine for R1,9m. working capital is R100,000. saving in cost of R1m per yr. wear & tear at 25% p/y, and is sold for R120,000 at useful life of 4 yrs. and firm tax is 30% and cost per capital is 20%.

calculate

Discount pay back, the NPV,the IRR less 10%,

## Rowen

new power stationconstruction cost R100,000,000 payable i 1 Jan,08. maintanace cost R7,000,000 plus R3,000,000 per 1m units of electricity consumed. consumption is 1m pa 2008, eskom borrowing full amount at an interest of 5% pa.debt is paid at income exceeding the expenditure. ignore tax

calculate the price unit of electricity to term of 50 years from 1 Jan,08- assuming the power station is worthless after 50 years. show calculations.

## Abanda

Thanks alot.I learnt alot especially from the second part thats the theory.I still have problems any way with the manual calculations

## fridah gacheri

great.

just what i needed for cost benefit anlysis

## John

I’m buying a small apartment building and will need to reconstruct it and sell the units as condos. I’m trying to calculate IRR but I’m stuck. Can you help? Do I use my initial purchase price, costs for reconstruction and THEN sale prices? I’m a bit lost. Thanks for your help!!

## Ramesh Babber

Initial investment Rs.1000000/- Expected Cash flow for yr(1)-450000,yr(2)-425000,yr(3)-300000, yr(4)-350000. What is the IRR of the project. Kindly solve this question. Thanks.Step wise.

## curmudgeonly troll

just wanted to point out that

- Opportunity 1 you’re investing money at 50%

- Opportunity 2 you’re borrowing money at 50%

clearly, when you’re a borrower a high rate is a bad thing but when you’re investing money it’s a good thing.

so you never want to use IRR to compare projects that are uses of funds and projects that are sources of funds.

but when you have complex cash flows, with multiple reversals of direction, there might be some periods where the project is a use of funds and others where it’s a source of funds. You might have multiple roots and valid IRRs. For instance:

- in 2000 you pay 1b for a nuclear plant

- for 40 years starting in 2001 you receive 100m per year

- in 2040 you receive the final 100m, but also have to lay out 3b to decommission the plant.

If you do this in Excel, = IRR(A1:A41) gives 8.7% . The $3b 40 years from now has a PV of only ~$100m at that rate, and reduces the 10% current yield by about 1.3%.

But the net cash flows over the lifetime of the project are 0, so IRR(range,0) gives 0, which is also a valid IRR.

in these complex cash flows, there is potential for multiple solutions and comparisons may be mislead comparisons.

the point about NPV being the superior is correct but I thought this might be a more real-life example.

## debt reduction

I must say that this article helped me to have a clearer perspective in terms of deciding where to place our company’s resources for investment. Thanks for the very helpful information!

## tarek fouad

im really appreciate that thank u very helpful i’m now knew what is it this IRR? thank you for second time and i hope u will never stop this great articles

## CasualSoul

Your two examples of how IRR is seriously flawed are themselves very flawed.

In example 1. you point out how much more I would make by investing $25K over $10K, but you ignore the fact that if I took the first example and invested the $10K, I could potentially invest the other $15K in another investment with similar yield.

You have the same flawed logic in example 2.

## Nigam

can u please give me the answer of the following question?

My initial investment £449,400

Annual Net Cash Flaw £100,000

Cost of Capital 14%

Length 10 years

So, how much are IRR and NPV?

Please possible to write down how u calculate because i am new in these sector.

## Faisal

I’m having a IRR of 74% of my new project. is it possible to have IRR of 74%?

## Faisal

Dear, NIGAM

Ur IRR is 18% and NPV is £ 63,343.48

## realbench

I personally used the internal rate of return mainly to rank several prospective real estate investments. Help me flush out bad investments and pick the most desirable when considering multiple ones. Your post gives me another angles on how to employ it in other areas I had overseen.

Good post

## DEBRAJ HALDAR

Please send me details about IRR formula for car loan and how to calculate the formula for car loan ………..

## DEBRAJ HALDAR

My IRR for a mini truck loan is 17…please calculate my rate of interest ……….

## Brian Rutter

Let me make a few points on the IRR discussion. First, a bit of history might make it more clear why the IRR method was adopted in the first place, and why it is probably not the best tool for corporate capital budgeting. The IRR was developed first in the Bond market. With bonds, periodic cash flows and terminal values are known with relative certainty. Apart from the initial purchase price, there are no negative cash flows to deal with, thus eliminating the situation where you can have more than one valid IRR for a project. Since bonds usually trade at a premium or discount to their face value, the IRR is a good tool to tell you the return you are making on your actual investment, as distinct from the nominal interest rate on the bonds.

When you start moving away from this simple scenario, you start getting more problems. However, the IRR is still appealing in the investment world because it gives you a simple means of comparing projects of different scale, while the NPV is heavily impacted by the size of the project.

To answer some of the questions from earlier comments, where you do not know the future cash flows with any degree of certainty, you should use some form of sensitivity analysis. That is, you derive your best estimate of the cash flows, and calculate the IRR on those. Then, you vary those cash flows up and/or down throughout what seems a reasonable range. Some people use 3 scenarios, a best estimate, an optimistic scenario, and a pessimistic scenario. I would say that the greater your uncertainty, the more different scenarios you should look at. You will have a range of IRR’s which should cover what will actually happen. Now, the finance text books will tell you to assign probability estimates to each scenario, and then you can calculate the probability that the actual IRR will be above a given level. However, I believe that if you are that uncertain about what the cash flows will be, those probability estimates will be essentially useless. Remember, that technique is what led Lehman Brothers, Morgan Stanley et. al. to believe they had adequate capital reserves.

One questioner was trying to include depreciation in his calculations. Remember, both NPV and IRR are cash flow concepts. You would not include depreciation, because depreciation is an allocation of up-front costs over the period in which the benefits are expected. You have already accounted for your initial investment as an initial cash outflow. Reducing future inflows by depreciation is double counting the initial investment.

And just out of curiosity, how many of those questions which gave very specific scenarios were test questions from finance courses?

## Allhyn

I am confused with the term “in flow and out flow”.

Here’s the case.

I am to compute the IRR of new project.

Their initial capital is not sufficient for the Project cost so investors are opt to have a loan from the Bank. My questions are:

1. Will I include the loan amount in my computation of IRR?

2. If yes, does it means Principal and Interest?

3. If no, how about the Interest Exp, will I include in Cash outflow?

Thank you so much

## michie

what if your initial investment is 3,729,300 and your NPV is 14,998,095.73 and your B/c ratio is 4.96. Well actually we used 12% as our MARR, what should be the IRR.

## Olusegun

Please help to write a program to compute internal rate of return of project in c-programming language.Thanks alot

## Mohammad Abul kashem

Please answer my following question:

how i would calculate IRR when in 10 % NPV is positive & 35% NPV is also positive.

I saw in many books they calculate IRR by putting two positive NPV in Formula.

Can you please tell me why?

## Urvesh

What’s is the difference between profit and irr ?

## indi

This is very clear and useful. Thank you very much.

## MU

I am currently evaluating a group of greenfield projects, which include hotel, property, golf ect. I have computed the project and equity IRR for each individual projects.

Problem arose when I consolidated all these projects which some of the projects are not wholly owned by my companies, as below:

1) For equity IRR, how should we treat the minority interest – shareholders’ cash flow or debt’s cash flow

2) Should I use the consolidated cashflow or just add on individual project free cash flow based on my effective interest ownership in the projects in computing the project and equity IRR? The minority injection into the cashflow will be reflected in the consolidated cash flow but if I did not assume any payment of dividend at respective project cashflow level, the minority interest would not share any of the future cash in flow

Please kindly share your thoughts on this matter

## Sebastian

Thanks helped a bunch!

## DIMAKATSO

donna is considering buying a car for R40 000.The bank has quoted her an interest of 18 percent per annum(compounded monthly).If she wishes to repay the principle amount over 54 months,calculate her monthly instalment.

## RUKAZAMIHIGO Samson

I thank you for explanations but iI have a problem which still be difficult and I need a help from you: I would like to know how to calculate IRR by using calculator

## Rhulz

donna is considering buying a car for R40 000.The bank has quoted her an interest of 18 percent per annum(compounded monthly).If she wishes to repay the principle amount over 54 months,calculate her monthly instalment.

## Theresa

For your help

Mpho Limited is investigating an opportunity to purchase a machine for R320 000 now. The machine is expected to save R80 000 per annum for five years. The machine is also expected to have a resale value of R40 000. Calculate internal rate of return

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