In the long, rich history of capital markets, investors have been asked to guess the value of some pretty weird stuff. Deep-sea mining, quantum computers, Martian colonies, breeders of lab monkeys — all have found homes and share prices on public stock exchanges. Now there’s a new challenge: valuing the big AI labs, with their unique potential to change the world or destroy it.

One of these is Anthropic, the AI outfit co-founded by Dario Amodei. The maker of the Claude chatbot was this month poised to file for an initial public offering that could value it at $2tn. Until, that is, fears of an AI apocalypse crashed their way into the mainstream.

Open AI, Anthropic’s chief rival, has also been planning an IPO, though founder Sam Altman has now pressed pause on that until next year, saying floating earlier would be “ill-advised”. The debate around whether AI companies’ future models could extinguish the human race has understandably tipped the spotlight away from the question of what investors should pay for their shares. But this remains a good moment to assess how, exactly, the valuation question can best be answered — and whether $2tn for Anthropic is the stuff of financial hallucination.

There are three ways to think about it. And along the way, investors will have to consider a giant unpriceable risk and a giant unpriceable opportunity. In a world where businesses make regular things in predictable ways, there’s a simple way to decide what they’re worth: forecast their earnings a year or two hence — or revenue if they have no earnings — and put that number on a multiple similar to that of listed peers.

The first reason this is tricky for Anthropic is that the company is changing so rapidly, even by Silicon Valley standards. Founded in 2021, the creator of Claude hadn’t even produced a dollar in revenue until 2023. By August, it was making around $65bn on an annualised basis, although such unofficial numbers should be treated with kid gloves.

This growth seems to have come as a surprise to Amodei too. Only 18 months ago, Anthropic expected its revenue in 2027 to be just $12bn. Now, some investors predict a revenue run-rate of $320bn by the end of next year.

They are not impartial, of course. But if they are right, then $2tn would represent a valuation of just seven times its 2028 sales. That’s a little less than Microsoft, according to LSEG.

Space X, meanwhile, trades at 16 times that year’s revenue. Take that as the benchmark — they are both companies with wild aspirations and charismatic leaders — and Anthropic could in future be worth $5tn. It might seem foolish to use near-term estimates to gauge the value of a company whose future is so hard to map out.

But that’s exactly what Wall Street does. In the case of Space X, underwriters Goldman Sachs and JPMorgan were among the many who set their generous target prices by taking a punt on profit one or two years from now, and slapping on a peer-group-inspired multiple. Fortunately, the financial community offers plenty of other ways to crack the valuation nut — some of which suggest Anthropic’s mooted $2tn price tag may be less generous than it appears.

Much debate about Anthropic’s worth will revolve around its “total addressable market”. The idea of deriving a company’s value from the size of the potential revenue pool is decades old but became common currency in the 1990s when analyst Henry Blodget used it to suggest Amazon was worth $400 a share — almost double where the stock was at the time. Now, TAM is de rigueur in any venture capitalist’s slide deck or IPO prospectus.

Its usefulness is another matter. Uber touted a $12.3tn TAM in its 2019 listing; its annual revenue today is less than $60bn. We Work’s $3tn addressable market of office properties didn’t save it from bankruptcy.

But for a company like Anthropic, TAM is as good a place as anywhere to start. Investors aren’t groping totally in the dark, thanks to Space X. Elon Musk’s company, which makes the Grok chatbot a...