# CAGR Formula

Article byWallstreetmojo Team
Edited byPallabi Banerjee
Reviewed byDheeraj Vaidya, CFA, FRM

## What Is CAGR Formula?

CAGR (Compounded Annual Growth Rate) refers to the rate of return that is achieved by an investment by growing from its beginning value to its ending value, based on the assumption that the profits during the tenure of the investment were reinvested at the end of each year.

For eg:
Source: CAGR Formula (wallstreetmojo.com)

The formula can be used to calculate the overall performance of various investment avenues or financial instruments like bonds, stocks, projects, etc which involve returns for a number of years. It is a valuable tool for evaluating the growth or decline in investment valuation in order to make analysis and financial decisions.

### Key Takeaways

• The Compound Annual Growth Rate (CAGR) is a financial metric used to calculate an investment’s average annual growth rate over a specific period, considering the compounding effects.
• CAGR offers a standardized method to compare the performance of various investments or assets over time, regardless of their initial value or the duration of the investment period.
• CAGR is particularly valuable for evaluating long-term investments, such as stocks, mutual funds, or real estate, as it incorporates the volatility of returns and provides a smoothed average growth rate.

### CAGR Formula Explained

It is calculated by dividing the value of the investment available at the periodās end by its beginning value and then raising the resultant to the exponent of the one divided by a number of the years and from further resultant subtract one.

It is important to understand how to calculate CAGR formula. It is calculated by dividing the value of the investment available at the periodās end by its beginning value and then raising the resultant to the exponent of the one divided by a number of the years and from further resultant subtract one.

CAGR Formula = [(Ending value / Beginning value) 1/No. of years ā 1] * 100%

The formula can also be expressed by adding one to the on investment (ROI), then raising the result to the power of reciprocity of the tenure of investment and then finally subtracting one.

CAGR = [(1 + Absolute ROI ) 1/No. of years ā 1] * 100%

where Absolute ROI = (Ending value – Beginning value) / Beginning value

Various types of investment can be compared using this method which have investment horizon that are similar to each other. The revenue CAGR formula provides clarity regarding investment performance. It however assumes that the growth rate remains the same throughout the entire time horizon of the investment. In case the investment is very volatile, then the results may not provide a clear picture.

### How To Calculate?

The compounded annual growth rate can be calculated by using the following steps:

1. Firstly, determine the beginning value of the investment or the money that was invested at the start of the investment tenure.

2. Next, in order to calculateĀ CAGR formula, we determine the final value of the investment at the end of the tenure of investment or the ending value.

3. Next, determine the tenure of the investment, i.e., number years from the start of the investment to the end of the same.

4. Next, divide the ending value of the investment by the beginning value and then raise the result to the power of reciprocity of the tenure of investment. Finally, subtract from the result and express in percentage terms to derive the compounded annual growth rate formula, as shown above.

### Examples

Let us understand the concept of revenue CAGR formula with the help of some suitable examples.

You can download this CAGR Formula Excel Template here āĀ CAGR Formula Excel Template

#### Example #1

Let us take an example of David, who invested \$50,000 in a portfolio on Jan 1, 2015, and the following portfolio return has been outlined below:

• On Jan 1, 2016, the value of the portfolio stood at \$60,000
• On Jan 1, 2017, the value of the portfolio was \$73,000
• On Jan 1, 2018, the value of the portfolio was \$70,000
• On Jan 1, 2019, the value of the portfolio was \$85,000

Based on the given, determine the yearly return and the CAGR for Davidās investment portfolio.

Use the following data for the calculation of CAGR.

Return for the 1st year

• Return for 1st year = [(Ending value / Beginning value) ā 1] * 100%
• = [(\$60,000 / \$50,000) ā 1] * 100%
• = 20.00%

Return for 2nd year

• Return for 2nd year = [(\$73,000 / \$60,000) ā 1] * 100%
• = 21.67%

Return for 3rd year

• Return for 3rd year = [(\$70,000 / \$73,000) ā 1] * 100%
• = -4.11%

Return for 4th year

• Return for 4th year = [(\$85,000 / \$70,000) ā 1] * 100%
• = 21.43%

Now, let us do the calculation of the based on the given information,

• CAGR = [(\$85,000 / \$50,000) 1/4 -1] * 100%

CAGR will be –

• CAGR = 14.19%

Therefore, the above example shows how CAGR encapsulates all the growth and de-growth during the investment period and provides an average annual growth rate during the investment tenure.

#### Example #2

Let us take an example of an equity portfolio that has value growth such that the absolute return over the period of five years stood at 57%. Do the calculation for the CAGR of the portfolio.

Therefore, the calculation of CAGR of the portfolio can be done as,

• CAGR = [(1 + Absolute ROI) 1/ Number of years ā 1] * 100%
• = [(1 + 57%) 1/5 ā 1] * 100%

CAGR will be –

• CAGR = 9.44%

Therefore, the CAGR of the equity portfolio after five years stood at 9.44%.

Thus, the above examples clearly explains how an analyst can calculate CAGR formula for days, months or years and evaluate the viability of any investment over a period of time.

### Calculator

We can use the following CAGR Calculator.

 Ending Value Beginning Value No. of Years CAGR Formula = Ā

 CAGR Formula = [(Ending Value / Beginning Value)1/No. of Years- 1] * 100% [(0 / 0)1/0-1] * 100% = 0

### Uses

Let us understand the uses of the annually or monthly CAGR formula in details.

• It is important for the analyst to understand the concept of the compounded annual growth rate because it can be used to calculate the average growth of an investment.
• Under certain circumstances, the market becomes volatile, and as such, the year-to-year growth of an investment may appear uneven and erratic. In such a case, the CAGR helps in smoothing the erratic growth rates that are expected due to market volatility and inconsistency.
• Another use of the CAGR equation is that it can be used for comparison of investments of different types.
• Nevertheless, the CAGR has its drawback: by smoothening the erratic returns on investment, the CAGR conceals from the investor returnsreturns on investment, the CAGR conceals from the investor the fact of how risky or volatile the portfolio has been during its investment tenure.
• The annually or monthly CAGR formula is useful for any finance professional who are into evaluation and assessment of investment performance in various fields. It includes bankers, financial analysts, stock traders, individual investors, financial advisors, etc.
• It helps in analyzing the performance using historical data and past CAGR calculations. This provides a view of the current circumstances, changes over the years, and a forecast based on current data and analysis.

However, despite the drawback, the CAGR remains a very useful performance indicator for investors and analysts.

1. How is CAGR different from the annual average growth rate?

CAGR (Compound Annual Growth Rate) is a geometric average considering the compounding effect over a specific period. It smooths out year-to-year fluctuations and provides a single growth rate for the entire period. On the other hand, the annual average growth rate is a simple average of growth rates over individual years without considering compounding effects.

2. Can CAGR be negative?

CAGR can be negative if there is a decline in the investment value over the specified period. A negative CAGR indicates a negative growth rate.

3. What are the limitations of the CAGR application?

Limitations of CAGR include not capturing volatility and fluctuations within the period, assuming a constant growth rate, sensitivity to the choice of the beginning and ending values, and potential distortion in the presence of extreme values or outliers. Therefore, it’s important to consider additional measures and analyze the underlying data for a comprehensive evaluation.

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