Carl Icahn recently disclosed a 9.39% stake in Family Dollar (FDO.DL) and has subsequently pushed the company to put itself up for sale . He points to the company's perpetually underperforming financial metrics and the current market environment as reasons to sell immediately .

Shareholders must watch closely as Family Dollar's decision to sell or not sell will have drastic implications on the company's future and their own share value.

Carl Icahn's plea
In a letter to Family Dollar's CEO, Icahn cited flat same-store sales growth of 3% as a main problem with the company, especially compared to Dollar General (DG -0.38%) and Dollar Tree's (DLTR -0.89%) respective 4.4% and 3.1% growth last year. Additionally, Icahn pointed to revenue growth and operating margins,  areas where Family Dollar has consistently underperformed against its dollar store competitors since 2011. Icahn believes some type of change is necessary for the company to compete with other retailers.

FDO Operating Margin (TTM) Chart

FDO Operating Margin (TTM) data by YCharts

A Family Dollar – Dollar General merger
One change Family Dollar should consider is a public buyout. The most logical public buyer of Family Dollar is Dollar General. Credit Suisse reports Dollar General could pay between $90 and $100 per share -- well above Family Dollar's current price of $65.79. The premium Dollar General is willing to pay could stem from a desire to lure Family Dollar away from other public and private buyers.

Overall, analysts suggest a merger of the two companies could ultimately result in $550-$600 million in cost synergies . That comes out to between $0.70 and $0.76 in annual cost savings per share, considering 417 million shares outstanding.

Dollar General may see vast potential in a merger, which could create a dominant convenience-based retailer . This combination would dwarf the third dollar store competitor, Dollar Tree. Furthermore, Credit Suisse also sees an opportunity for Dollar General to move into its next phase—possibly further expansion or business differentiation--which might not be able to happen if it was solely reliant on internal opportunities .

In reality, there is significant potential for increased shareholder value and subsequently high shareholder returns if a Family Dollar-Dollar General merger goes through.

Going private
Conversely, a move to the private sector could free up Family Dollar's time and money to be spent working toward long-term goals. The transparency and short-term measuring stick in the public sector can drag on share price when expectations are not met, which is similar to the pressure Family Dollar is feeling in the face of its current underperformance. A move to the private sector might take pressure off Family Dollar while creating an opportunity to work for greater profitability instead of investor expectations.

Analysts see a bid from a consortium of private-equity firms as the most likely privatization route . While no formal bids have been offered, analysts see any privatization move as an easier path to the significant cost-cutting that Family Dollar must undergo in order to turn its recent underperformance around. In the end, shareholders could reap the profits of a lucrative buyout similar to what Dollar General might offer.

What the future holds for Family Dollar
A sale of Family Dollar is not imminent . Family Dollar's stock continued to rise in the past few years from $27.83 in 2010 to $64.33 today, which complicates the search for a buyer. Simply put, Family Dollar, despite its blemishes, may be too expensive to buy.

In terms of a public buyout by Dollar General, Dollar General does not seem to want to risk its current success on a merger with an underperforming business with little upside . The recent retirement announcement of Dollar General's CEO Rick Dreiling further pushes a Family Dollar-Dollar General merger into uncertainty. The upcoming transition period for Dollar General likely means a merger decision will indefinitely be put on hold.

Final thoughts
Some change seems necessary to turn around Family Dollar's chronic underperformance against competitors.

Privatization seems most likely, and may pay a lucrative share buyout. But it has the least upside. On the other hand, a public buyout could provide shareholders with hope for higher stock returns in the future.

Dollar General's hypothetical share buyout of $90-$100, plus the possibility of massive cost synergies and potential for growth, means a merger is the best hope for Family Dollar shareholders. While it does not seem likely, Family Dollar shareholders should hope Dollar General views the chance to merge with its biggest competitor as too good to pass up.

No matter the outcome, Family Dollar shareholders should be pleased with Icahn's plea for change. They will likely benefit as a result.