Internal Rate of Return & Net Present Value

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Click on the calculator's "Help" button for usage details. __It is VERY important that you understand about dates and cash flows__.

Related - Some investors like to use the Modified Rate of Return Calculator (MIRR). It calculates a more conservative IRR since the user can enter a different reinvestment rate.

It is the discount rate (think of it as you would an interest rate) that results in a net present value of the cash inflows (investments) and cash outflows (returns or withdrawals) equal to zero. More weight is given to the earlier cash flows than to the later cash flows because of the time value of money.

For the investor, the IRR is important, but an often overlooked number.

It's an important number because it is the tool that gives the investor the ability to compare investments. That is, the IRR normalizes the results for different investments.

Take for example two rental properties that are for sale. The offer price for both buildings is about the same. Projected rents are about the same. However one will have a higher upfront renovation cost while the other has higher property taxes. How does an investor know which purchase represents the better investment?

They can use an IRR calculator to make this determination.

A note of caution. When comparing investments, never make the comparison using internal rates of return calculated with different calculators.

Why is that?

Because two different calculators may calculate the results slightly differently. Neither one of them will necessarily be wrong either. (Consider for a moment that Microsoft Excel has two IRR functions that may calculate different IRRs for the same cash flows.) You don't need to get hung up on this idea. But it is something to be aware of so that you understand how to use the results correctly.

For the record, this calculator calculates the IRR by counting days (some calculators count periods).

In finance jargon, the net present value is the combined present value of both the investment cash flow and the return or withdrawal cash flow. To calculate the net present value, the user must enter a "Discount Rate." The "Discount Rate" is simply your desired rate of return (ROR).

The NPV is the calculation investors use to learn if they are paying too much for an investment (or if they could pay more) relative to the rate of return they want to earn. If the net present value is negative, the initial investment is too high for the investor to meet their goal ROR. If the NPV is positive, the investor can pay that amount more for the investment, and they'll still earn what they want to earn.

Here's an example....

Jack invests in already issued mortgages. Jack can buy a mortgage for $190,000 that has 210 remaining monthly payments of $1,235.90 each. The next payment is due on June 1. Jack wants to earn 6% on his investments.

Is this a good deal for Jack?

Follow these steps.

- Enter -190,000.00 for the "Initial Investment"
- Set "Initial Investment Date". In this case, that's the date Jack plans to purchase the mortgage. Use May 22 to follow along.
- Click on "Add Series". Create 210 monthly entries of $1,235.90 starting on June 1.
- Enter Jack's personal "Discount Rate" i.e. 6% — the ROR he wants to earn on his investments.
- Click "Calc"
- IRR = 3.847%
- NPV = -$27,198.22

At 3.8%, Jack will not earn the 6% he desires.

What is Jack to do?

This is where the NPV calculation is useful. It tells Jack that he is paying $27,198.22 too much for the investment. See for yourself. Change the "Initial Investment" to $-162,801.78 ($190,000.00 - $27,198.22) and click "Calc" again. Now we have:

- IRR = 6.0%
- NPV = 0.0

Jack is now a happy man assuming he can negotiate the price he needs.

Note: When the NPV is positive, that is the amount the investor can increase the initial investment by and still receive the desired ROR.

I think users will find these enhancements useful:

- "Add Series" option. Create repeated cash flows easily. Work with hundreds of cash flows without manual entry.
- Creating entries with "Add Series" does not populate the existing dates with values or reset the existing values. It creates NEW entries. If a cash flow entry exists on July 1, and you then use the "Add Series" feature to add monthly cash flows starting on June 1, you'll have two entries for July 1.
- "Add Series" feature can be used to add additional "0" entries that you can manually edit. There is no longer a restriction to 96 inputs.
- Use the "Remove 0's" feature to be left with a nice clean look.

- Now prints all cash flows
- Optionally removes zero entries so as not to print.
- Net Present Value Calculation - NPV
- Dates created from "First Cash Flow Date" not "Initial Investment Date."

Calendar Tip: When using the calendar, click on the month at the top to list the months, then, if needed, click on the year at the top to list years. Click to select a year, select a month and select a day. Naturally, you can scroll through the months and days too. Or you can click on "Today" to quickly select the current date.

If you prefer not using a calendar, single click on a date or use the [Tab] key (or [Shift][Tab]) to select a date. Then, as mentioned, type 8 digits only - no need to type the date part separators. Also, because the date is selected, you do not need to clear the prior date before typing. If your selected date format equals mm/dd/yyyy, then for Dec. 1, 2016, type 12012016.

And one more time: you do **not** need to enter the cash flows in date order. You have a computer. It and this calculator are smart enough to sort the cash flows for you once you've clicked the "Calc" button. :-)

IRR is the annualized return on an investment expressed as a percentage.

The investment can be made up of a series of cash flows. That is, there can be more than one investment or one withdrawal. (However, there has to be at least one or each.) The cash flows may occur on any date and for any amount.

It is important to use the right sign (positive or negative) for each cash flow. How do you know what the correct sign is?

Think of it this way. When you first invest, you have to write a check or transfer funds. Writing a check decreases your account balance. Therefore, enter all investment cash flows, including the "Initial Investment" as negative values

When you earn money back on your investment, you can deposit it into your checking account. The return increases your account balance. Therefore, enter all investment returns, including the final liquidation value of your investment, as positive values.

The scheduled dates update every time you change the "Cash Flow Frequency." The new dates are calculated based on the "First Cash Flow Date." But the "Cash Flow Frequency" has no direct impact on the IRR result per se. The calculator only uses the "Cash Flow Frequency" setting to create dates that most closely match your investment cash flows. If, in general, you only make additional investments (or withdrawals) twice a year, then set "Cash Flow Frequency" to "Semiannually" for example.

**Also, zero amount cash flows have no impact on the IRR result.** You may set the frequency to "Monthly," and if there are only four cash flows in a given year, you just leave eight set to 0. (This also applies to 0 cash flow amounts after you've entered the final liquidation value as well.

**You do not need to enter cash flows in date order.** The calculator will sort them before calculating the result. This feature is handy, of course, if you realize that you missed entering a cash flow. Enter the amount in any available cell. Then change the date associated with that cell. Click "Calc" to sort.

If you mistakenly duplicate a cash flow, simply set one of the duplicates to "0".

Changing the "First Cash Flow Date" will reset the dates without clearing the values you've entered.

Depending on the order you use "First Cash Flow Date," "Remove 0's" and "Add Series," the "First Cash Flow Date" will frequently not be the first date in the input area. This is not a bug. Changing "First Cash Flow Date" initializes a series starting on the date selected. However, the user can change the date, or it can be removed with "Remove 0's" if the value for the start date is 0. Finally, a user can insert a series with a date before "First Cash Flow Date."

What a great tool. Thank you so much. I am astounded at how many investment professionals don’t understand that IRR is the only accurate way to measure an investment. I do have one suggestion. When you print your inputs and results, the printout only shows the first 18 input fields. I input about 50 fields, but had not way to print out all of the data, along with the results, to put into my file But I am quibbling. Thanks again.

Thanks, Larry, and you are correct about the lack of understanding around IRR. Stay tuned, this calculator is being updated as we speak.

Thank you Karl…that one enhancement will make this calculator a 5 star resource! I just began using it yesterday and it is very easy to use. Many thanks!

Larry, I released a major update to the IRR calculator. One of the enhancements made was to the printing routine so that a proper schedule can be printed. Please see the web page for the other enhancements. Thought you might like to know.

Hi,

I am business management student. I want to calculate IIR for the Solar project:

please help me to do the calculation.

Total investment coast= $ 58,000,000.00

Debt- 75%

Equity=25%

Annual electricity price inflation rate= 16.3%

Project duration= 20 yrs

Tax rate= 25%

Annual saving interest rate= 5%

best regards

Suranga

I’m happy to help, but I’m not going to do your homework for you. 🙂 What questions do you have about how the calculator works? An IRR ultimately boils down to an analysis of the cash flows. I don’t know how you would calculate cash flow from the parameters you’ve been given. Do you?

The IRR calculator does not seem to be taking cashflow inputs today. When I enter the cashflow – I see a brief yellow bar flash across the entry area. And, the cashflow cell remains blank after the input. Please advise. Very much appreciated.

Fixed. (If you try it, and it still does not work, then do a hard refresh of the page so your browser picks up the latest code change. A hard refresh is done by press Ctrl-F5 on Windows. Not sure about a Mac.)

Thanks for letting me know. It looks as if I broke this calculator this past Monday or Tuesday morning when I updated another calculator.

Probably close to a 1,000 people may have tried using it since then and you are the only one who to the time to mention the problem to me.

I would appreciate it, if you could define “Gross Return”

Thanks

Sure. It’s the percentage gain or loss. If the amount invested, in total is 1,000 and the amount returned is 1,500, then the gross return is 50%. Timing or the investments or their individual amount do not figure into the calculation.

Do you have a calculator that will tell me what my APY is when multiple investments have been made on irregular dates? I am trying to calculate the APY for a 529 – I have invested multiple times once a year but on varying dates. The IRR calculator seems to be only for consistent investments weekly, monthly, etc. It’s not too complicated but I haven’t been able to find a calculator to do it, here are my investments so you can see what I mean.

01/03/2014 – invested $4000

12/24/2014 – invested $4000

12/20/2015 – invested $4000

12/23/2016 – invested $4000

I have not removed any of the money invested and the total value is now $18,952.29. Thanks for your help!

Hi Mac, thanks for posting here.

The IRR calculator is designed to handle your calculation. The "Add Series" feature was recently added to reduce the need for repetitive data entry.

If your cash flow isn’t regular, you should be able to click on a date once and the calcultor will go into edit mode. If you click on it twice, a calendar will pop up. You can change the date to what ever you need. (Note the image of the calendar on this page. You can click on the month or year to make date selection faster.)

Also, you do not need to keep the entries in date order, the calculator will sort them once you click on the calc button. So if you miss entering a cash flow, just stick it on the end with the correct date.

Hope this helps.

I think I figured it out, thanks Karl!

You’re welcome, and thanks for letting me know.

I am trying to calculate the IRR for a single payment immediate annuity. Initial payment is 400,000 starting 9-1-2018 with monthly payments. It is not generating correctly. Thanks

Sorry you are having difficulties, but this sounds like a pretty vanilla type calculation to me. What do you mean by "it is not generating correctly?" Are you expecting a particularly IRR and the calculator is calculating a different result? Or are you not getting a result at all? Do you see any error messages?

4-2-18

What calculator do I use to illustrate a dollar invested on a certain date followed by a withdrawal on a certain date followed by an ending value on a certain date?

Pat

Thanks for the follow-up Pat. It helped. You want to calculate the rate of return.

This calculator will do just fine (as would the other one).

Taking your example, you would enter the values this way:

–200,000*)*****It is not necessary to change the date because this date is only used as a starting point to generate the empty cash flows with dates below. Since you have only 3 values, I simply entered them into the calculator and set the dates as needed. All other entries with 0 amounts are ignored.**These are positive values. The initial value is negative as the investment (you wrote a check, symbolically at least, decreasing you checking account balance). The final two values are positive, because they represent an actual withdrawal as well as the ending value which is a potential withdraw (money going back into the checking account increasing its balance).Note, the annualized rate of return (IRR) is negative. Not sure if you already realize that. This make sense, because the total of the withdrawal plus the ending value is less than the total amount invested.

I’ll leave it to you to do the actual calculation.

This is a good question. I’m also going to answer it later on the Ultimate Financial Calculator page in case you were interested in learning how that calculator works.

Fortunately for me, you’ll get the same answer regardless of which calculator you select. 🙂

Dear Karl,

can you please explain about discount rate? what actually discount rate means? i am trying to make some calculation with different discount rate, i notice that higher discount rate result in lower NPV and vice versa, can you please explain what is the relation between discount rates and NPV

i am a rookie in financial calculation, sorry.

I’ll certainly try. Here are a couple of things to think about.

Take just the word "discount," it means a reduction for the usual amount. Take any amount and increase the discount and the result will be lower than it would be if the discount were less.

As applies to this calculator, "discount rate," discount rate could have also been labeled "investment rate of return (ROR)." The difference in the two depends on your perspective. The ROR is the rate you would apply to a starting amount and futures cash flows to find out the ending value. But in this case, since we are starting considering all the cash flows and the ending value and we want to know what their net

presentvalue is, that is, we are discounting the cash flows, we call the rate the "discount rate."If this isn’t clear, just say so. But as I say, it’s a matter of perspective.

Now, this brings me to your comment about trying different "discount rates." Normally one doesn’t try different rates. The discount rate is the rate you expect that you can earn on your investments. Generally, one enters a "safe" rate. You do this so you can compare a different investment your expected safe investment. If you can invest at a 2% safe rate, then use 2% as the rate. THen enter the cash flows for the investment you are considering. Say you buy a rental unit for -$300,000 (initial investment) and you rent if for $1,200 a month and then sell it for $390,000 in 5 years. If you enter those details and then the NVP is a positive amount, the calculator is telling you, in dollars, how much more you are earning than your safe investment would return.

If the NPV is negative, then you aren’t even earning your safe return.

Dear Karl,

Your explanation is awesome, i am clear now, my other question is, can i consider the discount rate as a cost of capital instead of ROR In case i take a bank loan to funding my investment?

Thank you for your explanation Karl, i really appreciate it, you are one of the few person in this world who would like to spend your valuable time for others, God bless you my friend

Regards

Hendrik

Thank you for your kind words. Glad it was useful.

Yes, you could also use your cost of capital rate for the discount rate. In that case, if the NPV is positive, your investment return is greater than your borrowing cost. (Certainly a good thing!)

HII I HAVE A VEHICLE LOAN 500000 ON THAT THEY CHARGES IRR 27,I CONFUSED WHAT THEY CHARGING THE MONTHLY INTREST

To see the monthly interest on a loan, please try the loan calculator.

Here’s one for you.

I invested $1,800,000 in 2008

the promise was that as a Preferred Investor I would receive a 20% IRR and my original investment before any common partners take any distributions.

I am waiting for my distributions and now it’s 2018.

So, what amount should I get in total at this point to satisfy the contractual promised return of IRR and original investment.

thank you

wayne

You can use this calculator.

Scroll down the page to the tutorials. See tutorial #2 for calculating the final value. Since the IRR is an annualized rate of return, set "Initial Compounding" to Annually.

Enter 20% for the interest rate. Now the interest rate is not exactly the same as an IRR. But if you go to "Settings" and click on &Analytics" there is an option for including the "IRR" on the schedule. You’ll see how close the final value is to the 20% IRR. When I used Jan 1, 2008 and Aug. 21, 2018, the final value calculated is within half of a percentage point of the 20% IRR. The difference is because the calculator is calculating the final value using an interest rate and not an IRR and the fractional year. But with this calculator, you should be able to back into the exact final dollar amount pretty quickly.

Hi, i need to calculate IRR and NPV for 3 projects. Where the cash flow is this for each project. With a market rate of 9%.

My problem is when i calculate for Gamme i get #NUM!? Also for Omega i get a IRR of 400%, is this correct? as it seems very high?

Alfa

Year 0

-1777776

Year 1

400000

Year 2

-224000

Gamma

Year 0

34400

Year 1

-80000

Year 2

48000

Omega

Year 0

-2000

Year 1

200000

Year 2

-50000

Let’s just take one example. The cash flows you are showing for Alfa, say there was an initial investment of -1,777,776. and a withdrawal in year 1 of 400,000 followed by another investment of -224,000 in year two. There is nothing indicating a final value. If the value of the investment is 0, then fine, but if the value as of the evaluation date is something other than zero, that amount has to be entered as a positive number as of the date you want the IRR. The reason why it is entered as a positive number is because that’s the amount the investor would receive if the investment were to be liquidated.

I don’t think that i understand this correct, is the IRR so 5% for Alfa og the NPV 605? for gamma no IRR og NPV of 1.290

Omega iRR=400% and NPV-23.610?

Sorry, but I can’t answer your question, because I don’t understand the cash flow and because you did not answer my questions. Most significantly, what is the ending value of the investment as of the day you want to know the IRR?

I dont get any ending value of the investment, so i don’t know what to do about it, the only information i get are these cash flows, and that the market rent is 9%. Then they want me to find IRR.

The IRR can’t be calculated without an ending value. Think of it this way, suppose an investor had made 3 annual investments and has received no income or made no sales. What could the IRR possibly be?

This is a very common scenario. What you do in this case is estimate the current value of the investment and enter it as a positive value on today’s date (assuming you want to know the IRR for the investment through today). The way you can estimate the current value is ask yourself how much you think you could sell it for if you were to completely liquidate the investment.

And to clarify something, when I say "ending value", I don’t mean the value of the investment when you plan to sell it some day in the future. I mean ending as in the last known or estimated value as of today.

I’m just not very familiar with IRR. I was trying to convert it to ROI terms so my brain could understand the numbers.

Here is how I’m thinking about it for ROI rate per year.

$1,000 investment, $2,000 paid back in one payment after one year =100% ROI rate

$1,000 investment, $2,000 paid back in one payment after 6 months=200% ROI rate

$1,000 investment, $2,000 paid back in one payment after 3 months=400% ROI rate

I just don’t know how to calculate the ROI rate when a payment plan is involved and I’m starting to get some of the money back before the end date. ROI is the number I’m looking for though if possible to calculate this way.

The results that you are showing for the annualize ROI after 6 months and 3 months are not correct. The ROI is much higher. For the 6 month term, it is just over 300%. And it doesn’t matter whether you use this calculator or the below-suggested calculator for when there is only a single investment and single withdrawal.

Please see ROI calculator.

Due to compounding and time value of money, the ROI calculation is not a linear function.

Think of it this way. If you already have $2,000 from a $1,000 investment after 6 months, and you continue to let the investment ride at the same growth rate, you’ll have more than $3,000 after 1 year (not $2,000) because you have the 2nd $1,000 returned in the 2nd 6 months plus the return on the return i.e. compounding. Therefore, the

annualized returnhas to be well over 200%.Annualized returnis about sustaining a rate of return for a year.I think I explained it wrong to start out with.

For my purpose it’s a one time deal where I don’t have the option to “let it ride”.

Let’s say I’m selling some inventory to someone and we’ve agreed on a price of $2,000 but I’m trying to figure out a length of term I can offer them.

I pay $1,000 for the inventory (my cost) and I sell it to them for $2,000. I would only make $1,000 not $2,000….sorry for confusion on that. I wouldn’t be earning interest or anything extra. $2,000 is all I’ll get out of the deal for however long it takes.

I’m just trying to figure out what the ROI rate per year would be for shorter periods of time with payments being collected along the way.

First, I’m sorry I missed your follow-up. For some reason, my admin panel did not show it as a new post.

I understand your point, but the thing is, if you want a rate-of-return annualized, then the annualization means to "let-it-ride". Or looking at it a different way, if you can turn $1,000 into $2,000 in 6 months, annualizing the rate means you are going to do that for a full year. Which means for the example given, the balance will be over $3,000, because your "rate"e; is a $1,000 return in 6 months. To not have over $3,000 means that the "rate" is changing.

But let’s go back to your original scenario with the cash flows. The IRR calculator calculates the annualized ROR (or ROI or IRR). The quicker you receive payment, the higher the ROR. Try it once with 5 of the 6 payments coming in as scheduled and set the final payment to be one year from the investment date. The result will be a lower annualized return. Then try it at 2 years. The rate will be even lower. And this makes sense. An investor would rather have their money sooner rather than later because it’s a higher rate of return. The annualization calculation allows you to compare different cash flows on the same footing.