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What is dilution?

Hi all,

I just ran into my first question. And its was a great question.

What is dilution? How do you calculate it?

In TomG's thumbnail valuation one has to guess how many shares there will be in a future time period. It is important to guess this number to perform many guesstimates about future earnings per share, or cash flow per share, so that you can apply a multiple. This latter word multiple may also need to be explained.

A PE ratio is a multiple of earnings.

In TomG's thumbnail valuation he uses a multiple of owner's earnings or cash flow.

http://newsletters.fool.com/04/issues/2004/08/01/08.aspx

Here is an article that explains dilution:
http://www.fool.com/news/mft/2003/mft03080402.htm?ref=foolwatch&vstest=search_042607_linkdefault

An increase in shares is not always dilutive. Or we can call it the good type of dilution. For instance, a company can issue shares to buy a company that is immediately accretive to earnings. At some point in time, the earnings add to the Company's numbers and more than offset the number of shares issued to purchase it. To tell whether a company acquired added value is to compare the earnings per shares before it bought the company with the earnings per share produced after the company was bought. Often, it takes some years for earnings produced by the acquired company to offset the number of new shares issued. But not always.

But regardless of the reason shares increase we need to keep the number in mind when we are running estimates about the future.

I will run an example using ANST - my company to follow:



Tools we need to use:
CAGR calculator
http://www.moneychimp.com/calculator/discount_rate_calculator.htm


ANST latest 10K - http://tinyurl.com/36p87p

Dilution may be one of the best reasons that support my viewpoint that long-term investors do a much better job understanding their company than analysts. As we study the 10Q and 10Ks we learn about the reasons behind every increase in shares issued. So a 3% boost in shares outstanding may be offset by future value creation. When shares increase because of an acquisition, long-term investors have better insights to whether they believe it was worth it or not. In the years to come we will look at dilution figures for all of our companies and add our own footnotes - something that analysts do not generally have time to do.

Numbers I need from my 10K:
ANST provides diluted share count from many previous years.

Year ---- Diluted share count
2002 ---- 27.298 million
2003 ---- 23.618 million
2004 ---- 26.496 million
2005 ---- 25.892 million
2006 ---- 25.851 million

When I look at the above, I already see an anomaly. What happened in 2003 that caused the numbers of shares to drop to 23.618 million from 27.298 million? In order to find out we would have to look at the 10Q before 2003 and see. They may have bought back shares. For the example, I am just going to continue without doing any more research on why. Instead I am going to skip to 2003.

Using my cagr calculator: I can find the dilution rate between 2003 and 2006
The CAGR calculator is linked above.

The inputs I use are:
23.618
25.851
3 years

Total dilution rate 3.05%

Now we can apply this to future years. The diluted share count was 25.851 million at the end of 2006. This is close enough for our calculations. If I want to guess how many shares are likely five years from now, I only have to apply a 3.05% dilution rate.

There are two ways to do this:
We can take the 25.851 * 1.0305 * 1.0305 * 1.0305 * 1.0305 * 1.0305
Or you can use the equation:

(1.0305 ^ 5) * 25.851

We can use our Microsoft calculator to do this very simply. Every windows based computer has a scientific calculator which will allow you to do this calculation very quickly.

Click 1.0305
Click x^y button
Click 5 (for five years)
Click x^y button again and you get 1.16

Multiply the diluted share count of 25.851 * 1.16 and you get the number of shares probable in year 2011 about 30.04 million.

This number is very important if we are trying to project earnings per share into the future. These calculations are just a guideline and should not replace an attempt to understand the business or running regular calculations for different time periods to help you see if your company is on track.

I generally use earnings per share.
Ansoft reported $0.69 in 2006

I checked yahoo estimates for growth and they believe that ANST will grow earnings by 13.8% next year. I can project those earnings out five years. However, I must warn you I am not ready to do this for ANST. I have no clue what they actually do or what type of earnings growth I can expect. But we should still project the earnings out to see what our company might look like if they hit these targets.

This is why so many people that use PE or cash flow multiples create such horribly wrong projections. They create future guesses based on analysts' estimates and we don't know how good they are. What we want to do is create a guideline and tweak it as the quarters pass to see how well our company stays on track. By doing this we can begin to accurately estimate a good value for our company. This takes quarters and years to get it where it actually starts creating accurate results and that is why long-term investors or long-term students of their stocks will do the best. Hopefully as we develop many such studies we will have many accurate models.

To continue:

In 2006, ANST reported $17.797 million in earnings. You can do the same with cash flow.

Cash flow calculation for ANST. I use a very simple formula.
Cash provided by operations – Capital expenditures = cash flow or operating cash flow or a myriad of other names.

Net cash provided by operating activities --- 25,970,000
Purchases of equipment and furniture 1,134,000
$25,970,000 - $1,134,000 = $24,836,000

We have $24,836,000 in cash flow
We have $17,707,000 in earnings

Again we are using inputs based on analysts' estimates that can be found at Yahoo. After we understand our companies better are projections are likely to be much better than theirs.

Yahoo believes ANST will grow earnings by 13.8% next year. But they do not give five year estimates for them. They will for some companies. So, we will project 13.8% as our projections for the next five years. This is not supposed to be a concrete prediction just a guideline which we will use year after year to see if our company is on track. If not, we will try to find out why and that is what creates a better model.

So, Cash flow of $24.836 million * (1.138 ^ 5)
$24.836 * 1.91 = $47.40 million by 2011

Earnings
$17.707 million * 1.91 = $33.82 million

In order to apply a multiple we have to know the earnings per share. We calculated that by 2011 ANST should have 30.04 million shares outstanding based on a dilution rate of 3.05%.

Cash flow per share in 2011 $24.836 / 30.04 million = $0.83 per share
Earnings per share in 2011 $33.82 million / 30.04 = $1.13 per share

How do you assign a multiple?

Well you can use the industry average or you can take a company average. This is also a part of the model best tweaked over time. Today ANST has a PE of 38, so if investors believe they are worth 38 times earnings in 2011, then the company would sell for $42.78.

But what if they only are awarded a PE of 20, then the future price target would only be $22.60 which is much less than today's price. So, now I know that investors believe they will grow earnings faster than 13.8% - I have to find out why. It generally takes me a lot of extra research to find out why. And I generally only motivated to dig this deep if I own a company, but for ANST I will dig very deep.

Please ask questions. Learning how to project future price targets is key to any valuation. The projections are seldom accurate; the key is creating a guideline and learning every quarter why the projection missed. They can miss on the upside or the downside and by learning what caused the deflection we begin to understand how best to predict future prices. If our projects are correct, we can begin to calculate the best prices to add money.

This is a very simple overview. As I study ANST I will show you how I tweak my models. If you have questions please ask. I did not proofread so the wording, spelling and even math may be off, so go through the numbers ask questions about the wording. We will improve this answer for future Nikitanites.


Tom e
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I was curious what Diluted Shares were and found this on Wikipedia...

http://en.wikipedia.org/wiki/Diluted_Earnings_Per_Share
Diluted Earnings Per Share

Diluted EPS is a company's EPS figure as calculated using fully diluted shares outstanding (i.e.including the impact of stock option grants and convertible bonds). This is important in showing the users of the income statement a "worst-case" scenario if everyone that could have received stock without purchasing it directly for the full market value, decreasing the "worst-case" EPS.

To find diluted EPS, basic EPS is calculated for each of the categories on the income statement first. Then each of the dilutive securities are ranked based on their effects, from most dilutive to least dilutive and antidilutive. Then the basic EPS number is diluted one by one by applying each one, skipping any instruments that have an antidilutive effect.


So "Diluted Shares" isn't actual shares in the float. It assumes all options and convertible bonds are exercised + float* + insider and restricted shares.

* Which lead me to the definition of float or "Free Float"...

http://en.wikipedia.org/wiki/Float_%28finance%29
The free float is usually defined as being all shares held by investors other than:

- shares held by owners owning more than 5% of all shares (those could be institutional investors, "strategic shareholders", or founders and other insiders holdings)
- restricted stocks (granted to executives that can be, but don't have to be, registered insiders)
- insider holdings (it is assumed that insiders hold stock for the very long term)


- Rafe
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Hi Rafe,

Yes, that is correct, diluted shares are all those shares that there would be if all convertibles and options were exercised that could be exercised.

tom e
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diluted shares are all those shares that there would be if all convertibles and options were exercised that could be exercised.

Tom,

Does this number include options whose exercise date is anytime in the future, or does it refer only to options which are eligible to be exercised at present?

Robert
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I could be wrong, but it sounds like ALL options.

I've noticed, while researching HPY, that they mention this specifically because they approve share buy-backs to compensate for the options grants. They count the future shares as shares for the buy back schedule.

- Rafe
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Hi Robert,

Fully diluted shares only include those options that could be profitably exercised at that moment in time - vested and in the money. If you really want to capture the complete dilution caused by an options compensation program, you need to go into the 10K and look at the tables they provide. Unvested options and those currently out of the money will most likely be sources of future dilution. I usually use 90% of the total number to account for cancellations due to employee attrition. This is critical for "option heavy" companies. Since Ansoft is a tech company, I'd almost bet that there is a lot of hidden future dilution coming down the pike - but I haven't looked to be sure. Not taking into account the real total dilution likely can serve to bias valuation estimates.

Regards,
Stan
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Thanks, Stan. That helps a lot.

Robert
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A follow-up question, Stan:

I checked the 10K for one of the companies I am following and it says this in the notes to the income statement:

Diluted income per common share gives effect to all potentially dilutive common shares that were outstanding during the period.

I'm trying to reconcile this with what you said earlier:

Fully diluted shares only include those options that could be profitably exercised at that moment in time - vested and in the money.

Do these two statements say the same thing, or is there some difference I am missing? I'm trying to get a handle on just which potential future shares are being used to compute diluted EPS.

Thanks.
Robert
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Hi All
Here is an example of how diluted shares is calculated.
http://boards.fool.com/Message.asp?mid=25583012
The quick summary is that diluted takes in to account all outstanding options (ignoring convertibles etc), but the figure is adjusted for the revenue and tax benefit.
In the case of ATHR 9.5M outstanding options make a difference of 3.7M shares.

Dean
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Thanks, Dean. The post you reference is very helpful.

Robert
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Greetings,

The quick summary is that diluted takes in to account all outstanding options (ignoring convertibles etc), but the figure is adjusted for the revenue and tax benefit.

This is not exactly accurate and I think your Atheros calculation was more coincidence than illustrative. I was attempting to explain for Robert the difference between basic and fully diluted shares outstanding, without getting too far into the esoterica, but obviously should have taken it a step further. The difference between diluted and basic shares only accounts for options that are vested and in the money. The calculation does take into account the resulting increase in earnings coming from money the company will receive when the options are exercised and any tax benefits incurred. Even this calculation isn't completely straightforward because incentive stock options (ISOs) don't qualify for the same tax treatment.

As of last year, the Financial Accounting Standards Board instituted the practice of requiring companies to expense unvested stock options. This is where the rest of the options are supposedly taken care of in the accounting. This technique requires using an options pricing model that estimates the value of the unvested options. This value is then amortized over the vesting period and taken as a charge against earnings each quarter.

So as long as you are looking at P&L statements that include options expensing and stick to using GAAP earnings numbers, then by using the diluted shares numbers, will get you to roughly the effect of all outstanding options. I say roughly because you haven't explicitly added in the shares that will be issued to support the unvested options, but rather have made an approximate charge against earnings. In theory, were a company to quit issuing options, in the quarter that the final options vest, the numbers would finally true up. As this is not a common case, I still want to try and estimate what the total effect of dilution is apt to be.

The easiest approach to use may be working on cash flow instead of earnings and just taking a charge to firm value that accounts for all the options. This would send us spiraling off into discounted cash flow land however. I should have known better than try to overly simplify my response, but I sometimes believe rules of thumb and being close enough is a reasonable place to start since this is a learning board.

Regards,
Stan
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Hi All,

Very useful thread! Understanding how to factor in ESO's is my most glaring hole in my investing knowledge. And having SMSI as my largest holding magnifies importance of the issue:)

As of last year, the Financial Accounting Standards Board instituted the practice of requiring companies to expense unvested stock options. This is where the rest of the options are supposedly taken care of in the accounting. This technique requires using an options pricing model that estimates the value of the unvested options. This value is then amortized over the vesting period and taken as a charge against earnings each quarter.

So as long as you are looking at P&L statements that include options expensing and stick to using GAAP earnings numbers, then by using the diluted shares numbers, will get you to roughly the effect of all outstanding options. I say roughly because you haven't explicitly added in the shares that will be issued to support the unvested options, but rather have made an approximate charge against earnings. In theory, were a company to quit issuing options, in the quarter that the final options vest, the numbers would finally true up. As this is not a common case, I still want to try and estimate what the total effect of dilution is apt to be.


I knew that companies were required to expense ESO's, but I did not realize that the expensing included amortizing unvested options. I thought it was only for accounting for the expense of options being exercised in the quarter.

Does this mean that (save for the benefit of the tax deduction) the number of options being exercised in a quarter will not affect GAAP earnings? In the particular case of SMSI, can I apply the previous quarter's ESO expense to an earnings estimate to get an approximate GAAP estimate?

Also, I know that 2.5% of total shares (as long as it is not higher than a certain number of shares) are available to be issued on the last day of the year. Are these given an amortization schedule at the time of issuance and thus I can calculate the additional GAAP expense for the coming Q1?

Thanks in advance for any help on understanding this subject.

Tom
(Sophistabubba)
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Thanks Stan
That is what I originally thought and then I confused myself with Atheros. I'm not sure how that happened as the article I used and referenced clearly says Diluted EPS Captures Some Options - Those That Are "Old" and "In the Money" http://www.investopedia.com/features/eso/eso1.asp

There is even a whole page describing how to calculate the out of the money options http://www.investopedia.com/features/eso/eso4.asp

Another doh! moment for Dean.

Anyway, I'm happy my error got us to dig a little deeper.
Dean
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Greetings,

At the risk of putting all the Nikita acolytes into a deep slumber, let me answer Tom's (bubba) questions.

Dean – it turns out that Investopedia link is really well written, now that I finally was spurred to look at it. Thanks for bringing it up. It is amazing what great info is out there if you know where to find it. Hint – Google is the beginning, things will get better. I want to invest in the company that leapfrogs Google. ;-)

I knew that companies were required to expense ESO's, but I did not realize that the expensing included amortizing unvested options. I thought it was only for accounting for the expense of options being exercised in the quarter.

There is nothing about FAS 123R that deals with any actual options exercising. It is merely an accounting convention to capture the expenses a company is incurring while transferring value from its shareholders to its employees.

Does this mean that (save for the benefit of the tax deduction) the number of options being exercised in a quarter will not affect GAAP earnings?

Yes. The purpose of FAS 123R is to make explicit the costs associated with what is on the books and not yet vested. If you use the fully diluted shares numbers you will account for all options able to be exercised.

In the particular case of SMSI, can I apply the previous quarter's ESO expense to an earnings estimate to get an approximate GAAP estimate?

That would probably be a good starting point, but you really need to understand the trajectory – whether they are continually granting a larger number of options or not. Unfortunately, these tech companies tend to do this as they grow and there are more people to compensate.

Are these given an amortization schedule at the time of issuance and thus I can calculate the additional GAAP expense for the coming Q1?

Well you could if you know all the parameters they are using. If you look at the last 10Q, you can ascertain what they used last quarter. The assumptions shouldn't change very fast. The Black-Scholes option pricing model is a partial differential equation. You can solve it iteratively. Gillies does it all the time, but I'm a little Excel deprived, so I can't give you a spreadsheet to accomplish the task. I think using the previous quarter would be a good guide, unless they issue a whole bunch at a particular time each year. The amortization schedule is generally done as a straight-line over the vesting period, updated regularly for current price, and potentially for volatility. It gets messy and it's probably better to just use last quarter as an estimate. This is my major problem with your baby, Smith Micro. Otherwise it is a great investment.

Sorry to go into so much detail, but hopefully a few of you folks can benefit, or at least come back to this later. Go Nikita.

Regards,
Stan
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Thanks Stan,

With your posts and the links Dean provided, I think I have a much better understanding of how to account for dilution. I will probably try to go through some exercises over the next couple of days to see if I can apply what I am learning.

Thanks again to both of you.

Tom
(Sophistabubba)
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Hi everyone,

I have added this thread to our archive. I am sure there will be many more questions. And hopefully someone will be able to answer them as thoroughly as Stan has about dilution.

I will start out keeping our question archive on the company archive until the number of the questions becomes larger then I will separate them.

tom e
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So as long as you are looking at P&L statements that include options expensing and stick to using GAAP earnings numbers, then by using the diluted shares numbers, will get you to roughly the effect of all outstanding options. I say roughly because you haven't explicitly added in the shares that will be issued to support the unvested options, but rather have made an approximate charge against earnings.

The easiest approach to use may be working on cash flow instead of earnings and just taking a charge to firm value that accounts for all the options. This would send us spiraling off into discounted cash flow land however. I should have known better than try to overly simplify my response, but I sometimes believe rules of thumb and being close enough is a reasonable place to start since this is a learning board.


Thanks Stan. Great posts. A couple more questions I thought of.....

If I'm valuing a company and adding back stock based compensation (as an adjustment) when calculating operating cash flow & free cash flow, does that mean that applying a compounded annual dilution rate to the current number of fully diluted shares might still understate potential dilution for a company? (because I added back the very charge that was to supposed to account for unvested options)

Additionally, I know you're not a big DCF fan, but if I calculate the number of diluted shares (at year 20) to come up with fair value for a company, how am I supposed to calculate for potential additional dilution during the terminal growth period?
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Greetings,

Jordan, you seem intent on putting me in a box.

I know you're not a big DCF fan

I really never thought about being a fan of an inanimate object. It's an algorithm and it is what it is. I often find it useful. Middleby is a good example. I view it like a hammer. It works well if you have a nail in your left hand, not so well if you are holding a screw.

If I'm valuing a company and adding back stock based compensation (as an adjustment) when calculating operating cash flow & free cash flow, does that mean that applying a compounded annual dilution rate to the current number of fully diluted shares might still understate potential dilution for a company?

Maybe. It depends on what you are using for the rate vis a vis, is the rate options are being extended currently higher than in the past. I've pointed you to this analysis in the past, but I'll do it again, because I believe it is the best example of a complete DCF analysis I've ever seen published on these message boards. It elegantly dodges the options issue by subtracting the liability from firm value post-DCF and pre-intrinsic value. If you study the five posts in this thread, you may be surprised at what you may learn.

http://boards.fool.com/Message.asp?mid=23861207&sort=whole

if I calculate the number of diluted shares (at year 20) to come up with fair value for a company, how am I supposed to calculate for potential additional dilution during the terminal growth period?

I used to have this wise CEO that I reported to. When I got into this situation, he would say, “Stan, you are dealing with mice nuts.” (he's from Oregon) I'm sure you could go through all kinds of contortions and adjust your terminal rate, but give me a break, if your explicit period is 20 years, how much does it matter. It's important to step outside and see the big picture, rather than polish a model that may only be valid for the next few months. Take care Jordan, and I'll follow your evolution because, if you are willing to learn, I think you have some real talent going for you.

Regards,
Stan
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Hi all,

TMFCanuck valuation was very complicated. Don't feel you have to do anything near this detailed. I don't - I don't even understand half of what Tmfcanuck was saying in those five posts.

I use a much simpler approach and its very effective. In fact, it will allow you to track many more companies. And the key to doing well in the stock market is not being too exact, but rather uncovering more stones.

I much rather measure the value of 100's of stocks broadly than a few too exactly. We miss too many opportunities trying to be too exact. Yet, since we may have hundreds working on this, you can be more exact, so if you want to learn how to do that, you only have to ask. I am sure we can get Stan and Jim to explain it to us.

But please don't feel you have to do MBA work for this project or to make money in the stock market. However, if you want to really get that deep - this is the place to ask those questions.

tom e
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Hey Stan!

I promise you I'm not intent on putting you in a box. :P That line was really just an aside, and added no substance to the point I was trying to make. I was just trying to get a better understanding of how one properly accounts for dilution when using a DCF analysis.

I will go back and re-read Jim's valuation on Form Factor. I've started to read over it a couple of times, but I haven't gone over it as much as I'd like. I also understand your point on focusing on the big picture and I think it's a valid point, but it's not going to stop me from wanting to learn. I have to see it to believe it, and that means I won't give up until I figure it all out. Some might call it overly persistent or obsessive, but I like to think of it as an extreme focus on detail.

Thanks Tom! I really like to dig deep and generally have an unlimited number of questions. I understand that the Nikita project doesn't require MBA type work, but I'll probably end up trying to do that anyways. Though MBA level work isn't necessary for me as an individual investor, it'll probably end up benefiting me if I do eventually fulfill my dream of running a successful hedge fund. I'm actually in the process of drafting some questions to Jim as well. I'm currently in the process of re-reading Jim's special “The Many Faces of FCF”, the investopedia link mentioned earlier in this thread, Jim's valuation on Form Factor, and I'm digging through some of NILE's past 10 K's and 10 Q's.

As I thought about stock based compensation last night, I realized that you can account for a majority of stock dilution by using a dilution rate. As long as you analyze a company's previous 10-K's and 10-Q's, you can get a better idea about the percentage of unvested options compared to their total outstanding options. As long as a majority of their options are already vested and in the money, the diluted outstanding shares figure should be fairly accurate. The so called “damage factor” isn't as bad as long as most of the options are already vested.

The only time it'll make a big difference is when a company is continually granting additional options that are unvested and out of the money or currently have a lot of unvested options that are just out of the money. In those situations, it'd be important to project a higher dilution rate going forward.

From my current understanding, if we analyze a company's stock-based compensation during the current period, we're expensing for the possibility that future unvested options become vested and cost the company money in the future. I guess this explains why stock based compensation is a considered a non-cash charge, because it's really just an estimate to account for future compensation. It may or may not end up costing them money in the future.

In fact, the stock-based compensation figure might overstate or understate the company's actual dilution depending on what the company's stock price does in the future. For example, if the stock price dove, most of the options (that are being accounted for in the stock based compensation charge), would be worthless and would have overstated the actual expense estimates. On the other hand, if the stock price continually rises (and the company has a lot of unvested options), the stock based compensation charge might even understate a company's actual expenses.

Anyways, I'm sure I'll have some more questions after I finish reading.

Jordan
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Greetings,

Just a few random observations on a Saturday night. I'm waiting for my exhausted 15-year-old to take a shower and get a second wind after 8 hours in the hot sun playing Paintball, so we can go to dinner, oh and by the way, he wants to have a friend sleep over so they can play multi-player video games into the night. I'm exhausted just thinking about it. I did get a few hours of yardwork in today. I remember those days of unlimited energy, but somehow can't quite get back to that place.

Jordan – go for it. You will only be comfortable when you convince yourself that you understand what you are doing. I'm not discouraging you, just adding some perspective on the side. Once you have a model you are comfortable with, it will be easy to introduce other factors, decide when to apply what, etc. Just an aside, running a hedge fund and being competent in analysis are two very different beasts my friend. Running a fund is all about fund raising. That is a far different skill than being a good analyst and stockpicker. If you want to run a fund, get your grounding in analysis and then hire some smart guys to do it for you and watch over them. Work instead on presentation and your pitch why someone should trust you instead of all the other multitudes of choices out there.

I also understand what Tom is saying. The last thing we want to have happen is people getting discouraged by analytical overload. The concept here on Nikita is clear. Start somewhere. You can learn as you go and add things to your toolbox. I encourage everyone to participate and start somewhere. If you aren't willing to commit something to paper, receive feedback, and learn, it is really hard to get beyond pure awe. It really isn't that hard once you get started. The whole concept of this project is to understand one company. That is what is important and the depth of understanding and analysis skills will follow. While I tend to answer some of the more analytical questions, don't think that I'm not reading every post. I'll chime in where I think I can be helpful, and I'm sure everyone else will as well.

Regards,
Stan
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