##### February 14, 2020

### XIRR v/s CAGR: Do you know the difference?

###### Jinay Savla

###### Founder, Indigenous Investors

**XIRR v/s CAGR: Do you know the difference?**

CAGR and XIRR are the most commonly used investment terminologies in the financial services industry while describing the investment returns to an investor. At times, an investor tends to get confused whether the two are the same or carry some stark difference. Well, so do advisors.

This article was nudged by Mr. Amit Bivalkar, Director of Sapient Wealth Advisors at one of the Network FP Masterclasses to understand the concepts of CAGR and XIRR in detail, how they are used by financial advisors and how the two concepts are different from each other.

Let’s start by looking at the definitions.

To understand the distinction between CAGR and XIRR, we need to understand their implication in case of cash flows of varied nature. I put forward two different observations:

__1. CAGR and XIRR will be the same in the case of a lump sum investment (with varied growth rates over a period of time.)__

** Scenario 1:** Rs. 1 lakh invested at the beginning grows at 5% in the first 5 years and 10% in the next 5 years

** Scenario 2:** Rs. 1 lakh invested at the beginning grows at 10% in the first 5 years and 5% in the next 5 years

**Observation:**

A reader would notice that in these 2 scenarios, Mr. X’s investment of Rs. 1 lakh will generate the same amount of corpus after 10 years. Compounding at different rates for different time periods don’t have any impact since there are no cash flows.

At this juncture, similarity between XIRR and CAGR ends. And there is a tendency to overlap between the two as they show similar returns.

__CAGR and XIRR are the same in both the cases.__

As our fellow advisors would have noticed that in mutual fund fact sheets, returns are shown on a 1 year / 3 years / 5 years basis which typically doesn’t involve any cash flows, there tends to be a confusion between XIRR and CAGR.

Only difference is that in Scenario 2, the investment will compound at a faster rate in the first 5 years and in Scenario 1, investments will compound at a faster rate in the remaining 5 years.

__CAGR and XIRR will be different when there are multiple cash flows due to which annual returns for each cash flow is variable (with varied growth rates over a period of time.)__

A brief background

Extending on the context of above two scenarios, suppose Mr. X, an investor decides to invest Rs. 10,000 every year for a period of 10 years. In the first scenario, the investments grow at 5% in the first 5 years, then 10% in the next 5 years. In the second scenario, the investments grow at 10% in the first 5 years and then at 5% in the remaining 5 years. Here, we are trying to figure out whether the CAGR and XIRR will be similar or different in both the scenarios.

*As part of the exercise, we recommend you to do a quick calculation in your mind as well.*

** Scenario 1:** Investments grow at 5% in the first 5 years and then at 10% in the next 5 years.

**Scenario 2**: Investments grow at 10% in the first 5 years and then at 5% in the next 5 years

**Observation:**

In the first scenario, Mr. X makes a decent Rs. 1,60,596 at the end of 10 years with an investment of Rs. 1 lakh. Whereas, in the second scenario, Mr. X makes Rs. 1,43,729 at the end of 10 years.__ A reader would observe here that the magic of compounding can lead to a better experience when the investments are compounded at higher rates towards the end of the tenure.__

**Whereas the interesting part here is that CAGR in both scenarios remain the same, in fact a reader would notice that CAGR has remained the same in all 4 scenarios, the reason for this is that CAGR is a geometric mean of returns and has nothing to do with cash flows during the period. Hence, a reader might feel that Mr. X will end with the same corpus because the CAGR is the same. That is clearly not the case.**

**Yet, there is a difference in XIRR. Sequence of returns matters, in case of recurring investments (or multiple investments).**

**How does an investor with a layman approach to finance looks at returns?**

‘Returns’ is the most important part of conversation for any investor. The objective is simple; money should make more money. Let’s say for example, a person born in 1960s or 70s has a very different way to think about investment return. The conversation with such a person is pretty straight forward, he or she bought a house in 1990s worth Rs. 10 lakhs which today can be sold at Rs. 1 crore. In their conversation, Rs. 90 lakh is their investment return. No second thoughts. But if you ask a person who understands finance, he would take out his calculator, run some numbers and say it’s just 8% Compounded Annual Growth Rate (CAGR) in a period of 30 years.

Since, a lot of investors tend to use CAGR for a house since they look at point to point investment returns as there is no cash flow in between.

In case of investments in mutual funds for instance, an investor tends to have multiple cash flows in the form of Systematic Investment Plans (SIPs) or partial redemptions for different periods of time. At such a time, an investor can calculate CAGR for each SIP which will be for a different duration at a different rate than other SIPs or XIRR can be simply used to ascertain the investment returns for the same.

**In a nutshell, an investor should look at XIRR when there are multiple cash flows and returns generated. But in case of point to point investment, CAGR can also be looked at since the XIRR too will remain the same.**

worth reading

Thank you very much

I think there is typographical error in column % return during the year of Scenario 2 of XIRR with cash flow option.

First 5 entries should be @10% and last 5 @5%

Yes there was an error when the article was initially posted. The same has been rectified, please let us know if you want to bring anything else to our attention.

Dear Sir, There seems to be a misprint in the 4th table. Kindly check and repost. Regards

Yes there was an error when the article was initially posted. The same has been rectified, please let us know if you want to bring anything else to our attention.

Very nicely explained

Thank you very much

Hi – can you also explain how the cagr was calculated for each of the cases ?

CAGR is arrived by calculating the geometric mean of all the returns in a year. Formula ignores the initial values and final values and only considers the annual returns.

Very nicely explained along with examples.

If you can share the formula (excel formula) for calculating both CAGR and XIRR, it would be a great help.