Recs

9

Speaking Mathanese: Compound Annual Growth Rate

Welcome back to another edition of "Speaking Mathanese," our Motley Fool series that tackles financial math myths and deconstructs the computations that make the biggest difference to your bottom line.

This week, our quest to make you smarter than a fifth-grader takes us from the tantalizing topic of total return to the confounding confines of the compound annual growth rate.

The myth
Sadly, there are no reader questions to kick off this week's lesson (come on, people!), so let's get right to it by reliving last week's lesson.

Remember, each time your investment doubles, you've gained 100%. Compound annual growth rate, or CAGR, goes further by calculating your average return per year that you hold the investment.

So, if I asked you what the CAGR was for these stocks, what would you say?

Company

Total Return

Years

Boeing (NYSE:BA)

100.1%

3

Caterpillar (NYSE:CAT)

108.3%

3

Goldman Sachs (NYSE:GS)

144.2%

3

Hewlett-Packard (NYSE:HPQ)

111.0%

3

Research In Motion (NASDAQ:RIMM)

196.3%

3

Source: Capital IQ, a division of Standard & Poor's.

Just divide the total return by 3, right? Right?!?

The math
Not exactly. CAGR isn't a perfect average. Heck, it's not even a real number. Here's how Investopedia defines it:

CAGR isn't the actual return in reality. It's an imaginary number that describes the rate at which an investment would have grown if it grew at a steady rate. You can think of CAGR as a way to smooth out the returns.

To do that, you'll need the math, which is:

 ((Ending value / beginning value) ^ (1 / years)) - 1              

Still confused? Believe me, I understand. CAGR gets complicated because, instead of averaging, we're using exponents, raising the initial result of our total return calculation to the one-third power.

Let's run through an example. Say your $10,000 invested in Goliath Extra-Large Cell Phone Company (TICKER: THUD) has grown to $15,000 in three years. Dividing 15,000 by 10,000 equals 1.5.

Now, if you have a scientific calculator, or Excel, you can punch in 1.5 ^ 0.3333, which equals the one-third root. Hang on while I join you. The answer is ... (key-punching sounds) ... 1.1446.

Subtracting 1 from that gives us .1446, which, when expressed as a percentage, is 14.46%. Voila! I give you the compound annual growth rate, 14.46%.

Questions? Submit them here. (Please!) And see you next week for more mathanese.

For more money ideas, get 30 days of free access to Motley Fool Green Light right now. There's no obligation to subscribe.

Fool contributor Tim Beyers writes weekly about personal finance and investing basics. Have a Foolish money tip? Tell him. Tim didn't own shares in any of the companies mentioned in this article at the time of publication. Tim's portfolio holdings can be found at his Fool profile. His thoughts on personal finance, Foolishness, and investing in general may be found in his blog. The Motley Fool's disclosure policy is lobbying its local school district for a course in beginning mathanese.


Read/Post Comments (0) | Recommend This Article (9)

Comments from our Foolish Readers

Help us keep this a respectfully Foolish area! This is a place for our readers to discuss, debate, and learn more about the Foolish investing topic you read about above. Help us keep it clean and safe. If you believe a comment is abusive or otherwise violates our Fool's Rules, please report it via the Report this Comment Report this Comment icon found on every comment.

Be the first one to comment on this article.

DocumentId: 529540, ~/Articles/ArticleHandler.aspx, 7/30/2014 7:54:48 AM

Report This Comment

Use this area to report a comment that you believe is in violation of the community guidelines. Our team will review the entry and take any appropriate action.

Sending report...

Tim Beyers
TMFMileHigh

Tim Beyers first began writing for the Fool in 2003. Today, he's an analyst for Motley Fool Rule Breakers and Motley Fool Supernova. At Fool.com, he covers disruptive ideas in technology and entertainment, though you'll most often find him writing and talking about the business of comics. Find him online at timbeyers.me or send email to tbeyers@fool.com. For more insights, follow Tim on Google+ and Twitter.

Today's Market

updated 10 hours ago Sponsored by:
DOW 16,912.11 -70.48 -0.42%
S&P 500 1,969.95 -8.96 -0.45%
NASD 4,442.70 0.00 0.00%

Create My Watchlist

Go to My Watchlist

You don't seem to be following any stocks yet!

Better investing starts with a watchlist. Now you can create a personalized watchlist and get immediate access to the personalized information you need to make successful investing decisions.

Data delayed up to 5 minutes

Related Tickers

7/29/2014 4:03 PM
BA $122.32 Down -0.74 -0.60%
The Boeing Company CAPS Rating: ***
BBRY $9.51 Down +0.00 +0.00%
BlackBerry CAPS Rating: *
CAT $104.69 Down +0.00 +0.00%
Caterpillar, Inc. CAPS Rating: ***
GS $175.54 Down -0.41 -0.23%
Goldman Sachs CAPS Rating: ***

Advertisement