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I've been looking all over for this. I suppose it has already been answered somewhere but, although I appreciate the spreadsheet work others have done, if I don't understand the calculations and how to make them I can't be confident in the ideas.

Thanks.
No. of Recommendations: 7
"I've been looking all over for this. I suppose it has already been answered somewhere but, although I appreciate the spreadsheet work others have done, if I don't understand the calculations and how to make them I can't be confident in the ideas." - seehim

I agree wholeheartedly. You must be able to see the underlying logic before the whole things "fits". Let me see if I can answer your question simply and in a way that makes sense to you. You will need a calculator...or lots of time.

Compound interest in a fairly simple concept but it is rarely really understood by most people. They hear the term and they know that a bank pays interest, but the compounding is a mystery. However, it is simple math.

"8% annual interest" means you will get an increase in value each year of 8%. Simple enough. But, if you graph the effects of 8% interest, you get a parabola. Most people think in straight lines...and that is where the confusion begins. There are no straight lines in investing. Every investment is a curve. That is what the BMW Method proves to us.

Anyway, if you have a calculator and input the number 1.08, you have mathematically defined the definition of 8% interest. If you start with a dollar and multiply that dollar by 1.08, you will see what the CAGR of 8% will do for you over time.

At the end of year one, you have \$1.08...but that extra \$.08 compounds in year two. Thus, at the end of year two you will have \$1.1664. The following year, \$1.2597. And, so on it goes forever. If you never touch that original dollar, in 60 years, you will have \$101.26.

But, you asked how to calculate the CAGR. That is a tough calculation by hand...it is downright impossible without a calculator with the "Y to the X" function key. The formula which you are trying to reverse is the (1.08) to the 60th power. Some folks can do a square root manually, the 60th root is tough. But, a calculator makes it easy.

Just as the square root of 81 = 9, the 60th root of 101.26 = 1.08. Well, actually it is 1.0800005 but, who's counting?

Back at the very beginning, someone posted a link to a mortgage calculator which automatically does the CAGR calculation. Maybe someone remembers that link. There was also a way to get to a calculator right here in Windows that has a "Y to the X" function key. You can do it all very easily without spending a dime. Or, you can buy a calculator to help you for under \$20.

I hope someone will walk you through the links...I have forgotten the access to them. I always use my hand held calculator to do my calcs. However, the answers are always the same. This is just math. There is no trickery here.

However, I love to equate any investment to it's CAGR. Isn't that what we are all looking for? That is why I start by looking at the 30 year chart. A ten year chart will not show the overall trend...30 years will. You want to see a nice parabola sloping ever upward.

Now, a stock will go up and it will go down. Thus, the CAGR slope is not exactly like that smooth curve that we can plot with a calculator using a constant CAGR over time. The closer the stock's curve is to a smooth curve, the more "stable" the growth is. However, a perfectly smooth curve could make any stock less attractive to an investor. Think about it.

If a stock plotted out a perfect 8% curve, why would anyone sell it? It would be like guaranteed bank interest at 8%...everyone would run to invest in that business. That is, unless there was another one with an 8.1% CAGR...or a 16% CAGR. In that case, why would anyone buy the 8% business? But, that is why stocks go up and down...people are always looking for a "Better Bank" inwhich to place their money. Everyday, millions of Americans move their money around looking for the best deal.

I refuse to do that. To me it is stupid. Why move your money all around when you can spot the best deals at any point in time? You can simply plot the CAGR of a business and see where it is today. Then, you can decide if you like that deal better or worse than what you already have. Plus, you can see when the price is at it's lowest levels and buy at that point. You will maximize your gain and your CAGR at that point.

Go back and read "BMW BASICS NUMERO UNO" and "NUMERO DEUX." You are your own competition. You must do the best you can do...what more can you ask of yourself. You cannot trust others. They have an agenda that may or may not match yours which is to be the best you can be. They may need to sell you something.

I am selling nothing. I am not even selling the BMW Method. I am giving it away.

Now, you need to decide if it is aimed at helping you or at some other purpose. I will be honest with you. It is aimed at more than making you rich. You will learn all that as you think about the BMW Method.

There is a method in this madness we call America. The BMW Method is the formula for sorting out the truth. Try it, you may learn something that you were not looking to learn. But, it will definitely help you if you are honest, straightforward and always do the right thing.

The right thing by my definition is, "Always do what is best for you as long as it hurts no other human being who is honest, straightforward and does the right thing." See, it works for everyone. We are all in this together...but we need to give back to get what is good for us.

Once you see this, the BMW Method will make complete sense to you. Of course, you will only find it by using the BMW Method to your advantage. You will find that it hurts no one and it will help you. The BMW Method was my greatest invention. I have spent my life inventing it. Now, I am giving it away to help others. That is why I am here.

Why are you here? Get to work! You have lots of learning to sock away into that brain of yours. I am here to help in any way that I can. If you have any questions about the BMW Method, just ask. I am here as long as I am still drawing breath.

No. of Recommendations: 5
seehim,

Here's an article that explains CAGR calculations:

http://www.fool.com/workshop/2000/workshop000302.htm

`CAGR = (End Value / Start Value) ^ (1 / No. of Years) - 1`

Hope that helps.

Rich
No. of Recommendations: 0
Thanks Rich. That helps a lot.

seehim
No. of Recommendations: 3
seehim,

And then when you get tired of calculating them by hand, you can use this online CAGR calculator:

http://www.moneychimp.com/calculator/discount_rate_calculator.htm

Rich
No. of Recommendations: 0
although I appreciate the spreadsheet work others have done, if I don't understand the calculations and how to make them I can't be confident in the ideas.

Hi seehim,

I agree with you wholeheartedly. Others have responded with good links for explaining what the CAGR is. This post <http://boards.fool.com/Message.asp?mid=20593554> explains what the gebinr/zrpurser spreadsheet is doing, as well as how the CAGR lines are calculated. It also describes how you can over-rule what the spreadsheet is calculating automatically.

IcyWolf's spreadsheet uses the same CAGR equation to calculate the growth rates.

gebin
No. of Recommendations: 4
CAGR = (End Value / Start Value) ^ (1 / No. of Years) - 1" - TMFCop

Maybe this is a good time to get into the "guts" of the math. I would guess that many of us have heard the term "Present Worth." It is normally used to determine the value of various alternatives so that the lowest cost choice may be seen in the proper context.

One of the more visable examples is the way we hear the dollar today described as being worth \$0.48 of a 1964 dollar or \$0.27 of the 1964 dollar. The "value" keeps dropping.

What this actually says, without actually saying it, is that inflation has averaged about 1-3/4% since 1964. If you subtract 1-3/4% from unity and raise that to the 40th power, you will get 0.4935. That multiplied by a dollar gives us \$0.4935 or about the \$0.48 2004 dollar versus the full dollar of 1964. Actually, inflation has been greater than that, it has not been constant and it is something that we need to deal with in investing.

Inflation is our worst enemy and our best friend. Inflation of 1-1/2 to 2% is very, very healthy. Inflation of 4% is bad. Inflation of minus 4% is devastating! That would be the "deflation" about which Alan Greenspan was so worried just a year ago. A little inflation is just right...too much or not enough is very bad.

When we hear that, "The GDP grew by 5% in the forth quarter of 2003," we need to subtract about 2% for inflation...the real growth was the total economic growth minus inflation. If economic growth was 5% and inflation was 7%, we are moving backwards but we have a hard time seeing that fact. Look at 1974 through 1983. America was in trouble. We had double digit inflation and single digit growth. The stock market hated that scenario. 30 year Government Bonds were forced to yield as much as 13% to find buyers. Today, that rate is at about 4%. The rule of thumb is 2% over the inflation rate. Thus, if you can get a 4% yield on your savings when the infltion rate is 2%, you are actually just "gaining" 2% on your money.

The last time I was in my bank, the rate on savings accounts was 3/4% per year. Money there is losing about 1-1/4% every year it is sitting there. CD's at 2% are breaking even...there is no real gain being made...except you are not losing money.

OK, back to the math. TMFCop said, "CAGR = (End Value / Start Value) ^ (1 / No. of Years) - 1". Let's look at that formula.

When we initially divide the ending price by the starting price, we do one thing that it is easy to miss. We immediately take away any real asssociation with "value". We have just defined the "Compound Amount Factor". The CAF is the inverse of the "Present Worth Factor"(PWF). Instead of our dollar going down in value as with any inflation, we have taken the right step in finding our real return over time.

By dividing \$ by \$, we have a dimensionless factor. The starting price went to \$1.00 no matter what it actually was. The ending price stopped being a price and became a ratio of values.

When I first started using the CAGR for evaluating stocks, I would search back in time until I found what I considered to be the point where the price was \$1.00/share. That then determined the number of years for my evaluation.

One day it occurred to me that it would be far less time consuming to merely set the number of years as a constant and divide the starting price into the ending price. That did the same thing much quicker and easier. I picked 30 years because I found that the parabolic curve was very obvious on any stock after that time, or it did not exist at all.

After ten years of studying stocks and their CAGRs, I can tell you that numbers over 15% are very rare. But, high returns of 12% to 14% are very normal and sustainable for great business franchises.

Now, that is where the BMW Method can be your anchor in a storm. You do not want to over emphasize your first reading of the CAGR, but if you find that, after 30 years, a business' stock price has grown at 13%, you need to become very excited to learn much more about that business.

But, as you look at the chart of that stock, you will see that the stock's price rises and falls in a fairly predicable pattern over time. The BMW Method is aimed at buying when the stock is at it's 30 year low price and selling as it reaches it's 30 year high. That is not that hard to do...your own graphing will show that to you.

But, here is the bottom line. Lets say that a given stock seems to go up for 4 years and down for two. The low CAGR is 12% overall. Here is what we are doing in reality. If we look at a six year period, the stock will be up 13% on average. So, lets start at a low point and see what happens. The stock goes up from that point at a CAGR for four years and then drops at a negative CAGR for two...at the end, the stock's low CAGR is up 12% from the previous low.

But, the high CAGR is about 14% since the CAGR is 13%. If we can cut out the negative CAGR by selling near the 14%, we can eliminate the negative CAGR almost completely and maximize our personal return on that stock. Simple enough?

Lets use an example. If we start in 1998 near a 12% low CAGR, a stock is at \$20/share. It then goes up to the 14% high CAGR by 2002 at \$48/share. Then it drops back down to the new 12% low CAGR at \$39/share. Next, it cycles back up for four more years to \$105/share.

The math says that everything works. \$39/\$20 = 1.95 gain in 6 years or a low CAGR of 11.7%. The high CAGR was \$105/\$48 = 2.08 also in 6 years so the high CAGR was 13.9%. But, what happened because we chopped out the down years?

Look at the \$20/share to \$48/share in four years from the low to the high...that CAGR was 24.5%...almost double the average if 13%!

Try the next cycle. \$105/\$39 is a 28% CAGR. Is that possible? The numbers say it is not only possibel, it is inevitable if the business continues to grow at the same rate as it has for over 30 years.

The only real risk is in missing the bottom by either buying too soon or waiting too late. The key is to tip-toe into the stock and make sure you get in at the bottom. If you wait until the bottom is obvious, you will miss the best returns.

To me, the CAGR is the investor's best tool. It is like a roadmap to the future. Past performamnce is never a guarantee of future success...but what is? There are no guarantees in life.

What confuses me is that I have never seen this idea discussed anywhere before. This is not rocket science...it is simple economics. The time value of money has been around for ages. But, no one seems to want to teach it to us. I wonder why?

No. of Recommendations: 2
"CAGR = (End Value / Start Value)^(1 / No. of Years) - 1"- TMFCop

What value do you assign for TMFCOP?

I think since all the great work he has done here and posting his graphs on his Yahoo Web Site, this is would be a hard value to assign!

Happy Easter All.

Goo

No. of Recommendations: 2
Here's a calculator to figure out the current CAGR-http://mortgages.interest.com/content/calculators/compound.asp
Here a calculator to help plot the CAGR curve on your charts-
http://texasstatebank.com/tools/compound-interest.html
Joe
No. of Recommendations: 0

http://mortgages.interest.com/content/calculators/compound.asp

cat
No. of Recommendations: 0
Here's an article that explains CAGR calculations:

http://www.fool.com/workshop/2000/workshop000302.htm

CAGR = (End Value / Start Value) ^ (1 / No. of Years) - 1

Finally! I was interested in giving this method a look & adding it to my other research & have spent TWO DAYS reading through this board & FC trying to find the mathematics behind this -- thanks!!

Wingenit
No. of Recommendations: 0
Here is quick calculator that will give you a CAGR in no time. It is for mortgages, but it is the same time value of money calculation.

http://boards.fool.com/Message.asp?mid=20549917
No. of Recommendations: 0
Thank you -- I'm trying to figure CAGR on a company that has only been publicly traded since 1990, and I'm not sure if I'm doing it right. When I have a few more minutes than I do now, can I ask if I'm using the right numbers? Would I post that to the board as a question or ask you directly?

Thanks,

Wingenit
No. of Recommendations: 1
I'm trying to figure CAGR on a company that has only been publicly traded since 1990

Hi Wingenit,

Post to the board. We all can learn. However, to preempt your question... :-)

In generic terms:
`     CAGR = (EndingPrice / StartingPrice) ^ (1 / #ofYears) - 1`
Suppose the stock was at \$30.00 at the end of May 1990 and ended May 2004 at \$90.00. That is 14 years. Your equation would look like:
`     CAGR = (90.00 / 30.00) ^ (1 / 14) - 1     CAGR = 3^(1/14) - 1     CAGR = 1.081633 - 1     CAGR = 0.081633 or 8.16%`
That means that the stock price increased by 8.16% per year, every year, for fourteen years. (The actual growth, of course, was not that smooth.)

Hope this helps.

gebin
No. of Recommendations: 3
Wingenit,

And in case it wasn't intuitive in what gebin was saying, while 1990-2004 is 14 years, you actually have 15 years worth of data (1990 being year 1 and 2004 being year 15), but 14 years of growth.

The reason I bring this up is that when using CAGR calculators that you find on various websites it will ask for the number of years you want to calculate. And many times, when people are looking at a list of numbers, say revenues, they count up all the years that are in the list and end up with one more than they actually have.

For example, if you go to a site like MSN MoneyCentral, you can find annual revenues for a company for the past 10 years. People will plug in the first year's revenues, the last year's revenues and then count that they have 10 years worth of data. That's true, but you're only looking at 9 years worth of growth.

Just as if you looked at revenue growth from this year and last year to find the growth rate, you have two years of data but only one year of growth.

Hope that didn't muddy the waters.

Rich

No. of Recommendations: 0
gebin,

One thing that is throwing me off is low CAGR, high CAGR, and figuring out which the current price is closest to.

Also, the stock price has gone up very dramatically during 2004. If I go through the end of 2003 it gives me a CAGR of about 14%. If I go through the first six months of this year & figure it as 14.5 years, I come up with a CAGR of over 17%. I don't know if this is because the timeline is so short, or what to do with this.

I'm going to try again with the spreadsheet & keep reading through the boards -- you can see how far I'm up to! I'm sure that many of my questions are answered on here somewhere & I hate to annoy everyone with basic questions.

Thanks!

Wingenit