# What is Compound Annual Growth Rate (CAGR): Calculations, Examples

by Angel One
CAGR is a crucial part of understanding the performance of any investment, be it stocks, mutual funds, ETF or even the GDP of a sector. It gives you a key perspective in understanding growth.

## Introduction

In the realm of finance and investment, understanding growth rates is crucial for evaluating the performance and potential of various assets, businesses, and investments. One of the most widely used measures of growth is the Compound Annual Growth Rate (CAGR). It is a powerful tool that allows investors and analysts to compare the performance of different investments over varying time periods, accounting for compounding effects.

In this article, we will delve into the CAGR meaning, explore the formula used by the CAGR calculator, provide real-world examples, and discuss its significance in the financial world.

## What is the Compound Annual Growth Rate (CAGR)?

CAGR is a measure of the annual growth rate of an investment or asset over a specified period, taking into account the effects of compounding. It provides a standardised way to express the growth of an investment, smoothing out the fluctuations that may occur over time.

## How Does CAGR Work?

CAGR operates on the principle of compounding, reflecting the actual growth experienced by an investment over time. It takes into account the increase in value that occurs when an investment earns returns on both its principal and accumulated earnings. By considering this compounding effect, CAGR provides a more accurate representation of an investment’s overall growth.

## What is CAGR in Stocks?

Calculating the CAGR of the stock price shows the rough average rate of growth in the price of the stock. It helps remove the fluctuations of each year while analysing how fast a stock is growing in value. This means short-term fluctuations caused by macroeconomic conditions and sector-related events get smoothened out and we get a growth rate that can predict at what rate the stock may grow in the long run, given no major changes take place.

## What is CAGR formula?

The formula behind a CAGR calculator is as follows:

CAGR = [(End Value/Start Value)^(1/n) – 1]*100

Where:

• End Value is the final value of the investment at the end of the specified period.
• Start Value is the initial value of the investment at the beginning of the period.
• n is the number of years in the investment period.

## Example of calculating CAGR

Suppose you have invested in two different stocks, Stock A and Stock B, over a 5-year period. While you bought Stock A at ₹150 and sold it after 3 years at ₹250, you bought Stock B at ₹350 and after 4 years, sold it at ₹600. Using the CAGR formula, we can calculate the growth rates for both stocks in order to compare and decide which stock performed better.

CAGR of Stock A = [(250/150)^(1/3) – 1]*100 = 18.56%

CAGR of Stock B = [(600/350)^(1/4) – 1]*100 = 14.42%

From the above calculations, we can see that Stock A has a slightly higher CAGR compared to Stock B. In other words, Stock A performed better than Stock B.

## CAGR vs Growth Rate

CAGR is a more appropriate reflection of the changing value of an asset where the compounding effect is present. In other words, CAGR considers the impact of increased/decreased value of the previous year, which a normal growth rate does not.

For example, if the NAV of a mutual fund grows from  ₹1000 to  ₹2500 in 5 years, the average increase per year would be:

(2500 – 1000)*100/(1000*5) = 30%

However, this does not mean that on an average, each year, the NAV grew by 30%. This is because this figure does not take into account the fact that the earnings of one year were reinvested the next year. Therefore, we calculate the CAGR which comes out to be:

[(2500/1000)^(1/5) – 1]*100 = 20.11%

Modifying the CAGR Formula

In case the total period that the person remains invested in the instrument is not a whole number but has to be expressed in fractions, the formula will have no problem in incorporating the fractional value.

For example if you have invested ₹1,000 and you remain invested for 5.25 years, to receive ₹2,500, then the CAGR will be:

CAGR = [(2500/1000)^(1/5.25) – 1]*100 = 19.06%

## How Investors Use the CAGR?

Investors use the CAGR to calculate the potential profits from an investment made today. If the investors expect that a ₹1 lakh investment would yield a CAGR of 15% per year, then they can use a compound interest calculator to find out that the investment will eventually be valued at roughly ₹2,01,136 after 5 years. Therefore, even before making the investment, they can know that the final profit will be around ₹1,01,135. With that knowledge, the investors can better understand whether an investment is good or not. They can also plan their finances and purchases based on that expected profit of ₹1.01 lakh.

Investors can use CAGR to figure out how much money they could make from an investment they make today. Assume you want to invest ₹1 lakh for 5 years in a mutual fund, which is has historically grown at 15% CAGR. On inputting these values in a compound interest calculator, you can see that after 5 years, this investment could increase to around ₹2,01,136. This way, you can estimate the profit to be around ₹1,01,135, even before investing in it. This helps you decide if the final amount would be sufficient to meet your goal or not.

Investors can also use CAGR calculator to find the hurdle rate of an investment or project i.e. the minimum yearly or overall return required to consider an investment or a project to be successful. For example, assume you have to put together ₹20 lakh for your child’s college 10 years from now, even though you have only ₹5 lakh capital right now. You can use a CAGR calculator to know that your ₹5 lakh investment needs to give at least 14.87% CAGR as returns in order to reach ₹20 lakh 10 years from now.

## Significance of CAGR

CAGR is valuable because it presents a single, comparable growth rate over time, regardless of any ups and downs the investment may have experienced. It helps investors gauge the performance of an investment against other alternatives. Moreover, CAGR allows for a better understanding of long-term growth potential, enabling more informed decision-making.

## Applications of CAGR

CAGR finds application in various financial scenarios, such as:

• Evaluating investment performance: Investors use CAGR to assess how well their investments have performed over time, especially for long-term investments like stocks, mutual funds, and real estate.
• Comparing different investments: CAGR facilitates the comparison of the growth rates of various investment options, aiding investors in making informed choices.
• Business performance analysis: CAGR is employed by businesses to analyse their revenue growth, profitability, and other financial metrics over multiple years.
• Projecting future values: By checking the CAGR, analysts can make predictions about the future value of an investment.

1. Normalisation of Growth: CAGR normalises growth rates over varying timeframes, enabling meaningful comparisons between investments with different holding periods.
2. Sensitivity to Compounding: By considering compounding effects, CAGR provides a more accurate depiction of long-term growth potential.
3. Smoothing Out Volatility: CAGR mitigates the impact of market fluctuations and short-term volatility, presenting a clearer picture of an investment’s performance.
4. Standardised Benchmark: Investors can use CAGR as a benchmark to evaluate an investment’s performance against industry standards or other investments.

## Limitations of CAGR

1. Ignores Interim Fluctuations: CAGR overlooks the ups and downs an investment may experience between the starting and ending periods, potentially masking periods of high volatility.
2. Assumes Constant Growth: CAGR assumes a steady growth rate, which may not hold true for investments with irregular or non-linear growth patterns. Two investments with the same CAGR may have different growth profiles over the same period
3. Not Suitable for Short-Term Analysis: CAGR is more suitable for long-term analysis of over 1 year. For short-term assessments of less than one year, other metrics like simple annualised returns may be more appropriate.

## What is a Good CAGR?

The assessment of a “good” CAGR depends on the context and the type of investment. Generally, a higher CAGR indicates stronger growth, but it’s important to consider the risk associated with achieving that growth. Risk and return are often correlated, meaning that higher potential returns often come with increased risk. Additionally, CAGR should be evaluated alongside other factors like market conditions, investment goals, and risk tolerance.

### Conclusion

Compound Annual Growth Rate (CAGR) is a powerful financial tool that allows investors and analysts to evaluate and compare the performance of investments over time. By accounting for the effects of compounding, CAGR provides a standardised growth rate, making it easier to analyse investments with varying timeframes. Whether you are an individual investor or a business owner, understanding and utilising CAGR can greatly enhance your decision-making abilities in the financial landscape.

## FAQs

### Is CAGR the same as average annual growth rate?

No, CAGR and average annual growth rate are not the same. While CAGR considers the compounding effect of growth over the entire investment period, the average annual growth rate only calculates the arithmetic mean of the yearly growth rates without considering compounding.

### Can CAGR be negative?

Yes, CAGR can be negative. A negative CAGR indicates a decline in the investment’s value over the specified period.

### Is CAGR always a reliable measure of growth?

CAGR is a valuable measure, but it has limitations. It assumes a steady growth rate, which may not accurately reflect the investment’s performance if there are significant fluctuations or volatility during the period.

### Can CAGR predict future performance?

CAGR can provide insights into historical growth, but it should not be solely relied upon to predict future performance. Past performance does not guarantee future results, and additional factors should be considered for accurate projections.

### What other growth metrics complement CAGR?

To gain a more comprehensive understanding, investors often use other metrics like Total Return and Standard Deviation alongside CAGR. These metrics offer additional insights into an investment’s performance, risk, and volatility.

### What does the CAGR tell you?

CAGR (Compound Annual Growth Rate) measures the average annual growth rate over a specified time period. It indicates the steady rate of return needed to reach an investment’s current value from its initial value.

### How do I calculate CAGR?

CAGR (Compound Annual Growth Rate) is calculated by dividing the ending value by the beginning value, raising it to the inverse of the number of years, and subtracting 1.