The activist investor, who recently bought 9 percent of the company, met with its leadership earlier this week. Afterward, he wrote a letter to CEO Howard Levine saying there was a "strong difference of opinion" and that "it is imperative that Family Dollar be put up for sale immediately."
In response, Family Dollar released a statement saying "we are always open to constructively communicating with our shareholders with the shared goal of enhancing value." It also noted that Morgan Stanley is acting as a financial advisor to the company.
"I agree with Carl Icahn," said portfolio manager Chad Morganlander of Stifel's Washington Crossing Advisors. "A strategic buyer could certainly come in—a Dollar General or perhaps Dollar Tree [though] I don't see a financial broad buyer like a private equity firm coming in."
The stock trades below its competitors, notes Morganlander. He believes it would make for a strategic acquisition by one of its rivals.
Dollar Tree (DLTR)
Morganlander also thinks Family Dollar's management has underperformed others in its space. "When you look at profitably, let's just say its woefully disappointing comparing it to its competitors," he said. "Management, well let's just call them not amazing. It hasn't been an operating performance story for quite some time."
Shareholders stand to gain should the company sell itself, Morganlander believes. "I'd say 15 to 20 percent upside if Carl Icahn gets his wish."
Mark Newton, chief technical analyst at Greywolf Execution Partners, doesn't think the charts are showing much reason to get excited about Family Dollar's stock.
"This discount store chain doesn't look like a discount on the charts," Newton said. A lot of this move in the Icahn announcement really seems to be baked into the share price at this point. It's had a very big move. We've gotten overbought."
Newton said two charts support his view. The short-term chart shows Family Dollar's stock breaking above an eight-month downtrend after it was revealed Icahn owned a stake in the company.
"The stock has moved a very long way in a very short period of time," said Newton. "So, it's gotten very overbought at these levels."
Newton's weekly chart of Family Dollar going back seven years shows a two-year period of consolidation after the stock had a four-year uptrend. "The stock has been basically range-bound between $55 on the downside and $75 on the upside," he said. "The recent move has taken the stock right back near the highs of this range. So, the stock is not necessarily bearish at current levels. It's just shown a little bit of a slowdown in the last couple of years and now it's gotten very overbought in the short run."
Upside is limited, said Newton. "It's not likely to get over $75 from a purely technical point of view," he added. "I wouldn't be buying the stock here."
To see the full discussion on Family Dollar, with Morganlander on the fundamentals and Newton on the technicals, watch the above video.
Disclosure: Morganlander and Washington Crossing Advisors do not have positions in Family Dollar.