Activist investor Nelson Peltz has once again set his sights on a U.S.-based food giant. This time, Peltz, through his investment firm Trian Fund Management, took a 7.1% stake in food distribution company Sysco Corporation (NYSE:SYY), according to The Associated Press. This amounts to a more than $1 billion investment, and instantly makes Trian Sysco's largest investor. Peltz and Trian partner Josh Frank have been added to Sysco's board.

Investors may recall Peltz from his previous investment in food and beverage conglomerate PepsiCo. However, Peltz was unsuccessful then in his efforts to have PepsiCo separate its higher-growth Frito-Lay snacks business from its slow-growth Pepsi business. That failed endeavor may cast a pall on what Peltz may be able to accomplish this time around.

But Peltz may not be investing in Sysco with the goal of breaking up the company. Here's a different take on what Peltz may be after.

Sysco's lack of growth is hard to swallow
On the surface, there don't seem to be many reasons to invest in Sysco right now. The company's profits have been in decline for several years. In fact, Sysco's earnings per share have fallen each year since 2010, from $1.99 per share then to $1.58 per share last year. That represents a 20% decline in profits over that four-year period.

Sysco thought it had found a solution by buying growth, proposing a $3.5 billion takeover of US Foods. Unfortunately, The Federal Trade Commission opposed the deal on competition concerns. Sysco soon abandoned the deal, and adding insult to injury, Sysco was forced to pay a $300 million merger termination fee to US Foods.

Sysco's profits are getting hit by an increasingly competitive industry, and a changing consumer landscape. The food distribution industry in the United States is extremely saturated, as Sysco noted in its last 10-K filing that there are approximately 15,000 competitors in the U.S. alone. And Sysco is fighting an uphill battle because American consumers are increasingly showing a desire for fresher, organic foods.

The stock isn't exactly a screaming bargain, either. Shares of Sysco exchange hands for 35 times earnings per share. Considering its deteriorating fundamentals, Sysco doesn't look like an attractive investment opportunity.

Sysco's hidden gold mine
Even though the company isn't growing, Sysco does have something that could be very attractive for Peltz: its balance sheet. Sysco has a lot of cash on its books, and even more in accumulated treasury stock. Theoretically, the company could unlock a huge amount of cash, which could be used to finance a major stock buyback.

Sysco holds $5.1 billion in cash and cash equivalents on its balance sheet, compared with just $2.2 billion in long-term debt. In addition, Sysco has another $4.5 billion in treasury stock on the books -- those are shares that have been bought back by the company and are currently held in its treasury.

After Sysco's failed merger attempt, it announced a $3 billion stock buyback authorization, which indicated management's willingness to return a lot of cash to shareholders. This may have caught Peltz's attention, and he may have noticed the potential for even more.

The bottom line is that, in theory, Sysco could access its cash on hand to finance a large buyback, or could leverage its balance sheet by taking out debt to fund a large cash return program. This could explain Peltz's significant investment stake in this seemingly troubled company.