[nerfhammer]

You're forgetting book value and future earnings valuation.

If a company earns $X billion per year, even if they don't issue a dividend, if their market cap dropped to fifty bucks an acquirer could swoop in and pay themselves the company's earnings directly for as long as it keeps running, or shut it down and sell off the book value for a profit.

If there's no dividend, any earnings + book value still exists as a potential profit to someone who would own the company. So you just have to assume that in the future someone would be willing to buy $X for $X-1.