Facebook estimated market capitalization?

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Hello all,

I started to study finance just some weeks ago and I couldn't understand this line I have just read
The Economist website: "It (Facebook) is seeking to raise $5 billion from its initial public offering, which would give it an estimated market capitalisation of $80-100 billion."

Now, as far as I know, the market capitalisation is the number of shares outstanding (so publicy tradable) times the price of the single share. If Facebook is seeking to raise 5 billion in equity I think that means that it will issue share for an overall value of 5 bilion right (so for example 100000000 shares at 50$ each)? So how is that possible that the market capitalisation will be 80-100 billion? I mean, shouldn't it be exactly 5 billion?

I have already asked to some friends of mine that are more experienced than me in finance but unfortunately they are not really experts themselves on the subject and these are two of the answer that I got:

1) 80-100 billion are referred to the total number of shares of the company, both the publicy tradable ones and the privately held. However this doesn't match with the definition of market capitalisation.

2) there is going to be a premium on the nominal value of the shares when issued. However, I think that if Facebook wants to raise 5 billion $ the premium is already calculated in these 5 billion.

Thank you all in advance to for your answers!