# Applying some Maths to stocks



## OFS (20 January 2014)

Hi all,

This is my first post after some time spent reading this great forum.

I've decided to register and make some questions to people more expert than me on financial matters.
I would like to play Maths with stocks, but not in terms of Moving Averages et simila, but working on fundamentals, instead.


First question is related to the Price-to-Earnings ratio, P/E. It can be calculated on past performance or future expectations.

P/E = Price / Earnings per share

Price = $540.67
EPS = $39.75

P/E = 540.67 / 39.75 = *13.6*

A P/E of 13.6 seems a bargain for a big company like Apple.
_Question 1: Would you agree on the above statement?
Question 2: How you pick stocks based on P/E ratios?_





The P/E/G ratio is similar but takes into account the growth rate estimated for the next 5 years.
P/E/G = Price to earnings ratio / growth rate next 5 years

P/E = 13.60
Growth rate for EPS in next 5 years = +12.10%

P/E/G = 13.60 / 12.10 = *1.12*

When referring to EPS in next 5 years, it seems that Apple isn't a good buy. P/E is bigger than growth, meaning it is overvalued.
_Question 3: would you agree with the above statement?_





If the above outcome seems unfair for Apple, let's what happens if we refer to the past performance (+41.52%):

13.60 / 41.52 = 0.33

In this case, if we refer to past performances of growth rate, the actual P/E seems to be a great bargain.
_Question 4: would you agree with the above statement?_



Next analysis is related to regarding the stock price as the discounted value of expected future dividends, that is:

P = D / K

Where:
P = Current stock price;
D = Current dividend rate;
K = Required rate of return.

We get:

D = $3.05 (declared on 28th of October 2013)
K = 10%

P = 3.05 / 0.10 = $30.50

Now, to get a decent return based on future dividends, the fair price for Apple should be $30.50. In terms of dividends, Apple is 17.7 times overvalued.
_Question 5: would you agree with the above statement?_

The return rate I get from Apple in terms of dividends is:
K = 3.05 / 540.67 = 0.6%
The return I get from dividends investing in Apple is an absolute "stay away".
_Question 6: would you agree with the above statement?_





The last analysis is fair for a no-growth company that gives satisfactions to its shareholders through dividends, but Apple is a growth-company, even a fast-growing one if we refer to past performance. Something different should be used, in this case:
P = D / (K - g)

Where:
P = Current stock price;
D = Current dividend rate;
K = Required rate of return;
g = growth rate in earning per share = 9.50% (estimates for next year)

We get:
P = 3.05 / (0.10 - 0.0.95) = *$610.00*

If we take into account the growth rate in earning per share, a fair price for Apple would be $610.0 versus the actual $540.67. In these terms, the actual stock price is slightly underestimated.
_Question 7: would you agree with the above statement?_



Let's stop here to avoid to make it too long.
You can decide to answer also to just some of the above 7 questions.


Best regards,
OFS


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## Value Collector (20 January 2014)

Hi,

One thing I would like to point out is that mathematics only get you so far. When it comes to investing you have to be able to assess the Quality of the business also, you may sometimes hear people discuss the two areas as being quality and quantity.

the reason it is important to be able to judge quality is that some companies may only be worth PE10, where others may be worth PE25, It's its not as simple as just looking at the previous growth in earnings, You have to be able to put your business man hat on and value businesses from the ground up, only after you have a understanding of the businesses quality can you judge what the correct PE ratio should be and whether it is under or over valued.


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## OFS (20 January 2014)

Value Collector said:


> Hi,
> 
> One thing I would like to point out is that mathematics only get you so far. When it comes to investing you have to be able to assess the Quality of the business also, you may sometimes hear people discuss the two areas as being quality and quantity.
> 
> the reason it is important to be able to judge quality is that some companies may only be worth PE10, where others may be worth PE25, It's its not as simple as just looking at the previous growth in earnings, You have to be able to put your business man hat on and value businesses from the ground up, only after you have a understanding of the businesses quality can you judge what the correct PE ratio should be and whether it is under or over valued.





Hi Value Collector,

Thank you for your reply.
I totally agree with your post and I share your same vision: a stock trader should be a good businessman first and then he should know some numbers basics. 
There are two different fields, as you point out: quality and quantity.

Let's say this thread is fully focused on quantity, well knowing that it is just one part of the whole picture.

I have some stocks on my watchlist that I would like to discuss in a separate thread, but for the moment I want just to be sure that I have the correct knowledge of the basic ratios.


Best regards,
OFS


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## pixel (20 January 2014)

Yes, "what he (Value Collector) said."

Plus, *Sentiment Rules. OK.* You can do all the Math and Fundamentals you like: It's the market perception that defines the value. Be prepared to accept that it may differ widely from your estimate. 
For example: Where do you get the next 5 years' earnings estimates? Do you accept brokers/ analysts' fore casts? If so: Which ones? 

I would suggest you obtain some past data and forecasts of a significant number of stocks (use some that you wish to trade) and apply your Maths retrospectively to those data. That way, you can answer Dr. Phil's stock question and work out "How's it workin' for ya?"


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## burglar (20 January 2014)

> “The stock market by its very nature is designed for you to lose money. The rallies and reactions within any trend ensure this process is at work constantly. It is created automatically. The market behaves this way because it has to! The weak have to perish so that the strong can survive. Professional traders are fully aware of the weaknesses in traders under stress and will capitalise on this at every opportunity.”





free download from “Master the Markets”, Tom Williams

Read more here:


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## pixel (20 January 2014)

burglar said:


> free download from “Master the Markets”, Tom Williams
> 
> Read more here:




Hey! I thought I had coined that phrase many years ago


> *The wide-spread promotion and use of derivatives facilitates the transfer of wealth from the less sophisticated Many to the powerful unscrupulous Few.*



in this blog: http://rettmer.com.au/TrinityHome/Trinity/Musings.htm#onhedgefunds


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## burglar (20 January 2014)

pixel said:


> ... It's the market perception that defines the value ...




A smallish correction if I may ... market perception defines *price*.

Given intangibles and assorted variables, no-one can correctly calculate the value.


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## Zedd (20 January 2014)

To your actual specific questions:



OFS said:


> A P/E of 13.6 seems a bargain for a big company like Apple.
> _Question 1: Would you agree on the above statement?
> Question 2: How you pick stocks based on P/E ratios?_




P/E gives a quick way of comparing a company to current market/industry valuations/sentiment, rather than a buy signal. I'd be comparing it to competitors - Microsoft, Google, Samsung? If it's significantly different to it's peers then it raises the valuable question of why? 

If you're looking for undervalued companies based purely on an earnings valuation then P/E will flag those for consideration. 



OFS said:


> When referring to EPS in next 5 years, it seems that Apple isn't a good buy. P/E is bigger than growth, meaning it is overvalued.
> _Question 3: would you agree with the above statement?_




Again, raises questions rather than black/white answers, but from this I'd think it likely that the market believes the company has something else going for it besides it's projected earnings growth.



OFS said:


> In this case, if we refer to past performances of growth rate, the actual P/E seems to be a great bargain.
> _Question 4: would you agree with the above statement?_




It's certainly an interesting POV. Personally never looked at this valuation. As a general rule though past performance is a dangerous place to look for future outcomes.



OFS said:


> Now, to get a decent return based on future dividends, the fair price for Apple should be $30.50. In terms of dividends, Apple is 17.7 times overvalued.
> _Question 5: would you agree with the above statement?_
> 
> The return I get from dividends investing in Apple is an absolute "stay away".
> _Question 6: would you agree with the above statement?_




All I'd be taking from these valuations is that you've correctly identified that there's no profit to be had at current dividend levels.



OFS said:


> If we take into account the growth rate in earning per share, a fair price for Apple would be $610.0 versus the actual $540.67. In these terms, the actual stock price is slightly underestimated.
> _Question 7: would you agree with the above statement?_



Yes - providing you're RRR is 10% and not 11%, and that you're confident they'll hit the earnings growth projected.

From reading the news I know Apple has experienced exceptional growth over the last few years due to it's largely unique product line but this market advantage has been worn down so growth is not expected to be as stellar in coming years. It has managed to amass a rather large amount of cash though so there's an expectation that the cash will be used to fuel growth through large R&D or acquisition. There's also been a shareholder movement pushing to have a significant portion of the cash returned to shareholders through a special dividend also. 

All of this is hinted at by your various valuations and that's what I like about the maths aspect of stock picking. In a matter of minutes you've managed to ask a number of valuable questions that point you in the right direction. 

The decision I then have in my mind is after understanding why it's valued where it is what am I willing to speculate on that isn't being allowed for?


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## Value Collector (20 January 2014)

pixel said:


> Plus, *Sentiment Rules. OK.* You can do all the Math and Fundamentals you like: It's the market perception that defines the value. Be prepared to accept that it may differ widely from your estimate.
> For example: Where do you get the next 5 years' earnings estimates? Do you accept brokers/ analysts' fore casts? If so: Which ones?
> 
> I would suggest you obtain some past data and forecasts of a significant number of stocks (use some that you wish to trade) and apply your Maths retrospectively to those data. That way, you can answer Dr. Phil's stock question and work out "How's it workin' for ya?"




Sentiment is the leading driver of market price, and companies can remain both undervalued and over valued for an extended period of time, which in my opinion makes a value approach less suited to trading. As they say, short term the market is a voting machine, long term its a weighing machine.

If you want to use the value approach you have to be willing to be am investor rather than a trader, for example when (TGR) Tassal was $1.50. I had it conservatively valued at $2.92, So I loaded up, But it took 2 years to get to $3.25 where it sits now, which more than compensated my waiting time of 2 years, especially with dividends, But a lot of traders don't have the will to stay in like that.


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## OFS (22 January 2014)

pixel said:


> Yes, "what he (Value Collector) said."
> 
> Plus, *Sentiment Rules. OK.* You can do all the Math and Fundamentals you like: It's the market perception that defines the value. Be prepared to accept that it may differ widely from your estimate.
> For example: Where do you get the next 5 years' earnings estimates? Do you accept brokers/ analysts' fore casts? If so: Which ones?
> ...





Hi pixel,

Thank you for adding your point of view to this thread.
I agree with you and I'm not confident at all on estimates and analysts' forecasts. I won't forget what I read on Peter Lynch's book: an analyst once published the following statement "given the recent bankruptcy, we are removing the company from our Buy List".

I'm also aware that past performances are not an indicator of future earnings.

- - - Updated - - -



burglar said:


> free download from “Master the Markets”, Tom Williams
> 
> Read more here:




Hi burglar,

Thank you for this great suggestion. I've downloaded it and it is in my list of books to be read.


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