They pull them out of their (*((

That's actually a great question. Valuation of public companies is part science, part art, and part total bullshit. You can go way down the rabbit hole on this sort of thing.

In days of yore you'd look at the fundamentals like:

- ability of the firm to service its debt

- profitability ratios

- revenue growth

- total addressable market

- competition

- market dynamics

etc.

You'd also pore over their quarterly and annual regulatory findings and see what's in the MD&A sections, assess the competency of senior leadership, look at how they view themselves, etc.

Then you'd look at comparable firms, i.e. companies doing the same or materially-similar things. Some of those are "pure plays", i.e. companies selling exactly the same product/service (e.g. TSMC, UMC, GFS) and some are not pure (e.g. red bull sells energy drinks but it also has a bunch of other stuff like a formula 1 team).

You compare your target company's fundamentals to those of its comparables, see what prices those comps are trading at, look at discounted cash flows, and then you pull a semi-informed number more or less out of your ass for the target as a forecast, based on your analysis.

These days, though, valuations are more or less completely disconnected from fundamentals. This is why Warren Buffett-style value investing is commonly said to be dead in today's market.