 # CAGR Full form & How to calculate It without a calculator?

CAGR Full form stands for compounded annual growth rate or CAGR and is calculated by the following formula, often used in investment decisions. Its the average rate at which an initial total investment grows for x number of years.

In this article, I will not only explain the calculation but also discuss a shortcut to calculating CAGR using mental maths.

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## CAGR Full Form and Meaning

I will cut to the chase and jump right into examples which is more helpful in understanding.

So, let’s assume you bought a piece of land in 2010 for \$10000; afterwards, ten years, you end up selling at \$20000. What is the Average annual growth rate ?

The usual instinct is to know if we did good, bad or ugly, right?

Now I could answer the good, bad or ugly in multiple ways;

1. Times the Initial total investment: I could say I made twice what I invested.
2. Percentage Change in the value: Which is to say, by how much % did it change from its initial value of \$10000?
3. Average rate: The average rate at the property increased in its value over ten years.

So, the correct answer depends on what makes more sense to you. None of the answers and approaches is incorrect, but here are the issues.

Firstly, option one doesn’t give you the time frame. This means if, in a similar situation, your friend had doubled the value in 5 years instead of 10, then this won’t be captured.

Secondly, option 2 suffers from the same problem as option 1, but only the format of the problem changes. E.g., My property increased in value by 50% but in how many years?

Hence, the third option is more practical to include the time factor along with the change in value.

## Key Meaning of CAGR Full Form

• Property Increased by 2 X
• Value increase by 100%
• The value increased at a rate of ((20000/10000)^(1/10)-1)= 7.17%. Or simply, the CAGR earned was 7.17%.

A very common confusion can be related to the (^ 1/n), which is nothing but a proportionate division of the 100% increase across ten years.

So 7.1% across ten years, but an obvious question might be 7.1% x 10 = 71% then how did the value increase by 100%?

And the answer is compounding, or interest on interest. However, I’ll keep the concept of compounding for another time.

## Rule of 72 For Compounded annual growth rate

Now, you don’t want to be that guy who always opens his calculator for every such calculation. There is a very easy method by which you can approximate CAGR.

E.g.;

• At 20%, the value doubles in 3 years
• At 7%, the value doubles in 10 years

So what’s the magical way?

Simply Divide 75/(No of years)= to get an approximate CAGR.

You could also reverse the formula and calculate the years it takes.

For eg; 75/ 7%= 10 years, 75/20= 3 Years approx.

So 75 is the number.

## How to calculate the CAGR in Excel

Chicken it is to calculate CAGR in Excel! Simply put following are how you could calculate CAGR.

• Rate Function
• Manual algebraic
• RRI Function

All are the same in output, but it varies depending on the data you are working with.

So, I’ll elaborate a little here.

Firstly, the rate function is used fully when you are dealing specifically with situations where you are also dealing with periodic additional investments or withdrawals, which is signified by the PMT(Payment Variable).

Notice that in this example, we don’t have any additional periodic investments or withdrawals hence PMT is zero. Also, notice that investment is shown with negative signs, which means outflow.

Secondly, the manual algebraic method is preferred when we are dealing with a single-cell calculation.

Thirdly the method of using RRI is good when you are not good with algebraic calculation altogether.

Notice that in the case of the RRI function, you don’t even have to worry about the signs. It automatically assumes that the investment value(PV) is negative.

However, in any of the three methods, the answer is the same.

## Use cases of CAGR

Majorly the use cases are in economics and immense in the case of finance.

Frequently you should see the use of CAGR in GDP Growth rates or inflation rates. Similarly, in finance, you will see mostly all investments coming with the calculation of CAGR in their brochures.

## Example

Imagine you have invested \$10,000 in a savings account. The return for three year period of time is outlined below : What is the compounded annual growth in the investment period?

Solution:

As you can see, the returns for every year are not constant. By using the formula, the CAGR can be calculated as follows:

The CAGR of 23.86% over the 3-year investment can assist the investor in comparing alternatives for his capital or making forecasts of future values. Furthermore, he can even predict what his returns are going to be after a few years.

Let us look at another example where the CAGR is known to us, and we have to calculate the future value. Say you have invested \$5,000 in a stock mutual fund with an average CAGR of 26%, and you want to find out your approximate returns after ten years. According to the CAGR formula, the final value will be,

After solving this, the value of the return after ten years will be approximately \$50,428.

## Importance of CAGR

CAGR is one of the most popular variables used to determine the profitability of an investment. One of CAGR’s advantages over an average rate of return is that it is not influenced by percentage changes that may yield misleading results. For example, look at the following example :

His example shows that the portfolio’s value increased by 25% to \$1,250. The following year, the returns dropped down by 25%, and the final value of the portfolio was \$937.5. Even though the average returns are 0%, there is a loss of \$62.5. Using these values, the CAGR comes out to be -3%. Hence the CAGR is more accurate than the average returns.

Let us look at another example where the CAGR is known, and we have to calculate the future value. Say you have invested \$5,000 in a stock mutual fund with an average CAGR of 26%, and you want to find out your approximate returns after ten years. According to the formula, the final value will be,

After solving this, the value of the return after ten years will be approximately \$50,428.

There are a few disadvantages of CAGR as well. The most important limitation of CAGR is that it calculates a smoothed growth rate over a period, Hence, it ignores volatility and implies that the growth during that time was steady. Also, CAGR does not account for when an investor adds or withdraws funds from his portfolio. Another disadvantage of CAGR is that it only represents past growth, and the investor cannot assume that the CAGR will be the same in the future as well. 

A third limitation of CAGR is its representation. Say that an investment fund was worth \$10,000 in 2016, \$7,100 in 2017, \$4,400 in 2018, \$8,100 in 2019, and \$12,600 in 2020. In 2021, the fund manager will represent that the CAGR was a whopping 42.01% over the past three years, but when it comes to the CAGR over the past five years, it is only 4.73%. 

## #Is 7% CAGR good for investments?

In case we are looking at investment portfolio returns, then a 7% CAGR is not good because the government bonds rate itself is 7.25% on a risk-adjusted basis. We have to look at things in context. E.g., a 20% CAGR for three years means your money doubles every three years. Rarely can anyone sustain such higher returns consistently for long periods? Hence in terms of investing, anything above 15% CAGR is superb. The rest is putting in the money and letting it work, and being patient.

Compounded annual growth rate calculations are very common in financial modeling.

## #What is a good growth rate for sales?

I can categorize this answer based on the stage of the company.

• A start-up can have a CAGR of 50% for the first 3-5 years. The reason is not that the company is growing that fast, but it’s starting from nothing hence the returns appear higher.
• Mid-sized companies targeting anywhere between 25-30% CAGR annual increment in sales.
• Large-size companies would be good even with a 15-20% CAGR.

I would like to point out that a higher CAGR should be hand in hand with growth in earnings too.

## #XIRR versus Compounded Annual Growth rate?

Consider the above example. If I had invested in the NIFTY 50 index in 2005 and withdrawn in 2021, then the regular CAGR calculation would have given me 12.622%.

However, when I use the XIRR function, it gives me 12.612%.

So, why the difference of 0.010%?

That is because, in an XIRR or IRR calculation, the formula assumes that each growing cash flow keeps getting reinvested in the ongoing CAGR.

Whether it is positive or negative. That’s precisely why we use internal rate of return when finding CAGR for uneven cashflows. For example, Mutual fund SIP CAGR can only be calculated using XIRR, not the rate function.

## Conclusion:

CAGR is a very useful method to calculate the growth rate of an investment. It can be used to evaluate past returns or predict the future returns of your investments. However, remember that CAGR works suitably only for lumpsum investments. Investors can analyze investment alternatives by comparing their CAGRs from identical periods. Also, a direct conclusion is that the higher the return, the higher the future value. So if you keep your capital in a savings account with a 4% annual return versus a 12% rate every year in a mutual fund portfolio, the value will be higher with the higher rate of return.

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