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How to calculate a compound annual growth rate

How to calculate a compound annual growth rate

Calculating an average rate of return over time provides a useful method of comparing the performance achieved by different firms or assets.

The formula to calculate a compound annual growth rate (CAGR) is:

[CAGR] = ( ( [Final Value] / [Inital Value] ) ^ ( 1 / ( [Ending Year] - [Starting Year] ) ) ) - 1

Key definitions

  • CAGR – Compound Annual Growth Rate
  • Ending Year – The final year of the period for which performance is being evaluated.
  • Final Value – The asset value at the conclusion of the evaluation period.
  • Initial Value – The asset value at the beginning of the evaluation period.
  • Starting Year – The initial year of the period for which performance is being evaluated.

What is a compound annual growth rate?

A compound annual growth rate ignores market volatility by providing a smoothed average return over a time period.

Why calculate a compound annual growth rate?

The compound annual growth rate provides a rough performance comparison method across firms. For example, how did the results of a group of fund managers or financial advisor compare over the last 5 years?

As with any statistic, using CAGR comes with health warnings. A compound annual growth rate provides a rear view mirror on what did happen but makes no attempt to project what may yet happen.

As an average the CAGR smooths away volatility, meaning the actual experience may have been a bumpier ride than the average makes it appear.

Always “trust, but verify” by being mindful of the context in which a CAGR is presented. A firm may boast of outperformance over the last 3 years, however their base may have been lower than their competitors after some dire results the year before the evaluation period.

Illustrative example

I want to calculate the 5-year compound annual growth rate of an investment property.

[CAGR] = ( ( [Final Value] / [Inital Value] ) ^ ( 1 / ( [Ending Year] - [Starting Year] ) ) ) - 1

[CAGR] = ( ( 684,000 / 492,500 ) ^ ( 1 / ( 2017 – 2012 ) ) ) – 1 = 6.79%

Next I want to compare that CAGR figure to the equivalent period return of the S&P500.

[CAGR] = ( ( 2,673.61 / 1,258.86 ) ^ ( 1 / ( 2017 - 2012 ) ) ) - 1 = 16.26%

Based upon these figures we can conclude that the compound annual growth rate of stock market outperformed the investment property over this period.

CAGR can tell a number of stories. Now consider the performance of the equity I contributed to the property, as opposed to the money borrowed from the bank.

[CAGR] = ( ( ( 684,000 – 443,250 ) / 49,250 ) ^ ( 1 / ( 2017 - 2012 ) ) ) - 1 = 37.35%

This time the property’s compound annual growth rate convincingly outperformed the stock market. When applied judiciously leverage can be a powerful growth accelerator. This highlights how important it is to understand the figures behind quoted CAGR values!

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