Compound Annual Growth Rate (CAGR)

Compound Annual Growth Rate or CAGR, is a metric used to measure the average annual growth of an investment over a specific period. It considers the effect of compounding, where earnings from previous periods are reinvested and contribute to future growth. This provides a more accurate picture of an investment's performance compared to a simple average of annual returns.

In this article, you will learn about CAGR meaning, how CAGR works, CAGR formula, and how to calculate CAGR in detail.

What is CAGR?

The Compound Annual Growth Rate (CAGR) represents the average annual growth rate of an investment over a period exceeding one year. It is considered one of the most reliable methods for calculating and analyzing returns on individual assets, investment portfolios, or any value that fluctuates over time.

For more clarity, let’s study an example. Say you put Rs. 2,000 into a specific mutual fund, which experienced a compound annual growth rate (CAGR) of 8% over seven years. This means that, on average, your investment would have grown by 8% each year. However, it is possible that the actual growth rate per annum might be different from this CAGR of 8%. Say, in the first year, it might grow by 6%, in the second year by 10%, and so forth.

How does CAGR work?

CAGR, or Compound Annual Growth Rate, is a measure of the average annual growth rate of an investment over a certain period (assuming the growth is compounded). One key benefit of CAGR is its ability to smooth out year-to-year fluctuations in investment returns.

It is worth mentioning that investments usually do not grow at a steady rate; one year might see a significant increase, while another might experience a slight decline. To smooth out this fluctuation, CAGR averages these variations and provides a single growth rate. This makes it easier for investors to compare the performance of different investments.

To better understand the workings of CAGR, let’s study an example:

• Say you invested Rs. 1,00,000
• Your investment grew to Rs. 1,55,000 over eleven years
• Now, to calculate the CAGR, you must use this formula:
  • CAGR = (Ending Value / Beginning Value)^(1 / Number of Years) – 1
• Upon calculation, the CAGR for this investment comes out to be 4.48%
• This means that, on average, the investment increased by 4.48% each year.

Moreover, CAGR considers the compounding effect. For those unaware, compounding in investments means that the returns earned in each period are added to the initial investment amount. This forms a new base on which all future returns are calculated. Due to compounding, you earn returns not only on your original investment but also on the accumulated returns from previous periods, accelerating your investment's overall growth.

As a result, the CAGR provides a more accurate measure of an investment's actual performance than a simple average of annual returns. While simple averages only give a basic arithmetic mean, CAGR accounts for the effect of compounding and shows how much an investment has grown on average per year by considering that the growth is reinvested.

Formula of Compound Annual Growth Rate (CAGR)

Calculating CAGR involves a simple formula:

CAGR = ((Ending Value/Beginning Value)^(1/Number of Years) - 1)*100

Here is what each part means:

• Ending Value: This represents the investment's worth at the end of the period you are analysing.
• Beginning Value: This is the investment's worth at the beginning of the period.
• Number of Years: This refers to the total duration of the investment period.

By plugging these values into the formula, you can calculate the average annual growth rate that considers compounding.

How to calculate CAGR?

To calculate CAGR, you can follow these simple steps:

• Identify the starting value, which is the initial amount you invested or the initial value you are measuring.
• Next, determine the ending value, which is the value at the end of the specified period.
• Now, calculate the total number of years over which the growth occurred.
• Use the CAGR Formula:
  • CAGR = (Ending Value / Beginning Value)^(1 / Number of Years) – 1
• Multiply the result obtained by 100. This will help you get the CAGR as a percentage.

For a better understanding, let’s see a hypothetical example:

• Starting value: Rs. 10,000
• Ending value: Rs. 15,000
• Number of Years: 5

Now, let us plug these values into the formula:

• CAGR = (15,000 / 10,000)^(1 / 5) – 1
• CAGR = 0.08447 or 8.45%

Here, we can observe that the CAGR is 8.45%. This means that, on average, the investment grew by 8.45% per year over the 5 years.

Example of compound annual growth rate (CAGR) calculation

Say, Ram, a mutual fund investor, invested Rs. 5,000 in a mutual fund scheme in 2021. In the next three years, the value of his investment grew to Rs. 6,500. Now, let’s calculate the CAGR of the investment made by Ram:

• Starting value (2021): Rs. 5,000
• Ending value (2024): Rs. 6,500
• Number of years: 3 years

Putting the above values in the CAGR formula:

CAGR = (6,500/5,500)^1/3 - 1

CAGR = 9.10%

Here, we can observe that the CAGR of the mutual fund scheme is 9.1% over a 3-year period. This means that the investments of Ram grew on average at a single rate of 9.10% in 3 years.

How to calculate CAGR in Excel?

It must be noted Excel doesn't have a specific built-in function to calculate "CAGR". However, you can still calculate it using several other functions, such as:

• RRI function:
  • This function directly computes CAGR by specifying:
    • The number of periods
    • Starting value
    • Ending value
• IRR function:
  • It can calculate CAGR when you provide a range of cash flows, including the initial investment.
• RATE function:
  • Usually, this function is used to calculate the interest rate for a series of equal cash flows—for example, loans or investments with regular payments.
  • When adapted for CAGR, this function can also be used to determine the annual growth rate of an investment.

Read our full article on how to calculate CAGR in Excel.

How to calculate the CAGR of a Company?

The Compound Annual Growth Rate (CAGR) of a company is a useful measure for assessing the average annual growth rate of an investment or company’s performance over a specified period. It shows the steady growth rate, assuming the investment grew at a consistent pace year after year.

To calculate the CAGR, you can use the following formula:

CAGR=(Initial Value/Final Value​)n1​−1

Where:

• Final Value is the ending value of the investment or company,
• Initial Value is the starting value,
• n is the number of years.

Steps to calculate:

1. Divide the final value by the initial value.
2. Raise the result to the power of 1 divided by the number of years.
3. Subtract 1 from the result to get the CAGR as a decimal.
4. Multiply by 100 to express it as a percentage.

For example, if a company’s value grows from Rs. 1,00,000 to Rs. 2,00,000 over 5 years, the CAGR would be around 14.87%. CAGR smoothens out fluctuations over the years, offering a more accurate reflection of long-term growth.

What is a good CAGR?

What constitutes a "good" CAGR (Compound Annual Growth Rate) depends on the type of investment, market conditions, and personal financial goals. Here's a breakdown:

1. Market benchmarks:

• Stock Market: A CAGR of 7% to 10% is generally considered good for long-term investments.
• Bonds: For bonds, a CAGR of 4% to 5% is seen as reasonable due to their lower risk compared to stocks.

2. Inflation:

• Beating Inflation: A good CAGR should outpace inflation, typically 4% to 5% annually. If your CAGR is below inflation, your real purchasing power decreases.

3. Risk and return:

• High-Risk Investments: For higher-risk assets like startups or emerging markets, a CAGR of 15%+ may be considered strong, reflecting the potential for larger returns.
• Low-Risk Investments: For safer investments like government bonds or savings accounts, a 2% to 5% CAGR may be acceptable given the lower risk.

4. Investment horizon:

• Short-Term: A higher CAGR (12%+) might be good for short-term investments (1-3 years).
• Long-Term: For long-term investments (10-20 years), a CAGR of 10% to 12% is often sustainable and strong.

5. Personal goals:

• A good CAGR depends on your financial objectives and risk tolerance. For steady, long-term growth, 7% to 10% might be ideal, whereas aggressive goals may target higher returns.

What is Negative CAGR?

So far, we've explored instances of positive performance. However, negative CAGR is a reality in the Indian financial market. When a portfolio or investment loses value over time, it exhibits negative growth, leading to a negative CAGR.

A negative CAGR is undoubtedly undesirable, as it signifies a decline in investment value. Just as investors aim for positive growth, companies strive to increase their earnings.

One intriguing aspect of negative CAGR is the reverse effect of compounding. With positive growth, the compound annual growth rate amplifies returns on an increasingly larger base. For instance, a Rs. 10 lakh portfolio growing at 10% CAGR over five years would be worth approximately Rs. 16.11 lakh. The power of compounding yields a total increase of over 61%.

Conversely, a negative CAGR diminishes the investment value at an accelerating pace. A Rs. 10 lakh portfolio shrinking at 10% CAGR over five years would reduce to approximately Rs. 5.90 lakh. The declining base value moderates the impact of the negative growth rate, resulting in a total loss of around 41%.

Uses of Compound Annual Growth Rate (CAGR)

Compound Annual Growth Rate (CAGR) serves multiple purposes in financial analysis.

• Performance Benchmarking: CAGR offers a standardised metric for comparing the performance of diverse investments over a specific timeframe. This method ensures an equitable evaluation, allowing investors to gauge investments uniformly based on average annual growth rates rather than absolute figures.
• Strategic Long-Term Planning: CAGR proves instrumental in long-term investment planning by estimating the potential growth trajectory of an investment over time. Investors can project the future value of their portfolios, enabling informed decisions grounded in expected average annual growth rates.
• Risk Analysis: CAGR functions as a valuable tool for assessing investment risk. Consistently positive CAGR over an extended period suggests a more stable and reliable growth pattern, particularly appealing to risk-averse investors.
• Historical Performance Assessment: Through CAGR, investors can scrutinize the historical performance of their portfolios. Comparative analysis against benchmark indices or industry standards facilitates the evaluation of investment strategy effectiveness and identification of areas for improvement.

Advantages of compound annual growth rate

Listed below are some advantages of Compound Annual Growth Rate:

• Simplicity: CAGR simplifies the representation of complex, multi-year growth rates into a single percentage, making it easier for investors to compare investments.
• Long-Term Perspective: CAGR is particularly useful for assessing long-term investments, as it smooths out short-term fluctuations and provides a clearer view of performance over time.
• Effective for Variable Returns: It is valuable when an investment has experienced variable or erratic returns over time. CAGR gives a single, consistent growth rate that encapsulates the investment's overall performance.
• Applicability: The CAGR concept is versatile and can be applied to various asset classes, including mutual funds, stocks, real estate and businesses, making it a valuable tool for investors across different domains.

What is CAGR in stocks?

The Compound Annual Growth Rate (CAGR) in stocks is calculated by calculating the annual growth rate of an investment in stock over a specific period. The CAGR indicates how much the investment has grown over the period relative to the average returns generated. The assumption for calculating CAGR is that the investment in stocks grows at a steady rate until it is sold to book profits, regardless of price fluctuations and volatility.

CAGR in stocks helps investors analyse the growth potential for a stock when invested for the long haul. As investing for the long term does not consider short-term price fluctuations, CAGR helps eliminate the risk associated with market instruments in the short term and helps analyse the stock’s potential performance in the long run.

CAGR helps investors compare the growth rates of different investments over time, providing a clear picture of how well an investment has performed. It allows for easy comparison of different investments or stocks, even if they have different levels of volatility.

What is CAGR in mutual funds and how does it work?

The Compound Annual Growth Rate (CAGR) is a vital financial metric that measures the performance of mutual funds over time. It measures the average annual growth rate of an investment in mutual funds by assuming that the investment has grown at a steady rate. CAGR in mutual funds helps investors compare various mutual fund schemes by understanding how well a scheme has performed, eliminating the effects of price fluctuations and volatility.

Suppose you invested Rs. 50,000 in a mutual fund five years ago. At the end of the five-year period, the value of your investment has grown to Rs. 80,000. You can calculate CAGR as:

CAGR = [(Final Value / Initial Investment) ^ (1/n)] - 1

• Beginning value: Rs. 50,000
• End value: Rs. 80,000
• n (years): 5

Applying the formula, you get a CAGR of 10.47%. This means that the mutual fund investment grew at an average annual rate of 10.47% over the five-year period.

What is CAGR in banking?

In banking, the Compound Annual Growth Rate (CAGR) is a measure used to evaluate the average annual growth rate of an investment, deposit, or loan over a specified period. It represents the consistent growth rate at which a bank's revenue, assets, or investments would have grown if the growth had occurred steadily each year. CAGR is particularly useful for comparing financial performance or investment returns over time, helping banks and customers assess long-term growth. It smoothens short-term fluctuations, offering a clearer picture of overall performance across multiple years.

What is CAGR in economics?

In economics, the Compound Annual Growth Rate (CAGR) measures the average annual growth of an economic indicator, such as GDP, over a specific period. It assumes that growth occurs at a steady, constant rate, smoothing out short-term fluctuations. Economists use CAGR to assess long-term economic trends, such as the growth of industries, national economies, or specific sectors. By calculating CAGR, policymakers and analysts can evaluate economic performance, compare it with other periods or economies, and make informed decisions. It provides a clear picture of sustained growth over time, making it a valuable tool in economic analysis.

Limitations of CAGR

While Compound Annual Growth Rate (CAGR) is a valuable metric for understanding the average annual growth of an investment over a period, it also has some limitations that should be considered:

Assumes Constant Growth: CAGR assumes that the investment's growth or decline is constant year after year, which may not reflect the actual market dynamics. In reality, investment returns can be volatile and fluctuate significantly over time.

No Insight into Intermediate Values: CAGR provides the average growth rate but does not offer insights into the investment's performance during individual years. It smooths out the data, potentially hiding periods of exceptional gains or losses.

Dependent on Time Frame: The CAGR value can change significantly depending on the selected time frame. For example, the CAGR for a five-year period may differ from that of a ten-year period, leading to different interpretations.

Not Suitable for Short-Term Investments: CAGR is best suited for evaluating long-term investments. For short-term investments with high volatility, the metric may not accurately represent the investment's performance.

Ignores Investment Timing and Cash Flows: CAGR does not consider the timing of investments or cash flows. It assumes that the investment was made at the beginning and held until the end of the period, which may not be the case for all investors.

Factors to Consider When Using CAGR

When using CAGR to analyse investments, there are several important factors to consider:

• Time period: The length of time used to calculate CAGR is critical. A longer period generally gives a more accurate picture of returns, while a shorter period might be misleading. Hence, make sure you are using consistent time when comparing different investments.
• Market fluctuations: Numerous studies have shown that market fluctuations substantially affect CAGR. There is a chance that an investment that shows high returns over a short period may not sustain those returns over the long term. Hence, it is always important to consider market trends and volatility when evaluating investments.
• Risk: CAGR does not account for the risk involved with an investment. A higher CAGR might indicate better returns, but it may not be the best choice if the investment is high-risk. Thus, you must always assess the risk level alongside the CAGR.
• Currency fluctuations: For investments made in foreign currencies, changes in exchange rates can impact the CAGR. Therefore, it is necessary to factor in these currency fluctuations when analysing returns.
• Taxes and fees: Taxes and fees significantly reduce the actual returns on an investment. Hence, while calculating CAGR, consider how these costs might affect the overall growth rate.

Key insights investors should know about CAGR

CAGR, or Compound Annual Growth Rate, is a crucial metric used to assess the average annualised rate of return on an investment over a specific period. It offers a clear picture of how an investment has performed, taking into account the impact of compounding.

For instance, if a stock's price rises from Rs. 200 to Rs. 242 in two years, it implies a CAGR of 10%. However, the stock's price fluctuations during this period might not be linear. It could have risen to Rs. 320 in the first year and then fallen back to Rs. 242. Despite these variations, the overall CAGR remains 10%.

This is because CAGR smooths out volatility, helping investors understand the long-term performance of an investment, even if it experiences short-term ups and downs. However, it's important to remember that CAGR is not a guarantee of future performance. Market conditions can change, and there's always inherent risk in any investment.

Additionally, CAGR is more reliable for longer investment periods. Short-term fluctuations can significantly impact the CAGR calculation, making it less accurate. Therefore, when calculating CAGR, it's preferable to utilise longer periods to ensure more accurate results.

Ultimately, CAGR is a valuable tool for investors to evaluate the performance of their investments. By understanding its limitations and using it in conjunction with other metrics, investors can make informed decisions about their financial future.

Differences between CAGR and XIRR

Factor	CAGR	XIRR
Calculation Method	Assumes constant growth rate over time.	Accounts for varying returns and irregular cash flows.
Time Intervals	Assumes equal time intervals (usually annually).	Handles investments with uneven intervals and dates.
Application	Best for single investments with constant growth.	Suitable for SIPs, loan payments, or irregular investments.
Flexibility	Limited to structured, consistent cash flows.	More flexible as it works with varying amounts and timings.
Simplicity	Easy to calculate with a straightforward formula.	More complex, often requiring software to compute.
Assumptions	Assumes reinvestment at the same rate annually.	Adjusts for varying investment returns over time.
Accuracy	Provides a smoothed average return.	Offers a more accurate reflection of actual cash flow timing.
Use Case	Ideal for evaluating long-term investment performance.	Better for portfolios with multiple and varying cash flows.

Both CAGR and XIRR offer insights, but their application depends on the structure of the investment.

Key takeaways

Here are a few points to remember about CAGR:

• CAGR does not solely measure sales growth within a specific time frame; growth concentration might vary, focusing on either the initial or final year of a project.
• Investments with identical rates of return could yield different profitability levels due to variations in the timing of growth; one investment might experience faster growth in the initial year, while another may see growth primarily in the final year.
• CAGR is commonly used for investment durations spanning three to seven years; however, for periods exceeding ten years, it may obscure intermittent patterns.
• It's important to differentiate between CAGR (Compound Annual Growth Rate) and the annual growth rate as they serve distinct purposes

Conclusion

Understanding Compound Annual Growth Rate (CAGR) empowers you to make informed investment decisions. CAGR goes beyond simple averages by factoring in compounding, providing a clearer picture of long-term investment growth. While limitations exist, CAGR remains a valuable tool for tasks like benchmarking performance, strategic planning, risk analysis, and historical assessment. Remember, a good CAGR is context-dependent, but surpassing comparable investments is generally positive. Utilise CAGR alongside other metrics to gain a comprehensive understanding of your investments' health and chart a course for financial success.

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