Clive Cooke, chief executive of the financial spread-betting firm City Index, had a large cheque to write out last week.

His company has lost £20,000 to a canny housewife who backed a view widely disparaged by many market professionals: that shares in Google would keep on rising.

Last Tuesday, as Cooke was preparing to pay up, Google’s stock price hit another new high, just shy of $300 (£165). That is more than three times the $85 price set last August when the American search- engine company joined the Nasdaq stock market after a difficult and controversial flotation.

That was only 10 months ago. But those troubles seem more like 10 years away. Google now looks set to join the S&P 500 index of America’s biggest companies, which includes Coca-Cola and General Electric.

In its short, public life, Google has repeatedly beaten expectations for its performance — and not modestly, but by a country mile. Riding the booming market in pay-per-click advertising, the internet’s big, friendly giant has grown much faster than even its most fervent fans thought possible.

The latest share surge followed results showing quarter-on-quarter growth in revenues of 22%. Its fast accelerating profits have already hit $443m a quarter, and Google is only just getting started in Europe and much of the rest of the world.

With so much potential for internet advertising, and with so many new services to drive more searching — and therefore more ads and revenue — the opportunities for Google seem almost endless. At least, that’s what the share price is saying.

It is this prospect that has so excited investors. And last week the company’s market value reached $80 billion, surpassing Time Warner and making it the most valuable media company in the world.

That’s right. Bigger than Disney. Bigger than Viacom, the owner of MTV, CBS and Paramount Pictures. Bigger than News Corporation, the ultimate owner of The Sunday Times. Bigger too, incidentally, than deeply troubled “old economy” businesses such as General Motors.

It would hardly be surprising to find Larry Page, 32, and Sergey Brin, 31, the Stanford University PhD students who founded Google, rubbing their eyes in disbelief. Google is only seven years old.

Any lingering scepticism left over from last year’s float is rapidly dissipating. Last week analysts at Smith Barney, part of Citigroup, placed a $360 target on Google’s shares. That would give the company a market value of $100 billion — or about 20 times the revenues Wall Street expects the business to generate this year.

Amid the euphoria, some of the calmest heads are to be found at Google. The founders are sceptical of Wall Street and its tendency to hype, then dump, companies. A look at their financial statements shows them to be far more cautious than many analysts. There are clear warnings that Google’s golden age may not last.

The company admits it faces “formidable competition in every aspect of our business”, particularly from Microsoft and Yahoo. New technology could block its ads, wiping out its revenues. “Our inexperience in the operation of our business outside the US increases the risk that our international expansion efforts will not be successful,” the company said.