Yahoo's board of directors has "unanimously concluded" that Microsoft's $31-per-share offer to acquire the company "is not in the best interests of Yahoo! and our stockholders."

The board concluded that the offer "substantially undervalues Yahoo! including our global brand, large worldwide audience, significant recent investments in advertising platforms and future growth prospects, free cash flow and earnings potential, as well as our substantial unconsolidated investments."

The official word came in a short statement just posted to the company's Web site. No formal word on the $40-per-share price range that Yahoo had indicated it might accept in press leaks over the weekend.

The ball is in Microsoft's court. We'll post the company's reaction as soon as we learn it.

Update, 7 a.m.: In early trading this morning, investors are bidding Microsoft shares down (off 52 cents, 1.8 percent, to $28.04) and Yahoo shares up (up 55 cents, 1.9 percent, to $29.75), perhaps thinking that Microsoft is willing to pay more -- one of the company's several options.

Update, 7:20: The Wall Street Journal has an interesting perspective on a potential increase in Microsoft's bid for Yahoo. It looks at five major institutional shareholders that have large holdings in both companies. "[T]hey all are deal arbitrageurs of sorts now," Heidi Moore writes in Deal Journal. "... What might be good for Yahoo in this proposed deal could be bad for Microsoft, and vice versa. Yahoo's shares may rise dizzily on speculation that the search and Internet advertising company can get a higher bid."

What do those shareholders think about the early trading today, in which the companies shares moved nearly equal amounts in opposite directions?