Who wants to invest in a company that has never made a profit, admits it may never do so and is on the brink of war with its global workforce? Probably a fair old chunk of Wall Street, as it happens. This week Uber, the ride-hailing and food delivery service, will put a price on the shares it will issue in the largest tech company float since Facebook in 2012.

The San Francisco-based company hopes to raise $10bn in a listing valuing it at $90bn. Dara Khosrowshahi, the chief executive, embarked on a pre-float roadshow last week, touring hotel function rooms from New York to London, addressing halls thronged with investors and asking them to give Uber a five-star rating.

Demand for the shares reportedly exceeds supply already, indicating that everything is falling into place for a barnstorming debut when the stock exchange bell eventually rings on the morning of the float.

The company has yet to give an estimated time of arrival for this, although if the accuracy of its ride-hailing app is anything to go by, that might be no bad thing.

Uber’s proposition is a curious one. With no profits to report – and none in sight – it is asking investors to part with their cash based on a belief in how the world will travel from A to B over the next 10, 50, even 100 years. Uber’s float prospectus, a doorstopping document that sets out the logic for investing in the company, features the word “trillion” no less than 63 times.

The message is that short-term profitability is as nought when compared with the virtually limitless opportunity ahead. So where exactly are these trillions to be found? Well, the company says its current “serviceable addressable market” for taxi rides – meaning the size of the markets in which it operates – is equivalent to 3.9 trillion miles a year, worth $2.5tn.

But its target addressable market, when including parts of the world where it doesn’t operate, is estimated at 11.9 trillion miles per year, or to put it another way, 25 million return trips to the moon. It estimates the value of those rides at $5.7tn.

It is asking investors to part with their cash based on a belief in how the world will travel in 10, 50, even 100 years

Throw food delivery into the mix and you’ve got, according to Euromonitor International, another target market worth $2.8tn, albeit including sit-down restaurants. Oh, and don’t forget a $3.8tn freight trucking market, which Uber also has its sights on, or its driverless car business, which is burning money at the moment but could, if it pays off, be the moonshot investment that puts a rocket under the company’s valuation.

Of course, all of these trillions represent a well of money from which Uber believes it can draw, rather than a guaranteed stream of income. But the fact that the well is virtually bottomless is key to Uber’s attempts to persuade investors to part with their readies. Still, at last the company also appears to recognise that it must back up its vaulting ambition with visible steps to address its high-profile mistakes.

These include legal and regulatory clashes in cities around the world, a data breach cover-up, its perceived lacklustre effort to deal with allegations of sexual assault against drivers, and clashes with its workforce over pay and conditions.

In comments that will ring true with anyone who regularly relies on Uber to get them home from a night out, Khosrowshahi said last week that “in getting from point A to point B, we didn’t get everything right”.

Such contrition should be heartening to potential investors, particularly when contrasted with the cocksure culture set by his scandal-hit predecessor, the company’s founder Travis Kalanick. For now, Uber’s destination may be uncertain, but at least it looks like the satnav is working.