Analysts do exactly this. They pick a handful of metrics and produce a range. For an IPO, this information is usually published by varying sell-side firms for the benefit of their clients and to attract new clients (unless they are underwriting the deal then there's a lock up period - 45 days, IIRC).

The company itself will also have a slide deck for its pre-offering road show that has this analysis done by management. You can usually find these slide decks on an investor relations website or on the SEC Edgar system. It also may be in the SEC registration statement under management analysis - or even under risks.

> But, why don't later investors insist on also learning the lowest possible imputed value, taking into account how investors are acting to protect themselves. Risk is hard to compare, but isn't this what Wall Street does all day?

Presumably the later investors ARE doing this. But it's not in the investors' interest to publish their internal research on the error bars and it IS in the interest of the startup to publish as high a valuation as possible. Combine that with the fact that big numbers get pageviews and there's no incentive for anyone to report on the lower bound.

One way that you know this analysis is happening is that it's needed for an S1 filing. There's just no reason to publish any of it before then.

> So why aren't startup valuations published as a range?

Because it's marketing hype and merely negotiation tactic. Newcomers always have the opportunity to get the truth before investing.

Who are the parties who care about accurate valuations enough to sue if they get lied to?

1. Investors 2. Banks & Insurance 3. SEC If you aren't one of those parties, then i'm guessing you can be told to trust any valuation on a whim.