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There is this concept of free cash flow. Now, I have heard is the amount of money left after you reduce from the net income all other expenses that relate to labor and investment and so on.

That is the money that you can use freely, and it is a fortune you have gained. If so, then why if a company has extra X in cashflow, its stock price doesn't grow as $\frac{X}{shares}$? Have you gained ideas too? and if you haven't?

In fact, the difference in price is closer to 20 or 30 times.

It is however used in the calculation of intrinsic price. So, I'd like to know how this magic is made.

Do you simply assume price/FCF is constant? Is it better than assuming PE is constant?

How can you roughly estimate how a company is worth given its FCF (and DCF)? and why is this factor of 20-30?

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You can't really estimate stock prices this way because it's forward looking (i.e. it considers the future, not so much the past). Example:

Suppose company A lost \$100 million this year, but next year it's going to earn \$100 million. How much is company A worth? If you naively used the P/FCF ratio (price-to-free-cash-flow) you would value company A as worthless today. If everyone agreed with you I'd buy 100% of the company's shares and pocket $100 million next year.

However, this is itself unclear because how can anyone guarantee that the company will earn \$100 million next year? What if, for example, there's another COVID-19 pandemic that hurts the company's performance? Then maybe it will only earn \$50 million. On the other hand, perhaps one of the company's products turn out to be a smash hit, and it earns \$200 million instead. Ultimately, how much the company is worth is going to depend on how much money it makes in the future, and the future is unpredictable. That's why we have a market. Bulls will generally believe that the company will make more money in the future than bears, and therefore value the company differently.

There are other differences, which are entirely dependent on market sentiment. As an example, consider AMZN. Amazon is one of the darlings of the market because the stock price keeps going up even though the company barely makes any money (just look at the P/E and P/FCF). This is happening because Amazon has been fantastic at growing its sales & earnings. There's also the perception that Amazon is working on innovative, cutting-edge things (like Alexa). Therefore the market assigns AMZN a high price. If you based your modelling around free cash flow, you would not have bought AMZN, even though that stock has been extremely lucrative for its holders in the past several years. Of course, this doesn't mean your modelling is wrong; if market sentiment on AMZN shifts its stock price will likely crash by a lot.

In the world of modelling stock prices there is no "right" or "wrong" way. Different people will use different methods or metrics. Further, there is no foolproof way to make money; if there were, then everyone would use it and it would cease to make money.

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This six page reference describes valuation models based on several distinct definitions of discounted cash flow analysis:

http://educ.jmu.edu/~drakepp/general/FCF.pdf

Stock prices in secondary markets are set by a combination of factors including concepts of market psychology.

In Sun Tzu, The Art of War, there are nine types of strategic ground. One strategic principle of warfare is "Take the high ground first." This is because it is easier to take the high ground first, and then defend the high ground, then it is to take the high ground away from the enemy in a fight. If the enemy is foolish enough to fight an uphill battle then there is an advantage to having the high ground first, and if the enemy is reluctant to fight an uphill battle then there is still an advantage to camping on the high ground. So in war and commerce one strategic principle is "Get there first."

The float of shares in any firm is relatively fixed in the short run. So ownership could be viewed as owning a chunk of the "strategic ground". If others want to get a share of that ownership at a premium in the future then you want to own those shares ahead of the premium buyers. Price to earning ratio will expand when there are wide expectations that the firm will throw off more free cash flow in the future but there is no deterministic model for predicting the valuation of shares in the market.

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