In a letter addressed to Yahoo CEO Marissa Mayer on Friday, Starboard — which disclosed a “significant ownership stake” — argues Yahoo is “deeply undervalued relative to the sum of its parts.” The investor, which generated some headlines recently for criticizing Olive Garden’s breadsticks strategy, said a combination of Yahoo and AOL could reduce the cost overlaps in their display advertising businesses, and cut both companies’ overhead costs.

“Importantly, we believe the combined entity would be able to more successfully navigate the ongoing industry changes, such as the growth of programmatic advertising and migration to mobile,” Starboard said.

Marissa Mayer, Yahoo’s CEO, responded with a statement late Friday by saying “we will review Starboard’s letter carefully and look forward to discussing it with them.” She also emphasized the strength of her company’s business and her commitment to creating shareholder value. Yahoo has helped to prop up its shares by buying back $6.3 billion in stock since July 2o12, Mayer said. She alluded the possibility of more by saying she will update investors on further capital spending plans during the next quarterly earnings.

Mayer, ranked 16th on Fortune’s Most Powerful Women in Business list, is facing pressure in the wake of Alibaba’s (BABA) initial public offering last week. At least three analysts have downgraded the company’s stock this week, citing the absence of a turnaround at Yahoo’s core business and limited upside to owning a slice of Alibaba. Yahoo still owns about 400 million shares of Alibaba, a stake worth more than $35 billion before taxes, The Wall Street Journal has reported.

Starboard’s move is also turning up the heat on Mayer to perform. Fortune earlier this year asked an important question: “Will Marissa Mayer save Yahoo?” noting that while the company’s stock value has climbed under Mayer’s tenure, the strength has had little to do with her turnaround efforts. While Yahoo has announced some high-profile acquisitions (including the $1.1 billion deal to buy Tumblr) the company’s ad business remains challenged.

Starboard points out that even after Yahoo’s “ill-timed and tax-inefficient” sale of Alibaba stock, the company’s remaining stake in Alibaba “is currently worth more than the entire enterprise value of Yahoo.” When adding in the company’s stake in Yahoo Japan, those two minority interests are worth about $11 billion, or $11 per share more than the current enterprise value of the company.

The activist investor claims the “valuation gap” is due to the fact that investors expect Yahoo management to continue past practices, including acquisitions at “massive valuations with seemingly little to no regard for profitability and return on capital.” Another problem, according to Starboard, is monetizing its non-core minority equity stakes in a tax-inefficient manner.

“We believe that Yahoo’s core business is valuable. However, given some recent operational challenges, we would expect it to trade at the low end of industry multiples,” Starboard said.

Yahoo’s shares (YHOO) gained 4.4% on Friday, based on the possibility of a shake-up at the company. AOL’s (AOL) gained 3.7%.

(This story was updated with a statement from Yahoo and closing stock results for Yahoo and AOL)