Family Dollar hasn't seen blue skies in a while. Image courtesy Mike Mozart under Creative Commons license.

When Carl Icahn disclosed a 9.39% stake in Family Dollar Stores (UNKNOWN:FDO.DL) on June 6, he noted in his SEC filing that he had purchased company shares "in the belief that they were undervalued." Paradoxically, Family Dollar's stock is undervalued only in the context of Icahn's and other hedge fund activists' interests. To understand why, let's take a brief look at the company -- without regard to activist shareholders, and again in the context of their ownership.

A struggling business in a difficult industry
Over the last few quarters, Family Dollar's momentum has deflated. The company's second-quarter fiscal 2014 earnings were particularly disappointing, as revenue declined 6.1%, and income before taxes dropped by 35% versus the prior-year period. Even adjusting for an extra week in the prior year, revenue was essentially flat, despite heavy promotions. Management blamed a mix of products that shifted toward lower-margin consumables, a poorly executed holiday season, and marketing missteps for the uninspired results. But the fact is that the market opportunity for dollar stores has dampened in recent years.

As the U.S. economy continues to improve, the core customer of dollar stores is still tapped out and financially exhausted. To illustrate, on Family Dollar's most recent earnings call, an analyst questioned the impact to the company of reductions in the Supplemental Nutrition Assistance Program, or SNAP, the federal program that administers food stamps, among other services. CEO Howard Levine responded that the result was "difficult to quantify but [I] can tell you that it's not a positive for our customers."

In a similar vein, Richard Dreiling, the CEO of Dollar General, pointed out earlier this month that his company is expanding the number of items it carries in the $1 to $5 range ("dollar stores" traditionally sell items within a range of $1 to $10) and "sharpening" price points. "We are not waiting on the economy to improve for our core customer as she continues to face headwinds in cost increases," he observed.

Challenges ahead dispute the concept of undervaluation
To turn its revenue and income trends around without any friendly propulsion from the economy, Family Dollar is permanently lowering prices on 1,000 basic items, tweaking its product mix, and closing stores. But these actions will strain operating cash flow, which has thinned lately. The company plans to close 370 underperforming stores this year, and will incur a cash burn of $53 million to $58 million associated with the closings. At the same time, management will continue its plan to "renovate, relocate, or expand" roughly 850 stores this year. In reconfiguring its product mix, Family Dollar has bumped up its inventory to levels more than 13% higher than the prior year. All of these actions are capital intensive: In the last two quarters, Family Dollar tapped unsecured credit lines for $296 million, bringing total borrowings to $796 million. This is roughly half of total shareholders' equity, and as a reference point, the company has $157 million of cash on hand.

The company has significant off-balance-sheet obligations as well. As Family Dollar's strategy is to avoid owning real estate locations, it carries a fair amount of operating lease obligations at any given time. Going forward, the company has some significant lease payments looming: $515 million, $475 million, and $427 million to be paid in fiscal years 2014, 2015, and 2016, respectively. These obligations contradict the notion that Family Dollar could be further leveraged to return palpable value back to shareholders -- a common strategy in takeovers of undervalued companies with clean balance sheets.

To draw together the themes discussed above, for investors to regard Family Dollar as undervalued, management would have to turn the revenue trend around via newly lowered prices, manage increasingly tight cash flow without overleveraging, and improve gross margins through its product mix and store closings. These are all entirely possible outcomes, but much depends on future results.

Valuation often depends on the control you can exert
Now, in Carl Icahn's hands, the entire complexion of Family Dollar shares changes because he can exert control in a way that you or I can't. The possibilities of Icahn influencing a merger with Dollar General or perhaps Dollar Tree have been widely covered in the financial press, as well as by my Foolish colleague Nickey Friedman. But I believe Mr. Icahn is also exploring more direct action, including seeking to influence or modify the executive management team, which would allow him to make more extreme changes in the near term.

The current team, led by CEO Howard Levine, has implemented changes based on a long outlook -- it's going to close less than 5% of its stores while continuing to expand the chain, although at a reduced new-store opening schedule beginning in fiscal 2015 (from 525 this year to 350-400 in 2015). Odds are that Icahn, who earned his billionaire street cred as a somewhat ruthless corporate raider earlier in his career, probably doesn't have patience with such a plan.

If Icahn gained control over the company, his marching orders might require new store openings to slow to a trickle, with a more significant number of store closings in order to boost margins. This would deplete some cash in the way of exit fees from leases, but there's ample room in the company's unsecured lines, which have increased from $700 million to $900 million, to absorb this hit. It may be a smarter move for Family Dollar to cede market share growth for now in order to become a smaller, more vigorous, and more profitable organization in the years ahead. Ironically, such actions would likely propel the stock price, justifying Icahn's investment.

A single pill won't solve the Family Dollar board's headaches
Family Dollar's board was quick to react to Icahn's ownership disclosure, adopting a "poison pill," or shareholder's rights plan, which essentially forces any owner of greater than 10% to pay a premium for control of the company. The rights agreement is in effect for one year, expiring on June 8, 2015. But fighting the tide may be folly, as there are too many strong hands around this particular poker table, with Trian Fund Management and Paulson & Co. also holding sizable, if slightly smaller, stakes. Between Icahn and his fellow strong-willed billionaires, we'll surely witness concrete actions to increase the value of Family Dollar, despite the possibility of strong resistance from its board. In this context, it's no stretch to say the shares are undervalued.