Introduction to compound annual growth rate

The compound annual growth rate (CAGR) is an investment’s rate of return (RoR) when profits are reinvested yearly. You can calculate CAGR manually or in Excel by inputting the data into a table and breaking the calculations out line by line.

Here’s how to perform the manual formula to calculate CAGR:

• Take the end value (the value of an investment at the end of the investment period) and divide it by the start value (the value of the investment at the beginning of the investment period).
• Take the result of the last equation and raise it to the power of 1 divided by the number of years (n) of the life of the investment.
• Subtract 1.
• Multiply the final number by 100 to convert it into a percentage.

CAGR can provide a consistent, annualized growth rate that assumes reinvestment of profits and smooths out fluctuations.

How to use the compound annual growth rate (CAGR) formula

Imagine you invested $10,000 into a new product development initiative for your business this year. By year-end, the value grew to $13,000, a 30% return. The next year, it increased to $14,000, or 7.69% and the year after, the value reached $19,000, delivering a 35.71% return that year.

While the annual returns for each year vary, the CAGR reflects the average annual growth across the three years using only the beginning and ending values.

Here is the formula to illustrate that:

CAGR = ([(EV$/BV$) ^ (1/n)] – 1) x 100

or

CAGR = ([($19,000/$10,000) ^ (⅓)] – 1) x 100 = 23.86%

What does the CAGR formula tell you?

In the earlier example, the business’s initial investment of $10,000 grew by $9,000 over three years, resulting in a compound annual growth rate of 23.86%. This figure represents the average annual return the investment or project would have earned if it had grown steadily with all profits reinvested each year.

CAGR smooths out short-term volatility and year-to-year fluctuations, providing a clearer, more consistent view of long-term performance. It simplifies uneven returns into a single annualized rate, making it easier to compare different investments over time.

For example, if you compare two uncorrelated business assets, such as a new product line to expanding into a different market, CAGR allows you to evaluate their performance on an equal footing, even if one asset had more ups and downs than the other. However, while CAGR is a valuable benchmarking tool, it typically doesn’t reflect investment risk or volatility.

Understanding the CAGR formula

Investors who understand the CAGR formula for past rates of return also know they can use the same formula to estimate future profits. You can also calculate a hurdle rate (the minimum acceptable rate of return or MARR).

For example, imagine you need $50,000 for your child’s post-secondary education in 18 years. With your initial investment of $15,000, what average rate of return do you require to reach your objective?

Use the CAGR formula as follows:

([(EV/BV) ^ (1/n)] – 1) x 100 = Required return

or

([($50,000/$15,000) ^ (1/18)]) -1 x 100 = 6.77%

This example rearranges EV and BV to the equation’s future and present value figures, helping you estimate the future values based on the expected CAGR. You can also determine your initial investment if you require $50,000 for your child’s education and are willing to accept a reasonable CAGR of 8%:

([(50,000/X) ^ (1/18)] -1) x 100 = 8.0%

What is X?

X = $12,500 (rounded)

In this example, you invest approximately $12,500 to achieve your objective of $50,000 in 18 years with a CAGR of 8%.

Initial value

The initial value, or the beginning or present value, is the amount you start with at the beginning of the investment period. This could be the initial capital for a new business venture, the starting balance in a corporate savings account or the value of a business unit before a growth initiative. It serves as the baseline from which all growth is measured, ensuring the calculated rate accurately reflects performance.

The initial value is essential for the CAGR calculation, as it is the baseline from which all growth is measured. Accurately identifying the initial value ensures that the calculated growth rate reflects the investment’s performance over the chosen period.

Final value

The final value, sometimes called the ending value or future value, represents what your investment is worth at the end of the specified time frame. This could be the value of your business after a period of growth, the ending balance in an investment portfolio or the revenue of a company at the end of a reporting period.

The final value shows the result of the investment’s growth over time. By comparing the final value to the initial value, you can determine how much the investment has grown and use this information to calculate the compound annual growth rate.

Growth rate

The growth rate is the annualized rate at which an investment increases value over a set period. Expressed as a percentage, it is calculated using the initial value, final value and the length of the investment period.

Adapting the CAGR formula

Rarely will you invest on the first day of the year and sell the investment on the last day of a future year. For instance, on June 1, 2010, imagine you invested $10,000 into a stock (the start value or initial investment amount) and sold it for $16,897.14 on September 9, 2015. You want to calculate the CAGR of that investment, but you’ll need the fractional remainder of n (the life of the investment).

To calculate the exact fractional exponent “n,” first determine the total number of days in the investment’s holding period. Divide this total by 365 to get your fractional remainder. Note that different compounding periods, such as annual, semi-annual or quarterly, can affect the calculation of returns, so it’s important to be aware of how often interest is compounded when comparing investments.

Using the above example:

• 213 days in a year
• 365 in the following year
• 365 in the next
• 365 in the next
• 365 in the next
• 251 in the final year

Totalling 1,924 days. Divide 1,924 days by 365 days, and the entire holding period of the investment was 5.271 years, which will take its place in the CAGR formula as follows:

([($16,897.14/$10,000) ^ (1/5.271)] -1) x 100 = 10.46%

The compound annual growth rate of that investment was 10.46%. Accurate timing and careful calculation of “n” are paramount for precise CAGR results, enabling more meaningful comparisons between different investments or business projects.

Revenue growth and CAGR

Revenue growth can be a fundamental indicator of a company’s financial health and prospects. By applying the compound annual growth rate to revenue figures, investors can better understand how consistently a company’s revenue has increased over a given period.

This can be useful when comparing companies in the same industry or evaluating their performance against their historical results.

IRR vs. CAGR

IRR (the internal rate of return) estimates the return on an investment. Since IRR accounts for the time value of money and varying cash flows, it can be a valuable tool for ranking your company’s potential investments or projects to determine which ones offer the best internal return profile.

While IRR and CAGR measure investment performance, IRR is suited for projects with multiple cash flows and varying timing, whereas CAGR assumes a single investment and consistent compounding.

Another important distinction is that CAGR is straightforward enough to calculate manually. In contrast, using IRR to calculate complicated projects or investments or those with varying cash inflows is typically best.

CAGR formula in Excel

When calculating CAGR in Excel, you enter a beginning value, an ending value and the investment period.

Best practices for financial modelling typically require all calculations to be auditable and transparent. To ensure clarity in financial models, structure your Excel worksheet with transparent, line-by-line calculations.

CAGR’s benefits

CAGR serves as a way to forecast the rate at which your investment may grow if it maintains a steady growth rate over the entire forecast period. Calculating CAGR offers additional benefits, such as:

Performance tracking

You may track performance or compare your company to other companies through various business aspects. For example, a large department store’s market share CAGR was 2.41%, but its customer satisfaction CAGR was -0.49% over the same period.

Detect strengths and weaknesses

CAGR can help you detect strengths and weaknesses throughout your organization. You can also use this strategy to monitor and analyze competitors, avoid factors that cause weakness, and mimic activities that add strength.

In the example above, the large department store’s customer satisfaction CAGR was -0.49%, which may not seem so low compared to a competitor’s CAGR of -4.92%.

CAGR’s limitations

There are some challenges when using the CAGR formula:

• Since CAGR smooths out the growth rate, it ignores volatility, which implies the growth was steady.
• CAGR does not account for investment risk, so it may not fully reflect the uncertainties and volatility associated with an investment.
• The CAGR formula doesn’t account for added funds or withdrawals during the measured period. Deposited funds would show growth and inaccurately inflate the CAGR; the reverse is true for withdrawals.
• Investors can’t rely on historical results, especially if the analysis period is short. The shorter the time frame, the less likely the actual CAGR will meet the expected rate. This is particularly relevant in dynamic markets like some sectors of the Canadian economy, where past performance may not reliably predict future growth due to unique economic cycles or industry shifts.

Tips for calculating CAGR

Here are some tips to keep in mind when calculating CAGR:

Date mistakes

A common mistake when calculating CAGR is incorrectly counting the investment period, especially when dealing with fiscal years that may not align with calendar years. Carefully read the dates to avoid accidentally adding or subtracting a year.

Let’s use year-end stock prices as an example:

• Year 1 = $100
• Year 2 = $120
• Year 3 = $125

Using a beginning and ending value and the number of investment years for the entire term, your calculation would look like this:

([($125/$100) ^ (½)] – 1) x 100 = 11.8%

When comparing annual sales figures to investment returns, the period often includes a partial year. A common mistake is choosing, for example, three years for the entire term when the correct value is two years. According to the above example, there are only two full years’ worth of year-end data between 2020 and 2022, so n=2.

Percentages

To use the formula correctly, you must convert annual price data percentages into dollars. For example:

• Year 1  = 10%
• Year 2 = 15%
• Year 3 = 4%

Convert the percentages to dollars and notice that you’re reading percentages for the fiscal or calendar yearly return, making the number of years in the formula three. This would be an excellent time to use the formula for CAGR in Excel because adding a helper column for percentage conversions to dollar values makes the calculation easier.

Understanding and applying the CAGR formula may give you a clearer view of how assets grow over time. While it doesn’t capture the full complexity of market volatility, it can be a reliable benchmark for comparing performance across different assets and periods.

Whether evaluating past returns or projecting future goals, CAGR can provide a consistent framework for making informed financial decisions for your business’s success.

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