 "Use the right measure of return")
Recently, the Reserve Bank of India (RBI) asked banks to pay interest to customers on their savings and deposits every quarter. The question is whether your deposit compounds annually or at shorter intervals (say, every quarter) makes a difference to the final sum you end up with. A person may have invested Rs 1 lakh in a bank term deposit for five years. If his money compounds annually, he will get a sum of Rs 1,43,563 at the end of his tenure. But if it compounds quarterly, he will receive Rs 1,44,995. Clearly the answer is yes.
CAGR and IRR
The Compounded Annual Growth Rate (CAGR) essentially gives the average annual rate at which an investment has grown. The average here is not the arithmetic mean but the geometric mean. CAGR is used in case of investments whose returns are not fixed but fluctuate from year to year. CAGR allows you to compare the returns of such instruments with assets that give fixed returns. Internal Rate of Return (IRR) is another measure of growth. Here, we shall look at different measures of return and the correct context in which each should be used.
CAGR: Frequently used parameter
CAGR is used for assets such as equity, mutual funds, precious metals, commodities and real estate, where the annual return is not fixed. For example. suppose you invested Rs 1 lakh in a gold fund. The value of the fund becomes Rs 90,000 at the end of the year due to a decline in gold prices. In the second year, gold prices zoom by 20 per cent and your investment becomes worth Rs 1.08 lakh. In the third year, it again goes up by 10 per cent, making it worth Rs 1.19 lakh. CAGR is calculated as follows:
Let IV = Initial investment value; FV = Final investment value;
n = number of years it took for your investment to become FV from IV;
CAGR (in per cent) = (power (FV / IV, 1 / n) - 1) * 100.
Here, the CAGR works out to be six per cent. This means that had the investor invested in another asset that gave a fixed return of six per cent every year, he would have ended with the same amount.
Similarly, we can calculate the CAGR for periodic investments at a fixed rate. The fixed rate becomes the CAGR in this case. For example, a recurring deposit scheme giving eight per cent annual return has a CAGR of eight per cent.
Though the simple rate of return is used rarely now, it is essential to know how it works. Interest is paid only on the principal amount and not on the interest earned. Hence, if you invest Rs 1 lakh in any asset at a simple rate of return of 10 per cent, you will receive 10 per cent of Rs 1 lakh, i.e. Rs 10,000 every year. If you invest this again at the same rate immediately, then it is as good as compounded returns.
IRR: A comprehensive approach
In the real world, people do not invest a lump sum amount and stop. They usually invest a little bit every month, say, through a Systematic Investment Plan (SIP). Unless the investment is in fixed-income securities, the returns fluctuate every year. This makes CAGR a cumbersome process to find out average annual returns. In such cases, we use the IRR.
Let us take an example. An investor invests Rs 2 lakh per year for 10 years in a mutual fund that earns 15, -15, -10, 50, 20, -10, -30, 100, -10 and 20 per cent respectively. The final value of the investment at the end of 10 years is Rs 35,25,682, yielding an IRR of 10.1 per cent.
In such a scenario, it will be difficult to calculate CAGR. IRR, on the other hand, makes it easier to calculate return in such cases. Applications like Excel make calculation of IRR simpler. The function to use in Excel is IRR.
Relationship between IRR and CAGR
Since both represent returns on investment, they may give the same result in some cases. For example, if there is a lump sum investment in an asset with a consistent return, a lump sum investment with fluctuating returns, or periodic investment with fixed returns, you can use either CAGR or IRR for such cases. CAGR is preferred because it is relatively better understood by investors. However, when there is periodic investment in assets with no fixed returns, IRR is the better measure to use.
When to use XIRR
Often, the investments are not spaced apart at exactly the same interval. In such cases, the date of investment becomes important. Here, XIRR needs to be used. If the periodic dates do not deviate significantly from one year spacing, IRR can be used, which is fairly accurate for small deviations.
In case of XIRR, the assumption is that people do not save a constant amount every year. They may get bonuses, salary hikes, or sometimes they do not have anything to invest because of sudden expenses. In this case, the average rate of return, as indicated by the XIRR value, is 10.95 per cent.
How to calculate rolling returns
This method calculates returns for various one-year periods rather than relying on a single date separated by one year. For example, you can calculate returns from January 1, 2013 to Jan 1, 2014, February 1, 2013 to February 1, 2014, etc., continue this for 12 months and take the average.
This will give the average return, which is not influenced by short-term events.
In the table (How to calculate rolling returns), we have taken month-wise data, but the same calculation can be done for day-wise data as well. This table calculates average rolling returns from December 1, 2013 to December 1, 2014. The average return, as indicated by rolling returns, is 22.36 per cent.
Analyse your investment pattern and choose the measure of return that suits your investment habits the most.
CAGR and IRR
Read more from our special coverage on "INVESTMENT"
The Compounded Annual Growth Rate (CAGR) essentially gives the average annual rate at which an investment has grown. The average here is not the arithmetic mean but the geometric mean. CAGR is used in case of investments whose returns are not fixed but fluctuate from year to year. CAGR allows you to compare the returns of such instruments with assets that give fixed returns. Internal Rate of Return (IRR) is another measure of growth. Here, we shall look at different measures of return and the correct context in which each should be used.
CAGR: Frequently used parameter
CAGR is used for assets such as equity, mutual funds, precious metals, commodities and real estate, where the annual return is not fixed. For example. suppose you invested Rs 1 lakh in a gold fund. The value of the fund becomes Rs 90,000 at the end of the year due to a decline in gold prices. In the second year, gold prices zoom by 20 per cent and your investment becomes worth Rs 1.08 lakh. In the third year, it again goes up by 10 per cent, making it worth Rs 1.19 lakh. CAGR is calculated as follows:
Let IV = Initial investment value; FV = Final investment value;
n = number of years it took for your investment to become FV from IV;
CAGR (in per cent) = (power (FV / IV, 1 / n) - 1) * 100.
Here, the CAGR works out to be six per cent. This means that had the investor invested in another asset that gave a fixed return of six per cent every year, he would have ended with the same amount.
Similarly, we can calculate the CAGR for periodic investments at a fixed rate. The fixed rate becomes the CAGR in this case. For example, a recurring deposit scheme giving eight per cent annual return has a CAGR of eight per cent.
Though the simple rate of return is used rarely now, it is essential to know how it works. Interest is paid only on the principal amount and not on the interest earned. Hence, if you invest Rs 1 lakh in any asset at a simple rate of return of 10 per cent, you will receive 10 per cent of Rs 1 lakh, i.e. Rs 10,000 every year. If you invest this again at the same rate immediately, then it is as good as compounded returns.
IRR: A comprehensive approach
In the real world, people do not invest a lump sum amount and stop. They usually invest a little bit every month, say, through a Systematic Investment Plan (SIP). Unless the investment is in fixed-income securities, the returns fluctuate every year. This makes CAGR a cumbersome process to find out average annual returns. In such cases, we use the IRR.
Let us take an example. An investor invests Rs 2 lakh per year for 10 years in a mutual fund that earns 15, -15, -10, 50, 20, -10, -30, 100, -10 and 20 per cent respectively. The final value of the investment at the end of 10 years is Rs 35,25,682, yielding an IRR of 10.1 per cent.
In such a scenario, it will be difficult to calculate CAGR. IRR, on the other hand, makes it easier to calculate return in such cases. Applications like Excel make calculation of IRR simpler. The function to use in Excel is IRR.
Relationship between IRR and CAGR
Since both represent returns on investment, they may give the same result in some cases. For example, if there is a lump sum investment in an asset with a consistent return, a lump sum investment with fluctuating returns, or periodic investment with fixed returns, you can use either CAGR or IRR for such cases. CAGR is preferred because it is relatively better understood by investors. However, when there is periodic investment in assets with no fixed returns, IRR is the better measure to use.
When to use XIRR
Often, the investments are not spaced apart at exactly the same interval. In such cases, the date of investment becomes important. Here, XIRR needs to be used. If the periodic dates do not deviate significantly from one year spacing, IRR can be used, which is fairly accurate for small deviations.
In case of XIRR, the assumption is that people do not save a constant amount every year. They may get bonuses, salary hikes, or sometimes they do not have anything to invest because of sudden expenses. In this case, the average rate of return, as indicated by the XIRR value, is 10.95 per cent.
How to calculate rolling returns
This method calculates returns for various one-year periods rather than relying on a single date separated by one year. For example, you can calculate returns from January 1, 2013 to Jan 1, 2014, February 1, 2013 to February 1, 2014, etc., continue this for 12 months and take the average.
This will give the average return, which is not influenced by short-term events.
In the table (How to calculate rolling returns), we have taken month-wise data, but the same calculation can be done for day-wise data as well. This table calculates average rolling returns from December 1, 2013 to December 1, 2014. The average return, as indicated by rolling returns, is 22.36 per cent.
Analyse your investment pattern and choose the measure of return that suits your investment habits the most.
The author is co-founder and CEO, BankBazaar.com