# How do you calculate your Mutual Fund Returns: CAGR, IRR or XIRR?

You invest Rs 10,000 on January 1 every year for 20 years.
In the first case, you earn a constant 6 percent p.a. for the first 10 years and 12 percent for the last 10 years.
In the second case, you earn a constant 12 percent p.a. for the first 10 years and 6 percent 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?

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 lakh vs Rs 4.91 lakh).
You ended up with a much larger number when you got a higher return of 12 percent 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 percent 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
1. You make a lump sum investment (single investment) and calculate returns for the same.
2. 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.
3. 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).
This article was first published on PersonalFinanceplan.in and can be accessed here.
Deepesh Raghaw is an alumnus of IIM Lucknow and Indian Institute of Information Technology, Allahabad. Deepesh has cleared all three levels of Chartered Financial Analyst program from the CFA Institute USA. Deepesh is also a SEBI registered investment adviser.

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