  # Compound Annual Growth Rate (CAGR)

Guide to Understanding the Compound Annual Growth Rate (CAGR) ## How to Calculate CAGR (Step-by-Step)

The compound annual growth rate, or “CAGR”, is the rate of return required for the value of an investment or financial metric to grow from its beginning value to its ending value between two dates.

Conceptually, the CAGR metric answers the following question, “At what growth rate must the metric grow at each [Period] to reach [Ending Value] from [Beginning Value] under the time frame of [Number of Periods]?”

The three inputs necessary to compute the CAGR are listed below.

1. Beginning Value
2. Ending Value
3. Number of Periods (t)

The process of calculating the CAGR can be broken into the following three-steps:

• Step 1→ Divide the Ending Value by the Beginning Value
• Step 2 → Raise the Resulting Figure to the Inverse Number of Compounding Periods (1 / t)
• Step 3 → Subtract One to Convert the Implied CAGR into Percent Form

## CAGR Formula

The formula for calculating the compound annual growth rate (CAGR) is as follows.

CAGR = (Ending Value ÷ Beginning Value) ^ (1 ÷ Number of Periods) 1
• Ending Value → The value in the final period.
• Beginning Value → The value in the initial period.
• Number of Periods (t) → The total number of compounding periods.

Suppose there’s a company with revenue of \$20 million at the end of the current period (Year 0).

Five years from the present date, the company’s revenue is projected to reach \$32.5 million (Year 5).

As a side note, we exclude Year 0 when counting the number of periods because we are counting only the periods when the revenue is compounding – i.e. we subtract the beginning period number from the ending period number (in this case, Year 5 minus Year 0 = 5 Years).

We would enter the following figures into the CAGR formula:

• Beginning Value = \$20 million
• Ending Value = \$32.5 million
• Number of Periods = 5 Years

In the first part of the formula, the ending value of \$32.5 million is divided by the beginning value of \$20 million.

The figure must then be annualized by raising it to the power of 1 divided by the 5 periods.

Lastly, once we subtract 1 from the return value, we are left with 10.2% as the CAGR as shown below.

• Compound Annual Growth Rate = (\$32.5 million ÷ \$20.0 million)^(1 ÷ 5 Periods) – 1 = 10.2% ## What is a Good CAGR?

The primary benefit of CAGR is that the metric can serve as a quick and informative growth measure of anything that rises (or falls) in value.

Because the CAGR can confirm whether the projections are in line with industry averages and/or historical growth, CAGR can also be useful as a sanity check.

Let’s suppose a company is projected to grow at a CAGR of 20% but the company’s closest comparables are expected to grow around 5% while the collective industry is being forecasted to grow 3% across the same periods.

If this were the case, the company’s growth assumptions likely warrant some adjustments, or at the very least, a closer look into whether the numbers are reasonable or not.

Since annualized growth metrics remove the fluctuations of year-over-year growth rates, this helps facilitate the comparisons of CAGR over time between two companies or investments, which would otherwise be very challenging to compare.

The main drawback to the CAGR is that fails to take into account the volatility associated with the underlying asset. Thus, the growth metric becomes vulnerable to misinterpretations, as the actual growth rate experienced year-over-year may vary.

For instance, a company’s revenue growth could in reality be disproportionate, with positive growth being front-ended in the earlier periods and ultimately tapering off or even flattening.

Without taking a closer look, the CAGR can be misleading by erroneously portraying the company as having consistent positive growth potential.

## CAGR Calculator – Excel Template

We’ll now move on to a modeling exercise, which you can access by filling out the form below. Submitting ...

## Step 1. Revenue Growth Forecast Assumptions

Suppose we are tasked with calculating the compound annual growth rate (CAGR) of a company’s revenue.

At the end of the current period, the company has generated \$100 million in revenue – and this figure is anticipated to grow by the following growth rates each year.

• Year 0 → Year 1: 10.0%
• Year 1 → Year 2: 8.5%
• Year 2 → Year 3: 8.0%
• Year 3 → Year 4: 6.5%
• Year 4 → Year 5: 5.0%

By the end of Year 5, the company’s revenue reaches \$144 million, after starting at \$100 million in Year 0.

## Step 2. CAGR Calculation Example in Excel

Just like the previous example, we are going to input the following assumptions into the CAGR formula:

• Beginning Value = \$100 million
• Ending Value: \$144 million
• Number of Periods: 5 Years

Our CAGR formula divides \$144 million (the ending value) by \$100 million (the beginning value), and then raises it to 1 divided by 5 (the number of periods).

In the subsequent step, we subtract by 1 to get 7.6% as the implied CAGR.

• Compound Annual Growth Rate = (\$144 million / \$100 million)^(1 / 5 Periods) – 1
• CAGR = 7.6%

The row below the revenue figures calculates the year-over-year growth rates of revenue.

Alternatively, the “RATE” function in Excel could be used. The COUNTA function can count the number of years (nper) for the first input, and we can hard-code a zero for the next input (pmt).

In the next steps, we can enter -\$100 million for the present value (pv), and \$144 million for the future value (fv), with a negative sign placed in front of either 1) the present value or 2) the future value. Note that calculating the CAGR is NOT as simple as averaging the YoY growth rates. Instead, given the beginning value and ending value and date parameters, the CAGR metric assumes the profits are reinvested each period and that interest is compounded annually.

## Step 3. CAGR Analysis and Implied Revenue Calculation

To ensure that you understand the concept of CAGR, we have also computed the implied revenue, which we link to the \$100 million assumption for Year 0 and then grow it by the CAGR of 7.6%.

At the end of Year 5, we can see how by growing revenue by the constant rate of 7.6% each year, the company’s revenue reaches \$144 million, confirming our calculation of CAGR was correct.

Annualized metrics like CAGR should not just be taken at face value to minimize the risk of understating (or overstating) the growth potential without understanding the volatility risks and core drivers of performance.

CAGR can be a useful tool for better decision-making, yet CAGR as a standalone metric still does not reveal the entire story. Step-by-Step Online Course

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