You invest Rs 10,000 on January 1 every year for 20 years.

In the first case, you earn a constant 6% p.a. for the first 10 years and 12% for the last 10 years.

In the second case, you earn a constant 12% p.a. for the first 10 years and 6% p.a. for the last 10 years.

**Will you end up with the same corpus in both the cases?**

After all, **Compounded Annual Growth Rate (CAGR)** is the same in both cases.

### What is CAGR?

CAGR is the return parameter we use to compare returns for our investments.

CAGR is nothing but the geometric mean of returns for all the years you stayed invested.

If you want to find out CAGR for your investment over 5 years, you need to find out annual returns of 5 years. Let’s say the annual returns for the last 5 years are 10%, 20%, -5%, 6% and 30%.

(1+CAGR)^^{5}= (1+10%) * (1+20%) *(1-5%) *(1+6%)*(1+30%)

(1+CAGR)^^{5}= 110% * 120% * 95% * 106% * 130%

1+CAGR = (1.73)^^{(1/5)}

1+CAGR= 1.1156

CAGR = 11.56%

**Clearly, in both the cases discussed above, the CAGR will be same at 8.96% p.a. **

This is because in both cases, you earned 6% for 10 years and 12% for the remaining 10 years. Just that the sequence of returns was different in the two cases.

**Will you also end up with the same corpus?**

### The answer is NO

### Case 1 (6% for the first 10 years, 12% for the last 10 years)

### Case 2 (12% for the first 10 years, 6% for the last 10 years)

The difference in ending corpus is too hit to ignore (Rs 6.34 lacs vs. Rs 4.91 lacs)

You ended up with a much larger number when you got a higher return of 12% in the last 10 years.

**Why did this happen?**

Because in the first case, a much bigger corpus earns a high return.

In the second case, a small corpus earns a high return in the beginning.

**Sequence of returns matters, when you make recurring investments (or multiple investments)**

### CAGR did not present the correct picture

CAGR is same on both the cases i.e. 8.96% p.a. because it considers only the annual percentage returns. You might feel that you will end with the same corpus because the CAGR is the same.

That is clearly not the case.

**However, you can see the IRR (internal rate of return) is different in the two cases.**

### What is IRR (Internal Rate of Return)?

IRR considers **periodic** cash flows inflows and outflows to calculate returns for you. You can simply use excel function **IRR** to calculate returns.

If you compound all your periodic investments at the IRR, you will get the requisite corpus. Let’s extend the example discussed above.

You can see, if you compound all the investment installments at IRR for the years these installments remain invested, you will end up with the right corpus amount.

### CAGR vs IRR: IRR and CAGR will be same when

- You make a lump sum investment (single investment) and calculate returns for the same.
- You make multiple investments but the
**annual return is constant**across years. These investments can be periodic like a SIP or recurring fixed deposit. By the way, returns in a mutual fund SIP are unlikely to be constant.

### IRR vs CAGR: IRR and CAGR will be different when

You make multiple investments and the **annual returns are variable**. This will be the case with any volatile investment such as equities.

**You should not use CAGR when you want to estimate returns for your mutual fund investments.**

Yes, many portals (such as ValueResearch) show 10-year returns (or 5 year or 3-year returns) are CAGR. ValueResearch is right in showing so because they are merely considering point-to-point returns. And CAGR provides a correct return value for point-to-point returns.

### IRR and XIRR

**IRR assumes that your investments are periodic.** If your investments are not periodic, IRR will not work. You need to use excel function XIRR to calculate returns. Even your mutual fund SIP installments may not be exactly 30/31 days apart. Therefore, if you want to calculate returns for your SIP, use XIRR (instead).

*If you liked the post, your friends may like it too. Please share with friends.*

Denny Anto says

Excellent and useful article.

Deepesh Raghaw says

Thanks Denny!!!

Rajeev Garg says

Very Good Comparison

Deepesh Raghaw says

You are welcome, Rajeev.

Zubin says

This has completely changed my perspective of looking at MF SIP’s. Thank you Deepesh. I was only looking at CAGR until now.

Could you kindly suggest any site which shows IRR for SIP’s?

Deepesh Raghaw says

You are welcome. Please share with your friends too.

For SIPs, XIRR is a better measure.

You can download such statements from CAMS/Karvy websites or AMC websites.

There are many portals such as ValueResearch where you can upload your statements and view XIRR.

राहुल says

I am managing my portfolio on valueresearchonline.com where my each and every transaction is entered and that shows CAGR and I am planning according to that return only.

Am I doing right?

Deepesh Raghaw says

Why do you think it is CAGR?

राहुल says

Thank you ? got the answer just got confused in article

bhavesh kamdar says

Comparison on IRR vs CAGR is really superb and thought provoking.. i think that IRR may not be useful in full extent, if there are dividend transactions in between cashflows..

Simple layman approach is to compare the Total cost with the final realized value..

Deepesh Raghaw says

Thanks Bhavesh!!!

You are right. You need to use XIRR.

If you have invested in dividend option, information about dividends in also needed.

To be honest, dividend option makes sense in only a few limited scenarios. Therefore, most should be ok.

Mihir says

Very well written and explained with help of good examples . Thank you for clearing the confusion .

Deepesh Raghaw says

You are welcome, Mihir!!!

stephen stanton says

Hello Deepesh -Can you provide a simple similar example assuming you invested $-100 in Year 0 and then get $41.67 in year 1, 2 and 3 (total $125). The ROI is a simple 25% (125-100)/100 the simple annual return is is 8.3% which is 25%/3, but the calculated IRR is 12.04%. How do you explain the an investor the difference between the 12 and the 8% return? I understand that it is time value of money, but does the IRR assume the cash flows are being reinvested? If so at what rate? Can you show the math? I have been racking my brain for days trying to explain this.

Deepesh Raghaw says

That is one of the drawbacks of IRR. It assumes cashflows are reinvested are IRR.

Sometimes, this might mislead investors.

There is great memo by Legendary investor Howard Marks on shortcomings of IRR. Please go through it.

R Varadarajan says

To put it simply – we have to use IRR for periodic investments like SIP ad CAGR for single/ one time investment.!!!!

Very well analysed report !!!

Deepesh Raghaw says

Thanks Varadarajan!!!

Yes, that’s right.

SK Sharma says

very informative article. Thanks.

Deepesh Raghaw says

You are welcome, Mr. Sharma!!!

Gopal Sureka says

Very useful and informative article. But perhaps you can guide how to calculate the IRR and XIRR using the excel function.

VIKAS SIVARAMAN says

Thanks Deepesh!!

Do you have an email ID I can connect with u on?

Deepesh Raghaw says

Hi Vikas,

You can write at the e-mail id given at the top.

Alternatively, you can also post your query as a comment.

Udayan Dasgupta says

My portfolio manager and I have been at loggerheads over use of XIRR. He claims that TWRR must be used which is mandated by SEBI and used by mutual funds to calculate NAV. Can you throw some light on this? My problem is that in the current context XIRR is near zero or negative whereas by his calculation the TWRR is a whopting 15%.

Deepesh Raghaw says

Hi Udayan,

Not sure if I got your question right.

MF NAV calculation does not require XIRR or TWRR.

Only PMS performance reporting does.

XIRR and TWRR have their pros and cons and such differences can come depending on timing and quantum of investment.