Takeover value, equity value in the event someone wants to own all (or a controlling part of) the equity, is a different beast. It includes the strategic optionality that comes with owning a company. Having to take what management doles out thus produces a different equity value than takeover value. Market cap is the best estimate of this passive investor's equity value.
A stock's price is essentially the first derivative (in calculus terms) of the company's value. Market cap is essentially assuming that the entire thing is linear, by taking the derivative and multiplying it by the total size. Stocks don't behave linearly, so this assumption isn't particularly good.
Which, when you read it, I'm sure you can come up with 10 counterexamples (obvious counterexample: ponzi schemes). I guess you could call me a disbeliever.
This is not unlikely when you have to pay your suppliers before you collect payments from your customers. And realistically that's the common case, not the exception. This is why cash flow is so important for any business.
If firms automatically became insolvent when liabilities exceeded assets, then no one would ever be able to start a firm with a bank loan, because from day one the liabilities (loan + interest) would outstrip the assets (cash).
It's also possible for a firm to have assets which exceed liabilities but still be insolvent, for example a property company with large fixed assets but little cash in the bank to meet its running costs.
No. A company is at risk of being forced into involuntary bankruptcy when it cannot meet its current obligations, which is different than having less assets than liabilities; but even when insolvent it doesn't have to enter bankruptcy, though its creditors can force it to do so (and, if it is profitable and expected to remain so, its creditors might not want to force it into bankruptcy, because they may expect the liabilities to be more fully paid, if delayed, if the firm remains in operation vs. bankruptcy.)
All this article does is point out that if you use that (flawed) method to value Yahoo, and then use the same method to value Yahoo Japan, and then use even less-reliable means to value the non-public Alibaba, and then subtract the last two from the first, you get an unexpected number.
And even if the assumptions underlying the "negative" valuation of the core business were inassailable, its quite easy to have a business to have a negative $10 billion value. Suppose a business has $11 billion in total liabilities, and $1 billion is total assets. Voila, Owner's Equity is -$10 billion.
And this can still be a profitable company. Obviously, making profits means that profit stream has a value (the current value of the stream of future income), but that doesn't mean that you don't have liabilities that exceed that (and the valuation of that stream is not just based on current profit, but expectation of its future continuation. A company can be profitable but the market can lack confidence that it will continue to be profitable.)