Yahoo!’s second biggest shareholder said yesterday that Microsoft will have to significantly increase its bid for the search engine to about $40 a share if it is to succeed in its takeover offer.

Legg Mason, which owns 6.6 per cent of Yahoo!, said that while it wants more than the $28.95 in cash and shares currently on offer, it does not think Yahoo! has a credible alternative strategy to resist.

Bill Miller, in a quarterly update to investors, the prominent fund manager at Legg Mason said that “Microsoft will need to enhance its offer if it wants to complete a deal,” adding that the firm’s “own valuation work” suggested the search engine was worth over $40 a share.

However, he also warned Yahoo! chief executive Jerry Yang that it “will be hard for Yahoo to come up with alternatives that deliver more value than Microsoft will be willing to pay.”

Yesterday, Yahoo! formally rejected Microsoft’s offer, highlighting the strength of its brand, traffic and value hidden in Chinese and Japanese properties.

Mr Miller said that he had met with Steve Ballmer, the Microsoft chief executive, after the software giant’s hostile bid was first made public, and that he had spoken to Mr Yang at Yahoo! The well regarded Mr Miller is known for helping the Legg Mason Value Fund that he runs outperform the benchmark S&P 500 for 15 years to 1996.

Yahoo! shares were down 19 cents at $29.19 in lunchtime trading in New York.

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