Microsoft will need to significantly increase its takeover bid if it is to acquire Yahoo, according to one of the search giant's largest shareholders.

In a letter to investors made public yesterday, Bill Miller places Yahoo's value in the range of $40 (£20) per share. Microsoft's original offer of $44.6bn (£22.4bn) was equivalent to $31 (£16) per unit.

"Our own valuation work puts the value of Yahoo in the range of those reported numbers, though, and we think Microsoft will need to enhance its offer if it wants to complete a deal," writes Miller, portfolio manager for asset management firm Legg Mason.

But Yahoo may have few options in the face of strong takeover bids.

"It will be hard for Yahoo to come up with alternatives that deliver more value than Microsoft will ultimately be willing to pay," says Miller's letter.

"This deal is a strategic imperative for Microsoft, and Yahoo is in a tough spot if it wishes to remain independent."

Miller's letter was dated 10 February, the day before the Californian search company formally rejected Mircrosoft's offer.