Yahoo Inc.'s rejection of Microsoft Corp.'s buyout bid will test whether the software giant is willing to pay a lot more for the Internet company -- or risk a truly hostile takeover attempt.

Microsoft may sweeten its offer, say people familiar with the matter. But any increase is likely to fall short of what Yahoo 's directors believe would fairly value the company, the people say, setting the stage for a protracted battle.

People close to Microsoft say the software giant is reluctant to launch a proxy fight to push out Yahoo's board. A fight could increase the odds that key Yahoo employees will leave the company, these people say. It is more likely to pursue less-hostile options, such as recruiting big shareholders to put pressure on Yahoo to negotiate with Microsoft for an acceptable price.

Yahoo directors concluded after a meeting Friday that the unsolicited offer -- worth nearly $45 billion when it was announced on Jan. 31 -- "massively undervalues" Yahoo, according to a person familiar with the situation. The board plans to send a letter to Microsoft today, spelling out its position.

Analysts have expected Microsoft to increase its $31-a-share offer. But Yahoo is pressing for at least $40 a share, according to a person familiar with the matter. Such a premium would increase the value of Microsoft's original cash-and-stock bid by more than $12 billion.