What is the difference between * Annualized Return*, Compound Annual Growth Rate (CAGR), Internal Rate Of Return (IRR) and XIRR in personal finance?

As you are aware that each and every investment comes with a risk. If you are not aware of the risks associated with the investments made, investing in any area is like playing on a casino table.

Investing in fixed deposit was very much in fashion for past few decades. This was the most preferred form of investment by our parents and their peer groups. They have a rigid structure with fixed return given for the money deposited at the bank. With interest rates now falling across the board, banks are forced to lower the interest rates and thus the income on FD’s have now reduced considerably. However, there is almost zero risk associated with investing in FD’s of reputed banks and the returns are guaranteed and timely.

Mutual funds have a disclaimer that mentions risks and perils of investing in an equity market. Within a given investing period of 5-10 years, mutual funds have been known to post a return of >14% CAGR depending on the funds purchased.

Why are these calculations important? Why do we see mutual fund websites highlight their CAGR performance and how do they calculate CAGR performance?

I am sure that if I do not provide the description of these concepts in the beginning itself, my readers will not be able to relate to the article and may not read this article completely and will leave them midway.

**What is an Annualized Rate of Return?**

The annual gain which you make on your investment is called an annualized return. It can be a simple annualized rate of return, an average simple annualized returns or compound annual growth rate.

**What is the difference between annualized return and absolute return?**

Absolute return is the total return that one gains throughout the entire span; where as annualized return is when you divide the returns by the number of years.

The difference between annualized return and absolute return is that the total return you have gained through a span of time is the absolute return. When you divide it by number of years, it becomes annualized return

Let’ look at this with an example – Mr. Sumit invested an amount of Rs. 100,000 in a mutual fund. After 5 years, his fund value has grown to Rs. 130,000. The absolute return in this case is 30% (130,000-100,000)/100,000) while annualized returns is 5.4%.

**Annualized Return, CAGR, IRR & XIRR – Where to Use**

- AAR is useful when you have invested your money in Fixed Deposits (FD), National Savings Certificates (NSC) or Kisan Vikas Patras etc. This will tell you the exact rate of annualized return in the span of 5-10 years.
- CAGR is useful when you have invested lump sum money in stocks or mutual funds and value of your money is fluctuating every now and then.
- IRR is useful when you are investing your money at regular intervals or on a periodic basis like SIPs. The amount invested may vary but the time of investment is at regular intervals.
- XIRR is useful when you are investing at irregular intervals on a random basis.

**Annualized Rate of Return Formula in Excel**

**Simple Annualized Returns- How do you calculate the average return? **

Average return is calculated in the following manner- If one invests Rs. 10,000 and gets a simple interest rate of 1% per month, your money will grow to Rs. 11,200 after one year and you will be entitled to 12% simple annualized returns.

**Average Simple Annualized Returns (ASAR)**

**How is an annualized return calculated?**

Let’s invest a sum of Rs. 10,000 for 5 years where the investment grows to Rs. 20,000 at the end of the 5 year period. The average simple annualized return in this case will be at 20%. Let’s see the breakup of the annualized return value:

- Average Simple Annualized Returns = (Final Value – Invested Value)/5*100
- ASAR = (20,000 – 10,000)/5*100 = 20%
- Average Annual Returns can also be calculated by arithmetic mean of returns in different years

Suppose you are investing (same amount) in different avenues every year:

2011 – 20%

2012 – 18%

2013 – 16%

2014 – 22%

2015 – 24%

AAR will be calculated at (20+18+16+22+24)/5 = 20%

**Compound Annual Growth Rate (CAGR)**

**How to calculate annualized return in excel? **

Compound Annual Growth Rate or CAGR calculates the annual compound interest rates which one receives on their investments. It takes into account the final value and initial value of the investment made. CAGR is normally used when there is wide fluctuation in the investments made during a particular period of time. This happens mostly in cases of stock prices or equity mutual funds.

For example, if you invest Rs. 10,000 for 5 years and your money grows to Rs. 20,000 after 5 years; your Compound Annual Growth Rate will be 14.87%. This is derived by using the below mentioned formula.

CAGR Interest Rates = (Final Value/Initial Value)^(1/n)-1=(20,000/10,000)^(1/5)-1=14.87%

The difference between ASAR and CAGR is that ASAR calculations are based on simple interest rates whereas CAGR calculations are based on compound interest rates.

CAGR is normally published on mutual fund websites to show the performance of their funds for more than one year period.

**How to annualize monthly/quarterly/daily returns**

The formula remains the same to calculate the annualized returns from monthly/quarterly and daily returns

CAGR Interest Rates = (Final Value/Initial Value)^(1/n)-1

For monthly returns – Change the value of n to 12

Quarterly returns – Change the value of n to 4

For daily returns – Change the value of n to 365

**Internal Rate of Return (IRR)**

IRR is calculated, when one invests at regular intervals of time such as SIP investments in mutual funds, where there is a date fixed or regular intervals for deduction of money from your account.

For example, if I invest in Mutual Funds SIPs, I will be eligible for the following rate of return on my investments. My investment of Rs. 1,000 per year will yield me Rs. 10,000 as the value of money in my 7^{th} year of investment. This means that the IRR will be 15%.

**How to calculate IRR manually?**

To calculate IRR manually, you need to use an excel spreadsheet and choose the financial formulas in excel

**IRR Formula Excel with example**

Go to Excel **-> **Go to Fx **->** Financial Formulas **->** IRR

Capture the values – Your invested amount will be in negative – Any dividend received or final value will be in positive.

**Internal Rate of Return for Irregular Cash Flow (XIRR)**

XIRR is typically used in cases where there are irregular cash flows. This is important for people who are not investing on regular intervals.

There can be various reasons for investing at irregular intervals:

- I am a businessman and I invest whenever I get excess cash flow
- Being a salaried person I invest whenever I receive my annual bonus
- I need to invest for my tax savings and I invest towards financial year and

**How to calculate XIRR – Formula?**

Go to Excel **->** Go to Fx **->** Financial Formulas **->** XIRR

Put the values – Your invested amount will be in negative – Any dividend received or final value will be in positive – Use any guess value like .5, 1 etc

**Conclusion**

In conclusion,I hope this article will help to calculate the returns according to your investments. Do not be misled by the advisors who show you the CAGR returns when you want to invest in SIPs or show you IRR when you are not investing at regular intervals.

Do share this article with your family and friends if you have understood the difference between Annualized Return, CAGR, IRR& XIRR finally.

Khalid says

Mr. Sumit invested an amount of Rs. 100,000 in a mutual fund. After 5 years, his fund value has grown to Rs. 130,000. The absolute return in this case is 30% (130,000-100,000)/100,000) while annualized returns is 5.4%.

If i divide 30,000 by 5, by the given formula, annualized return should be 6% instead of 5.4%? Please let us know if it is a typo, or i understood it incorrectly.

MoneyChai says

Hi Khalid

The annualized returns would be 6% and CAGR would be 5.4%