Saturday, June 13, 2009

Rule Of 72! It Doesnt Get Easier Than This!!!


Now a days I am learning a bit of fundamental analysis and I find myself in good company of fellow bloggers who have been more than welcoming in answering my queries and doubts. Anyway this post is about compounding since that forms the very basis of fundamental analysis. Albert Einstein seems to have said about compound interest "It is the greatest mathematical discovery of all time". And indeed it is! A beautiful story explains compounding can be read here.


One of the very basic calculations that one can perform about how long it takes to double your money given a particular interest rate is to use the RULE OF 72! It’s just a simple calculation and you won’t need a calculator to do it. For example if someone offers you a rate of interest let’s say 15% then if you divide 72 by 15 you get 4.8; that’s the number of years you will need to double your money at 15% rate of interest. Rule of 72 enables you to do quick mental calculations without the aids of calculators or spreadsheets. Before you proceed read about Rule of 72 here and here! Yup you won’t get the exact figure to the last decimal but it can get you close enuff to the exact figure!


A brief example on use of Rule of 72 to perform some simple calculations to find growth rates without the aid of calculators or spreadsheets. See the table assuming that it’s the EPS for company X over the period of 10 years.

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

0.25

0.30

0.50

0.50

1.05

1.50

1.75

1.75

1.90

2.05

Ok so we have company X EPS from 2001 to 2010 and we now want to calculate the growth rate. First we need to calculate how many times it has doubled in last nine years from 0.25 to 2.05. For this we take 25 (discard the decimals for time being) and double it once to get 50 and then double again we get 100 and double it yet again we get 200 which is almost near our figure 205. So we safely assume it has taken 3 doubles to reach 2.05 from 0.25 in nine years. We take 9(years) and Divide by 3. We get 3; it’s the number of years it takes to approximately double the EPS once. Now we take Rule of 72 and divide it by 3 and we get 24%. Therefore we assume EPS has grown at 24% over the last 9 years. Ok if using calculators or spreadsheet you would have got 26.34% as the EXACT answer. But like I said in the beginning Rule of 72 helps you to make rough calculations mentally if you don’t have the other aids at hand when needed!


Comprende?? Me neither when I first got into it, but now with a lil practice it’s a cake walk to calculate all those growth rates and surprise a few friends!!!


11 comments:

Bhoomitrader said...

Brilliant.

Manish said...

this is interesting...great!

deepak said...

As another friend was telling that 69 is more accurate. Whole idea is, to understand power of compounding and knowing that spending time on the technical indicators should not be the excuse to ignore researching fundamentals. Rich dad says I call the person as illiterate who cannot read a balance sheet. In a way, by writing this, I’m convincing myself to learn to interpret the balance sheet, even when I'm so called CA by education. We got to do it buddy as the saying goes. All said, Rule of 72 so brilliantly explained in the article and applied to EPS growth. Still if you find it difficult to compute then there is a calculator at Ruleoneinvestor.com.After all we need to live with our positive points.Have a wonderful weekend.

Tryin2Trade said...

Bhoomitrader Hi,

Love to see you here...thnks for appreciating the work!!!

Cheers

Tryin2Trade said...

Manish Hi

Thnks you found this interesting!!!

Cheers

Tryin2Trade said...

Deepak Hi'

Its a pleasure to have you commenting here. Well considering the fact you writing from Calgary I can boast of international connections.

Yes the calculator is available on the site you mentioned. Let me add to this this work itself was inspired by reading Phil Town's book Rule #1 which I feel should be on every novices table!!!

Cheers!

mayur said...

simply brilliant

Manish Chauhan said...

@Manoj

Nice stuff .. I tried to go deep and investigate why this rule of 72 works .

I did this .

(1+r)^N = 2 , should be the equiation which tells how much N will be given some r to making our money 2 times .

If you do some high school algebra , (1+r)^N can be expanded as 1+rN + (N^2)*r(r-1)/2 + Some other smaller terms which can be ignored .

So (1+r)^N = 2 can be written as

1 + Nr + (N^2) * r*(r-1)/2 = 2

This gives a very nice quadratic equation as

r(r-1)/2 * N^2 + r*N -1 = 0

If this is compared with aN^2 + bN + c =0 and we solve this equation with Shridharacharya method which we learned in High school

you can get

N = [ -r +- Sqrt(3r^2 -2r) ]/(r^2 -r)

Making it more neat and to simplyfy it ... I removed (-2r) under sqrt and make (r^2 - r) and (r^2) .

That gives a better and neat equation as

N = [-r + sqrt(3 * r^2)]/r^2

which actually is

N = [-1 + sqrt(3)]/r

so N = [sqrt(3) - 1 ]/r

now sqrt(3) - 1 = .731 approx

Which gives N = .731/r , as r is taken as actualy rate of interest (in decimal form)

We can say for N = 73.1/R (where R is like 12% or something like that) ..

To Make is appear better and something magical , that number is 72 ..

Hence it explains the reason why its 72 , atleast I am convinced :)

Manish
http://www.jagoinvestor.com

Tryin2Trade said...

MAnish HI,

Lets keep Rule OF 72 simple and the way it should be at least for zero math tolerance ppl like me.

The calculations you did are what occurs behind the scenes of this simple rule!

I thank you for your comments because your comments complete the post. What I wrote was a simple interpretation and what you wrote was what really goes behind this so called SIMPLE Rule.

I guess that makes it a complete picture!

Once again thanks and do keep on visiting!

Cheers

Manish Chauhan said...

@Manoj

Thanks , The main reason behind doing the maths was to let people know that even a general person can do same kind of stuff and its not a big deal , It can motivate them to try out stuff on there own .

Now people can come up with Rule of X for tripling there money ;)

Manish
http://www.jagoinvestor.com

michale wong said...

I find doing KLSE stock analysis is much more like following certain rules to get the result.