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XIRR or extended internal rate of return is a measure of return used when multiple investments (at different points in time) are made in a financial instrument. A look at what XIRR represents and how it is different from CAGR.

## What is CAGR?

First, we need to answer a much simpler question.

If I invest Rs. 12,000, and after 5 years the value is Rs. 22,991. What is the *average *rate at which my investment has compounded year after year?

To find this, we write

22991 = 12000 x (1+ CAGR)^5

or

22991 = 12000 x (1+ CAGR) x (1+ CAGR) x (1+ CAGR) x (1+ CAGR) x (1+ CAGR)

Here CAGR represents the year on year compounded growth and is known as *compounded annualized growth rate*

In the present case, CAGR = 13.9%

CAGR is obviously necessary only when the annual returns vary. If the returns are the same (like in an FD), the maturity value will be known the moment you create the FD.

## CAGR vs XIRR

Suppose I invest Rs. 12,000 *once a year* for 12 years and wish to know what is the average rate at which my investment**s **have compounded year after year, the quantity that gives me information is the **XIRR**.

We will now see what the XIRR represents and how it is calculated.

This is the annual SIP investment schedule. The investment is made once at the start of each year. A monthly SIP will follow the same logic but is a bit more difficult to perceive.

The total value after 12 years is **5,17,524**

The same schedule can be viewed in a different way.

The first instalment has 12 years to grow. The second instalment has 11 years to grow, and so on.

We now calculate the final value of each instalment.

The first instalment after 12 years grows to 1,42,693 at a CAGR of 22.9%

The second instalment after 11 years grows to 73,308 at a CAGR of 17.9% and so on.

Each instalment has its own CAGR as the investment tenure varies. The total value of all the investments must be equal to **5,17,524**

Instead of assigning each instalment a different CAGR, what if we assigned a common CAGR?

That is each instalment is *perceived to grow at the same CAGR. *The aim is to adjust this common CAGR until the total value of all the investments becomes equal to **5,17,524**

## How is XIRR calculated?

The last column is the adjusted CAGR. Now all instalments have the same CAGR and total value of all the investments is indeed equal to **5,17,524**

**This adjusted CAGR is known as XIRR**

So our aim should be to **adjust** the CAGR until the total value of all the investments equals the *actual *total final value.

Excel does this adjustment for us automatically using an approximation technique called the Newton-Raphson method (remember that from school?). The technique is not without flaws. Read more here: IRR/XIRR : Limitations of Calculating Complex Cash Flow Returns

In the above illustration, the investments are spaced exactly 365 days apart. In an actual annual or monthly SIP, due to non-business days, the spacing will be greater/less than 365 or 30 days. The spacing does not matter for XIRR. If the spacing is exact, things become simpler and this is often known as an IRR calculation.

## Download a free XIRR Returns Calculator

**About the Author**M. Pattabiraman(PhD) is the author and owner of freefincal.com. He is an associate professor at the Indian Institute of Technology, Madras since Aug 2006. Follow @freefincal “

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Loved this different yet simple to understand approach of explaining XIRR.

Loved this different yet simple to understand approach of explaining XIRR.

Thank you.

Thanks a lot pattu sir.

A very nice article.

Thanks a lot pattu sir.

A very nice article.

A very nice article.

A very nice article.

Dear Mr. Pattu,

This is a good one and timely for the common investors and those initiating into the world of investments, fiance, excel, etc. although day in and day out used by investment bankers like me !!

Dear Mr. Pattu,

This is a good one and timely for the common investors and those initiating into the world of investments, fiance, excel, etc. although day in and day out used by investment bankers like me !!

dear sir

a TRUE PROFESSOR. excellently explained. a very systematic approach.

THANK YOU

dear sir

a TRUE PROFESSOR. excellently explained. a very systematic approach.

THANK YOU

thank you for the post. till i understood the concept, but did use cagr and xirr interchangeable , but now i grasped exact meaning of cagr and xirr and probably irr terms.

thank you for the post. till i understood the concept, but did use cagr and xirr interchangeable , but now i grasped exact meaning of cagr and xirr and probably irr terms.

So for a long term MF returns we should consider XIRR.Right ?

I have also seen sme websites declare annualized returns. Does it serve any purpose in evaluating fund performance

annualised returns calculated is same as xirr for some fixed a/m at the start or sip for the period mentioned, so definitely serve the purpose of studying past performance of the fund. however if we invested , different a/m at different time in the same fund for the same period, we have to calculate our investment xirr through excel , or some other way, and naturally differs from the annualised returns stated on the the site.

Thanks a lot Sir…..nice explanation

Thank you.

The XIRR being shown in cra-nsdl (for NPS website) fluctuates wildly daliy !!!

From +12.5% on one day to -3.5% on the other immediate day in my case (50%C – 50%G)…(first investments done just a few days back)

Any idea y?

You mean in your account? I have not seen that. Anything that fluctuates that wildly daily is not XIRR.

It is XIRR…but i should have framed my question differently…the returns are fluctuating (and so is xirr)….from +42 to -20 to +35 etc…(25000 invested)…but I think it may be because of deduction of charges from my investment (since this is my first investment)..xirr is now stabilizing…

lovely post and a much needed one.

is there a download for the XIRR calculator pattu sir?

Thank you. Yes, this one: XIRR Returns Calculator

Thank you so much. Loved the detailed, clear and most importantly how simple you made it for me to understand. Three cheers to you Sir