Activist investor Starboard Value delivered a letter to Yahoo's board expressing concern over reports that the company may be considering a large-scale acquisition.
Recent news articles had suggested Yahoo was interested in acquiring Scripps Networks, or a tie-up with AOL. Although in showing concern about the Scripps reports, the activist firm reconfirmed its push for an AOL combination.
Starboard stressed in its letter that Yahoo should monetize noncore minority equity investments, and that it should significantly reduce costs to improve profitability.
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"Within the past week, new speculation has emerged that Yahoo is considering a cash-rich split-off as a structure to separate its noncore minority equity interests. The resurfacing of rumors about a cash rich split-off at this juncture is particularly troubling given your acknowledgment ... that this option would be clearly inferior to a spinoff structure or other available alternatives to unlock the full value of the stakes in Alibaba and Yahoo Japan," Starboard wrote in its letter.
Starboard, which first expressed similar views on a Yahoo-AOL combination in September, disclosed a 7.7 million-share stake in Yahoo and a 1.9 million-share stake in AOL in November.
The activist firm concluded its letter with a challenge to Yahoo's executive team.
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"Should you instead choose to proceed down a different path by pursuing large acquisitions and/or a cash-rich split, both of which have been speculated, such actions would be a clear indication to us that significant leadership change is required at Yahoo," Starboard wrote. "We hope our concerns are unfounded and would like to continue our constructive dialogue."
Yahoo's shares were up 1.4 percent at $49.28, while AOL was up 3 percent at $47.52 in early trading Thursday.
A spokeswoman for Yahoo declined to comment on the newest Starboard letter, telling CNBC "we believe our comments at earnings, and in response to their first letter, pretty well cover our position on the matter."
—Reuters contributed to this report.