Thank you for all of your answers! I've gotten nearly everything from you, you've been very helpful. But I do have a couple of remaining questions. (This comment is not as llong as it seems.)

Discussion of pre-money valuation
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First of all I have a fundamental followup question that cuts across literally everything around equity raises.

I don't understand why you continually use the pre-money valuation for how much a stake is worth! Usually post-money is used, isn't it?

This is how I think about it - tell me if I'm wrong: let us see if pre-money or post-money is the more appropriate metric, by looking at the extremes. You create a machine that poops bars of gold and show me. I want to buy 99.9% of your company for a billion dollars. You say okay, because you want to go invent something else using a billion dollars, and anyway you're pretty sure I can grow it to a seven hundred billion commodities company, which will make your remaining stake - which might come with anti-dilusion or ratchet clauses, so you always have 0.1% of the company - worth a further $700M. And the rich guy takes all the risk regarding whether he can actually grow it to $700M or fucks it up. You have your $1 billion today, either way, and obviously anyone who can invent a machine that poops bars of gold has good R&D ideas for how to use $1 billion. So you agree.

Ground condition: you had owned 100% of the company. A $1b investment for 99.9% of the company implies a post-money valuation of (1/99.9%) * 1 billion = $1,001,001,001. It implies a pre-money valuation of $1,001,001,001 - $1B = $1,001,001.

So how is the $1M relevant in anyway?

If the pre-money valuation is $1M then would the founder who just accepted $1B for 99.9% of the company, also accept a 50% buyout of the company for $2 million? After all, it's TWICE the pre-money valuation offer he just received!

Of course faced with two options - a 99.9% buyout of the company for $1 billion or a 50% buyout of the company for $2 million, he would accept the first one and not the second one, which to any reasonable person values the company at a much lower value.

As an even more extreme example, if the $2 million were for 100% of the company, then any reasonable person would understand that that offer values the company at $2 million. But the pre-money valuation is $0.

Which also OBVIOUSLY doesn't make any sense whatsoever. How does a 100% buyout offer of $2 million value a company at zero? Obviously it doesn't.

Would a guy looking at a 99.9% buyout for $1 billion and a 50% buyout for $2 million consider the second one to have a higher valuation? Of course not. But the pre-money valuation of the first one is just $1 million and the second one is $2 million - twice as high.

So we have three examples of absurd results from using pre-money valuation.

1. A hundred billion dollar investment for 99.9999999% of the company values the company at $100 pre-money ((1/99.9999999%) * (100,000,000,000) - 100,000,000,000 = $100). This is absurd.

2. A 100% buy of any company at any price values the company at $0. This is absurd.

3. A $4 million valuation (50% for $2m) can value the company higher than a $1 billion valuation - as long as the pre-money of the latter is lower. Again, absurd.

All of these absurd results make it totally unrealistic to use pre-money valuations so I really don't understand why you're doing it! Please explain in detail, as I've been used to using post-money valuations to talk about the value of a company. I thought this was standard.

Maybe I've grossly misunderstood something, so it would be very useful if you told me what!

Your other answers
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Thank you for the other answers.

Your answer number 2 essentially means these kinds of clauses are only possible where there is not a VC on board, (because if there were, they wouldn't allow it and have protections against it in their standard docs), right?

You gave a partial answer to number 3 ("yes, but it would usually be in the form of bonds or loans") but as a practical matter would banks loan money to a company (say, against its assets as collateral) that was explaining to its loan officer at the bank that it was borrowing money to buy out one partner through another? At a practical level I didn't get whether this is something the company would probably be successful doing or probably fail doing. I have no experience with this. So I am asking whether banks would agree to that.

Thank you for all of your answers by the way! I am particularly interested in your list of reasons for using pre-money. It doesn't seem useful for me, or match people's intuitive definitions of valuation.