Compound Annual Growth Rate or CAGR

Calculate Total Return and Compound Annual Growth Rate or CAGR

Evaluate Your Investment Performance By Calculating Total Return and CAGR

Learning how to calculate both total return and the compound annual growth rate of an investment, or CAGR, are two of the best gifts you can give yourself if you want to get ahead financially in life.

You can learn how to calculate an investment's total return and an investment's compound annual growth rate, also known as CAGR, in just a few minutes. This should help you evaluate your investment performance more easily as you'll be able to gauge how much richer or poorer you are from your investments in various asset classes such as stocks, bonds, mutual funds, gold, real estate, or small businesses.

 An Introduction to the Concept of Total Return
The total return on investment is straightforward and easy. Basically, it tells the investor the percentage gain or loss on an asset based upon his purchase price. To calculate total return, divide the selling value of the position plus any dividends received by its total cost. In essence, this works out to capital gains plus dividends as a percentage of the money you laid out to buy the investment.

How to Calculate Total Return

An investor had a cost basis of $15,100 in PepsiCo stock (she purchased $15,000 worth of Pepsico stock and paid $100 total commissions on the buy and sell orders). She received $300 cash dividends during the time she held the stock. Later, she sold the position for $35,000. What was her total return?

We can plug the variables into the total return formula to find our answer. First, we take $35,000 received upon the sale of the stock and add the $300 cash dividends received to get $35,300.

Next, we divide this by the cost basis of $15,100. The result is 2.3377% or 133.77% total return on invested principal (remember that 1.0 of the total return is the principal so we must subtract it out if we want to express the gain or loss as a percentage; 2.3377 - 1.0 = 1.3377, or 133.77% expressed as a percentage.

Had the result been 1.5, the total return expressed as a percentage would have been 50% (1.5 - 1.0 = .5, or 50%)).

 

Was this a good rate of return on the investment? Total return can't answer that question because it doesn't take into account the length of time an investment was held. If the investor earned 133.77% in five years, it is cause for celebration. However, it took her twenty years to produce such a return, this would have been a terrible investment.

An Introduction to the Concept of Compound Annual Growth Rate (CAGR)

Needing to account for the length of time it took to produce a given total return, the investor is in need of a metric that can compare the return generated by different investments over different time periods. This is where CAGR comes to the rescue. CAGR does not represent economic reality in a certain sense but rather, it is a valuable academic concept. A stock position might be up 40% one year and down 5% the next. CAGR provides the annual return for such an investment as if it had grown at a steady, even pace. In other words, it tells you how much you would have to earn each year, compounded on your principal, to arrive at the final selling value. The real-world journey could be (and often is) far more volatile.

 Practically all of the best stock investments in history have experienced declines of 50% or more, peak-to-trough, all while making their owners fabulously wealthy.

 

"Couldn't you just take the simple return and divide it by the number of years the investment was held?" you may ask. Unfortunately, no. To understand the reason, go back to our PepsiCo example and assume the investor had held her position for ten years. A person who doesn't understand the mathematics might divide the total return of 133.77% by 10 years and calculate that her annual return was 13.38%. Try to check the math using the future value of a single amount formula. If you do, you'll discover that had the investment of roughly $15,000 grown by 13.38% annually, it would have been worth an ending value of $52,657; a far cry from the $35,000 for which the investment was sold.

The reason for the disparity is that this flawed method doesn't take compounding into account. The result is a gross misstatement of the actual return the investor enjoyed each year.

How to Calculate Compound Annual Growth Rate (CAGR)

In order to calculate CAGR, you must begin with the total return. In our above example, the total return was 2.3377 (133.77%). We also know the investment was held for ten years.

Multiply the total return (2.3377) by the X root (X being the number of years the investment was held). This can be simplified by taking the inverse of the root and using it as an exponent. In our example, 1/10, or .10 (had the number of years been 2, you could have taken 1/2 or .5 as the exponent, 3 years would be 1/3 or .33 as the exponent, four years would be 1/4 , or .25, and so on and so forth.)

In our above example, CAGR would be calculated as follows:
2.377^(.10) = 1.09, or 9% compound annual growth rate (again, recall the 1.0 represents the principal value which must be subtracted; ergo, 1.09 - 1.0 = .09, or 9% CAGR expressed as a percentage).
In other words, if the gains on the PepsiCo investment were smoothed out, the investment grew at 9% compounded annually. To check the result, use the future value of a single amount. In essence, this means that if the investor had taken the roughly $15,000 to a bank for ten years and earned 9% on her money, she would have ended up with the same balance of $35,300 at the end of the period.

More Examples Showing You How to Calculate Compound Annual Growth Rate (CAGR)

Thirty years ago, Michael Adams purchased $5,000 shares of Wing Wang Industries Inc. He recently sold the stock for $105,000. During his holding period, he received a total of $16,500 in cash dividends. Both his original and selling commissions were $50 each. Calculate the total return and CAGR of his investment position.

Step 1: Calculate Total Return
$105,000 received upon sale + $16,500 cash dividend received = $117,000
----------------------(divided by)----------------------
$5,000 investment + $100 total commissions = $5,100 cost basis
= 22.94 total return (remember, had you wanted to express total return as a percentage, you would have to subtract 1 (e.g., 22.94 – 1), to get 21.94, or 2,194%.)

Step 2: Calculate CAGR
Find the inverse of the X root (1/30 years = 0.33)
22.94 (.033)= 1.1098, or 10.98% CAGR
(Again, remember that in order to express as a percentage, you must subtract the result by 1 (e.g., 1.1098 – 1 = .1098, or 10.98% CAGR.)
All in all, this is a decent return for the time period.

Up for trying another? Good. Let's go.
Jasmine Washington purchased $12,500 of common stock in Midwest Bank Inc. She recently sold the investment for $15,000 and received cash dividends of $2,500 during her holding period of four years. She paid a total of $250 in commissions. What is her CAGR?

Step 1: Calculate Total Return
$15,000 received upon sale + $2,500 cash dividends received = $17,500
----------------------(divided by)----------------------
$12,500 investment + $250 commissions = $12,750 cost basis
= 1.37 total return

Step 2: Calculate CAGR
1.37 (.25)= 1.08, or 8% CAGR

Some Final Thoughts About Total Return and CAGR

I've talked quite a bit in the past about how investors are duped into ignoring total return, which is ultimately the only thing that matters once you've adjusted for risk and moral considerations.  One illustration is the way most stock charts are structured.  This has important real-world consequences because you can materially improve your understanding of your investment performance, and make better-informed decisions as a result, by focusing on total return.

Consider a former blue chip stock, the now-bankrupted Eastman Kodak.  With the shares getting wiped out, you'd think that a long-term investor did poorly, wouldn't you?  That he or she would have lost all of the money put at risk?  Not by a long shot.  Though it could have turned out much better, obviously, an owner of Eastman Kodak for the 25 years prior to its wipeout would have more than quadrupled his or her money due to the total return components are driven by dividends and a tax-free spin-off.  In addition, there were tax benefits to the ultimate bankruptcy that, for many investors, could shield future investment profits, further softening the blow.  It's related to a phenomenon I call, "the math of diversification".

On the topic of compound annual growth rate, the important thing is to internalize how extraordinarily powerful it can be over long stretches of time.  An extra percentage point or two over twenty-five or fifty years, which most workers will be fortunate enough to enjoy if they begin the investing process early, can mean the difference between a mediocre retirement and ending up on top of a sizable fortune.  Whenever the news is filled with yet another minimum-wage earning janitor dying and leaving behind a secret multi-million dollar portfolio, one of the common themes is that the person who built the private empire harnessed a good CAGR over many, many, decades.  This is one of the reasons it is important to avoid things like shorting stock, trading on margin, and exposing yourself to blow-up risk.