That values Ann at about $2.29 billion to $2.52 billion—a premium of as much as 47 percent to Friday's closing price, which valued the company at $1.72 billion.
Ann should conduct a strategic review, said Engine Capital, which describes itself as a value-oriented special situations fund that invests both actively and passively in companies undergoing change.
But the fund said a committee to conduct the review should consist only of independent board members with its own legal and financial advisers.
Engine Capital said it was "concerned about management intentions and, in particular, are aware of (CEO Kay) Krill's preference for the status quo of remaining a public company."
The fund's small stake will make it difficult to drive change without support from other investors, said FBR Capital Markets analyst Susan Anderson, adding that Ann wouldn't sell itself unless forced.
"It just doesn't seem like it would be on their cards,'' she said.
In March, Golden Gate Capital became Ann's largest shareholder with a 9.5 percent stake. The private equity firm said while the stock was "significantly undervalued'', it did not intend to push for Ann to sell itself and that it was impressed with the company's management.
Ann trades at 16.8 times forward earnings, a discount to its peers' average valuation of 17.9 times, according to Thomson Reuters data.
Engine Capital said on Monday if Ann's board decided a sale was not in the best interest of shareholders, each board member should buy back stock roughly worth twice their annual compensation as "a sign of confidence."
The fund also asked Ann to consider borrowing $600 million to buy back a third of its stock at $40 per share, which it said would "better enhance shareholder value."
The company said it welcomed communications with its shareholders and that it was "committed to creating value'' for all shareholders.
Ann's revenue grew 5 percent in the year ended February, the slowest since 2010. But, quarterly profits have beaten market estimates for the past two years, making it one of the few apparel retailers that have weathered the enduring weakness in U.S. consumer spending.
The stock was up more than 4 percent. The shares have barely budged since Golden Gate announced its stake in the company on March 20.
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