# Compound Growth Rate

Indicates the growth rate over multiple periods

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Expertise: Consulting | Private Equity

Updated:

August 15, 2023

The compound growth rate indicates the growth rate over multiple periods. If it is calculated for a period of one year, it is known as the Compound Annual Growth Rate (CAGR).

The compound annual growth rate measures your average investments over a given period. It also provides the "smoothed" average rate of return on your investments over a year.

CAGR is helpful for investors because it accurately measures investment growth or declines over time.

The formula for calculating CAGR is as follows:

• The ending balance is the value of an investment at the end of the investment period.

• Beginning balance is the value of an investment at the beginning of the investment period.

• n is the number of years you have invested.

You might utilize CAGR to check the presentation of various shared assets to decide the acquiring potential. For example, it might consider the investment tenure providing you with a precise image of the profit from your mutual funds.

It can also be used to consider the authentic returns of bonds, stocks, or mutual funds. In addition, it assists you with measuring the profits from your investments over the entire investment tenure.

## How to Calculate the Compound Growth Rate?

Let us say we want to calculate the Compound annual growth rate (CAGR) of the revenue of a company ABC. The company ABC generated a revenue of $200 million at the end of the current period. This revenue increases each year at the growth rates given below. • Year 0 to 1: 15.0% • Year 1 to 2: 12.0% • Year 2 to 3: 10.5% • Year 3 to 4: 08.0% • Year 4 to 5: 06.5% The company's revenue reaches$ 300 million by the end of the 5th year.

Let's take a look at the solution:

• Number of years (n) = 5
• Beginning value = $200 million • Ending value =$ 300 million

The Compound annual growth rate formula is:

By substituting the company values in the above formula,

Therefore, the Compound annual growth rate = 7.79 %

## Verification of CAGR VALUE

We don't know whether the percentage of CAGR is correct or not. However, we can use the below formula below to verify its value.

Ending balance = Beginning balance X (1+CAGR)^n

If the Ending balance calculated from this formula matches the company's value, then its value is correct. If not, it's wrong.

Example for verification: Let us say we want to calculate the Compound annual growth rate of the revenue of a company ABC. The company ABC generated a revenue of $200 million at the end of the current period. This revenue increases each year at the growth rates given below. • Year 0 to 1: 15.0% • Year 1 to 2: 12.0% • Year 2 to 3: 10.5% • Year 3 to 4: 08.0% • Year 4 to 5: 06.5% The company's revenue reaches$ 300 million by the end of the 5th year.

The solution is:

By taking the values from the before example,

• Number of years (n) = 5
• Beginning value = $200 million • Ending value =$ 300 million
• CAGR = 7.79 %

Ending balance = $200 million X ( 1 + 7.79%)^5 =$ 300 million

Hence, the Ending balance is matched with the company's original value. Our calculation is correct.

## Calculating Compound Growth Rate in Excel

There is no CAGR function in Microsoft Excel, so that we can use the RRI function alternatively.

The syntax in excel is:

RRI(Nper, PV, FV)

Where,

• Nper is the returns of the number of periods for an investment
• PV is the present value
• FV is the future value

You can create the formula for CAGR in Excel using the same value mentioned above.

= (FV/PV)^(1/Nper) - 1

Setting up this function in Excel will produce the same result as the RRI function.

Here is an example of calculating the CAGR using the RRI function. The General formula for the RRI function is

(FV/PV)^(1/Nper) - 1.

Calculating CAGR using the RRI function:

YearValuePercentage Change
020000-
1220009.09
2225002.22
32500010.00
42800010.71
53200012.50

The Average compound growth rate is 9.86%

## Note

The standard RRI condition incorporates more variables, yet you just need the above three to compute your CAGR.

• In column "Year," the number of years is mentioned.

• In the column "Value," the company's value is mentioned.

• In the column "Percentage change," the percentage change in the company's annual growth is mentioned.

• In the example shown, the manual formula for the Average compound growth rate is (32000/20000)^(1/5)-1. Instead of this RRI function can be used here, i.e., RRI(5,20000,32000).

• Thus, the Compound Annual Growth Rate is calculated using excel sheets.

## IRR and CAGR

IRR stands for internal rate of return. It uses multiple investment cash flows to calculate the discount rate, which we can utilize in other complicated situations.

IRR can gauge the possible return of traditional investments like stocks, bonds, securities, and mutual funds.

It is likewise a beneficial device in corporate finance for looking at the potential returns on an internal investment such as a capital spending project.

In many cases, IRR is done on a theoretical basis. However, the investment's projected cash flows are utilized to find the IRR. These might eventually be the incomes that are acknowledged from the investment.

CAGR thinks about the start and finishing upsides of the investment or the portfolio toward the finish of the suitable period. IRR assumes the speculations in all the incomes, like the initial investment and any succeeding investments.

CAGR checks out at starting and finishing values. For an individual investment, cash flows such as dividends or interest will only be considered if reinvested back into the holding.

They wouldn't consider whether these appropriations are taken in real money and redeployed to another record or recently spent.

This might be less of an issue assuming the estimation is being finished on a portfolio and the money conveyed from different speculation properties was kept in a money market account or other cash options essential for that portfolio.

## CAGR vs. absolute return

Returns from an investment can be assessed utilizing both absolute returns and CAGR. From one perspective, absolute returns are a proportion of the total return from an investment, irrespective of the time period.

CAGR, then again, is the return from an investment during a particular period.

Absolute returns and CAGR are utilized to decide an investment's return. However, both use various ways to calculate the return.

Two key differences exist between these two methods of calculating returns on an investment or portfolio returns.

1. Absolute return is the total return of the investment from one point to another. It doesn't consider the annual time periods and the cash flows from the investment or the portfolio over the holding period.

CAGR is the return from an investment during a specific period. It gives a total image of gains made on the investment. It allows you effectively to analyze two investments held for various periods.

2. It includes only the change in value over two points in time and does not consider the volatility of the annual returns on the investment.

The absolute returns computation doesn't consider the period or residency of the venture during which the profits have been procured. Instead, it thinks about the underlying investment and maturity amounts.

Utilizing absolute return alone, one can't decide if the investment is significant or not as the residency of the investment isn't known.

In this way, absolute returns tell how much the investment was devalued or appreciated. However, it doesn't tell how quickly the investment developed or fell. Subsequently, it can't utilize absolute returns to correlate two different investments.

## Absolute return formula

Absolute returns are calculated as below:

Absolute Returns (%) = (Current Value – (less)Principal Investment)/Principal Investment * 100.

Example: Let us say that you have invested 2,000 $at some point in the past, and today this investment is valued at 3,200$.

Absolute Returns (%) =(3200–2000)/2000*100 = 1200/2000*100 = 60%

Due to that investment, you have earned 60% absolute returns.

You might have achieved this 60 % profit over merely months or many years. In this way, choosing exclusively upon the absolute returns is challenging, whether the investment is excellent or not.

Absolute returns just let you know how much your investments developed; they don't let you know anything regarding how quickly they grew.

While looking at investment instruments and their procuring potential, you can know how quickly and by how much they are similarly significant.

Absolute returns record for the last option, and hence we can say it is just half as productive in deciding the development potential of the investment.

## CAGR for Mutual Funds

Let's assume you start with an investment of $2 lakhs today. Following a year, it develops by 100%, and your investment becomes$ 4 lakh. Tragically, in the subsequent year, your investment falls significantly; $4 lakh becomes$ 2 lakh. How much is your return?

Your average return in this period might be an arithmetic mean of +100% and - 50%, which is 25%. In any case, the CAGR of the portfolio will be 0% as the portfolio brought in no cash in two years. Furthermore, this is the right end. You began with $4 1 lakh, and following two years, you are currently at$ 1 lakh.

Be that as it may, as you might have seen, CAGR conceals a great deal. It never gives you the total picture.

Because of an investment path such as mutual funds, you want to determine whether it is worth investing in it or not. In addition, you want ways of working out your prosperity over a given timeframe.

The reality sheet of the mutual fund provides the fund with growth rates over different time horizons. Therefore, judging the fund's result in light of various variables might appear confusing.

Going against the norm, on the off chance that you could know how it developed consistently, things could become less complex.

CAGR helps when the single annual growth rate is provided here. Along with this, the principle of compound interest is likewise positioned in the scene.

Most investment strategies, including mutual funds, use compound interest to reckon the returns. CAGR would, hence, be an acceptable method for estimating the investment standard.

## Absolute Return Vs CAGR in a mutual fund

Let us say the absolute return is the increase or decrease of an investment over a given time period, expressed in percentage terms.

You can calculate the absolute return for an investment using the following formula:

(End Value – Beginning Value) / (Beginning Value) * 100

For example, an investment of Rs 20,000 in May 2022 has appreciated to Rs 28,000 in May 2025.

The absolute return is given as

Absolute Return = (28,000 – 20,000) / (20,000) = 40%.

You might consider Compound Growth Rate to be a fictional number that shows you the rate at which the investment would have developed.

Say, Rs. 2 lakh is invested in a mutual fund scheme. There is a return of Rs. 1 lakh from the mutual fund scheme.

This Rs. 1 lakh is the Absolute return.

Thus, Absolute Return = Total investment - Principal Investment,

After all, it's good to have a return of Rs. 1 lakh, which is 50% of the principal investment. The profit earned is good only if it is earned in one year. If the same profit is earned in 20 years, it's not good.

So, along with the returns, the time period it takes is also essential. Thus, CAGR is helpful here. It gives the average return of the investment per year over a specific period of time.

Taking the same values from the example mentioned above:

CAGR = (Ending balance/Beginning balance)1/n-1

CAGR = (28000)/(20000) ^ (½ ) -1

CAGR = 18.32%.

## Benefits of CAGR

CAGR is a significant variable utilized to quantify any investment's average performance. It permits investors to assess the returns in different situations.

These are some of the merits of using CAGR.

• It provides you with a complete thought of your return on investment.

• Compares the stock performance of two similar industries

• It is a valuable instrument to compare investments over the same horizon.

• Easy to calculate

• Calculating the average returns of the investment funds

• Compares the performance of investment decisions

• The future growth rate of the company can be forecasted.

• Analyze the behavior of any metric that changes over time

• It's a great way to reveal strengths and weaknesses within the company.

• You might compare the CAGR of a shared asset with a benchmark return to be aware if it gets along nicely or is available.

• To calculate the increase in the investments in equity funds.

• Quick comparison tool for investment decisions.

• Helpful in financial planning and budgeting.

• The future performance of the company is forecasted based on historical data.

• The compound annual growth rate calculator can be used to think about stock performance in the companion group, similarly to the record, to check whether the stock or asset administrator is improving or more regrettable than the market benchmarks.

• Over an extended period, absolute returns can be misleading. In such cases, the CAGR can assist you with contrasting with other instruments to know whether you are showing improvement over the market.

## Drawbacks of CAGR

While CAGR is broadly utilized as a device to assess the performance of any organization or portfolio of investments, it has a few limits.

These limits are mentioned below:

• Since the growth rate is constant in the Compound annual growth rate, the smoothed average rate of return gives different results from the actual situation in case of high investments.

• If the company's growth rate is misappropriated, then the CAGR values can mislead us by conveying the consistently positive growth potential.

• CAGR ignores the volatility, and the cash flows between the two points in time.

• It is reasonable just for significant investments. However, on account of SIP investments, the planned investments at different time intervals aren't considered as just the beginning value for the computation of CAGR.

• It does not provide the exact answer that the investor wants.

• CAGR considers the calculations regarding the beginning and ending values. It expects that development is consistent over the length of time and doesn't think about the part of the volatility.

• It doesn't represent the inside risk of an investment. Regarding equity investment, risk-adjusted returns are a higher priority than CAGR. Therefore, it would be best if you utilized Sharpe's Ratio and Treynor's Ratio to the risk-return reward of the investment.

## Conclusion

CAGR is a magnificent analytical instrument that can smoothen out the returns of investments, compare industrial performance, analyze metrics over a series of periods, and forecast future development.

CAGR can be used to check the presentation of various shared assets to decide the acquiring potential. For example, it might consider the investment tenure providing you with a precise image of the profit from your mutual funds.

The growth rate will take a compounding investment from its present value to its future value. It is a preferred proportion over a standard yearly return, as it thinks about misfortunes.

A few monetary experts contend that the Compound Annual Growth Rate isn't a reality but an educational idea.

Notwithstanding, it is still a robust and insightful instrument over extensive periods that permits us to look at the presentation of investments and different financial measurements.

It is fundamental to recall that a CAGR gives a 'smoothed variant of the natural world, and wiping out unpredictability can be perilous in financial planning and modeling.

CAGR is a precious strategy to compute the growth rate of an investment. Assessing the previous returns or gauging what's to come can utilize the returns of your investments. Nonetheless, recall that CAGR turns out appropriately for lumpsum investments.

In the event of Systematic Investment Plans (SIPs), it doesn't consider the occasional investments as it just thinks about the initial and final qualities of the computation.

In general, the CAGR calculator is a precious device, and it can assist you with analyzing your investments.

While CAGR can't be viewed as a sole boundary in assessing the exhibition of any fund or investment portfolio, it can't be overlooked too. CAGR is one of the significant measures investors must take in making investment decisions.

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Researched and authored by Chinmayi Gobburu | LinkedIn