If activist investor Nelson Peltz had his druthers, beverage giant PepsiCo (NASDAQ:PEP) would calve off its drinks business, and focus on just the snack-food portion by buying Mondelez (NASDAQ:MDLZ).

While Pepsi management hasn't warmed up to the idea, there is some sense to what Peltz proposes, even if, as a huge shareholder in both Pepsi and Mondelez, it's a bit self-serving.

In Peltz's 59-page manifesto, the investor spells out a case of underperformance due to Pepsi's beverages unit. Pepsi, which has suffered from more than five years of negative volume growth, and more than a decade of declining per capita volume, is perennially No. 2 to Coca-Cola, which he says is a more-focused competitor with structural advantages. 

Conversely, the snack-food business already comprises two-thirds of its revenues, has the top market share in salty snacks, and is experiencing volume growth across all its business lines. By getting rid of the beverage unit, which includes Pepsi and Gatorade, it could achieve significant increases in shareholder value worth at least $33 billion by merging the remaining snack foods business with Mondelez, whose stock has languished since splitting from Kraft Foods Group last year. 

Peltz points out that there are numerous examples of other such successful acquisitions and divestitures to support the move, including Pepsi's own spinoff of Yum! Brands back in 1997. He estimates the merger could lead to an implied value of $175 per share for Pepsi, and $72 per share for Mondelez, by the end of 2015.

Kellogg was launched into the No. 2 position behind Frito-Lay after it acquired the Pringles chips business from Proctor & Gamble last year. The 12% increase in revenues it enjoyed last quarter were helped along by the strength of Pringles sales.

Analysts feel that using Mondelez' global distribution network would help Pepsi continue on its snack-food growth trajectory, because even though Frito-Lay is expanding, it's nevertheless been losing market share in North America. Organic growth has decelerated from 6% annually between 2002 and 2009, to 3% between 2009 and 2012, which Peltz feels is due to being weighed down by the beverage business.

Although the best outcome of a merger would be the elimination of the Mondelez name, which was horrible from the beginning, and which Peltz likens to sounding like a disease, his Plan B is to go ahead and divest the beverages business regardless. 

Pepsi management has said thanks, but no thanks, intimating that it isn't going to get rid of its beverage business, and isn't going to make any big purchases like Mondelez; but the underperformance Peltz has highlighted, and the solution he's offered, could create investor pressure to do something, if not follow this plan exactly.

Peltz has a history of shaking up staid corporations, having driven Cadbury to split its drinks and candy business in two, then pushing Kraft to acquire it. He then pushed for the Kraft split-up. So look for some sort of deal to bubble up soon, if not tomorrow, then in the near future. A $170 billion snack food giant might not be out of the question.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.