Individuals' maximum allocation of 500 shares had risen in value by pounds 278 by the day's end - though they will not be able to trade them until next Monday, when they receive their share certificates.
Thousands more who missed out yesterday will be wondering whether they should join the rush, even at the newly raised price, bearing in mind that Amazon.com, best-known as an Internet bookseller, is worth more than the supermarket group Sainsbury's despite the fact that it has never made a profit.
Others fear that buying "net.stocks" is too risky, and that they are just the latest speculation stampede, like the Dutch tulip craze or the South Sea Bubble, doomed to end in financial tears.
But yesterday saw more than 95 million Freeserve shares changing hands by the end of trading. "They are moving in big blocks - it is institutional investors doing the buying, probably in the US, rather than private investors," said Miles Saltiel at the stockbrokers WestLB Panmure. Mr Saltiel was wary of the excitement that surrounded Freeserve's arrival as Britain's first major Internet flotation. In an official report, he suggested yesterday that Freeserve shares really only have a "fair value" of 60p.
"We reckoned that on an international comparison, Freeserve is really a portal to other sites, rather than an Internet provider, and so we judged it on that basis," Mr Saltiel said. "It has been deftly marketed: we didn't doubt it would be a successful issue."
But Panmure will not buy any shares until the price hits 60p, he added. Meanwhile at Credit Lyonnais, the IT analyst Peter Wyatt said a comparison with Freeserve's American equivalents suggested a valuation nearer to 100p.
How can the potential Internet investor evaluate a stock when traditional measures such as past profits and growth rates do not exist? "You have to look at how far-reaching the management's vision is," advised Brian Ashford-Russell, head of technology investment at bankers Henderson Investment. "When people first invested in Amazon, they might have thought they were just buying a bookseller - but it has diversified into other fields."
Yahoo!, the Internet portal to other sites, has had a higher valuation than General Motors since last January. Amazon, eBay (an "auction" site) and other Internet stocks such as the search engine AltaVista (sold off from Compaq Computer) have all attracted high values without making commensurate profits - in some cases without turning a cent in profit.
In the UK, there have been far fewer Internet flotations. One of the first was in 1995, when another Internet provider, Unipalm, was floated for 100p per share. It was bought within the year for 740p per share by the US group UUnet.
More are on the way, like QXL, a UK-based auction company. "Bankers are falling over themselves to do deals with companies looking to float," said Mr Ashford-Russell. "Overall, there are considerable advantages in a company's being the first mover into a market niche. But the most valuable methodology is looking at value per subscriber or per committed user."
Chris Bell, manager of the "Netnet" fund of global Internet stocks at Framlington Investment, suggested that the private investor should be wary of putting too much into Internet stocks. "If you're investing in a diverse range of these stocks, they should only be 5 per cent of an already diverse overall share portfolio," he recommended. "Picking out one or two stocks and putting it all on those is still very risky."
Mr Saltiel agreed: "Private investors should recognise that Internet stocks are risky, and not necessarily appropriate for them. There's no answer on how to evaluate them easily."
The safer option recommended by all the analysts is to invest in technologies used by Web companies - such as Cisco's networking systems or Microsoft's software.
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