By Geoff Colvin
June 13, 2013

The pressure is finally off Indra Nooyi, so you can’t blame her for sounding relieved — at least for the moment. Only 16 months ago her situation looked desperate. Several Wall Street analysts were calculating that PepsiCo, the company she runs, would be more valuable busted up into separate beverage and snack companies, a move she vehemently opposed. Activist investor Nelson Peltz, who helped force the breakup of Kraft Foods, bought a stake. Conventional wisdom held that in her six years at the helm she’d tanked the stock. It wasn’t true — its total return to shareholders matched the S&P 500 — but the misperception (caused by several months of a flat price) fed the growing disaster scenario. The New York Post repeatedly quoted “a source close to the board” saying the directors were fed up with her. Published rumors suggested that Nooyi would resign to join the Obama administration or become president of the World Bank as “a graceful exit.” (For more see “Indra Nooyi’s Pepsi Challenge.”) The deathwatch was on.

Nooyi responded by telling Wall Street that 2012 profits would go down — for a good reason. She promised to spend $500 million to $600 million more on advertising and marketing of the company’s biggest brands, like Pepsi-Cola and Doritos, which they badly needed. She’d fire 8,700 employees, which would cost money in severance before it saved money. Profits would fall 5%, she told investors, but then the chart lines would turn around. It was a sufficiently plausible plan to buy her a year.

The year is up, and the plan is working. Since May 1, 2012, PepsiCo stock has returned far more than the rocketing S&P, 30% vs. 21%. No one is calling for Nooyi’s resignation, and whatever the board may be thinking, it isn’t being leaked to the tabloids. With the stock at an all-time high, she even indulged in a bit of self-congratulation at the recent annual meeting: “It takes great courage to live in the moment and look beyond it at the same time.”

It would all be a nice, neat story but for a couple of intriguing complications. One is Nelson Peltz. After selling the shares he’d bought in the dark days, he started buying again last year, and SEC filings in mid-May show that he has built his stake to 12 million shares, worth about $1 billion. He also doubled his stake in Mondelez International, the snack business that Kraft split off at his urging. He won’t say what he’s thinking, but no one seems to doubt that he wants somehow to combine Mondelez with PepsiCo’s super-dominant Frito-Lay to create the ultimate global snackosaurus. PepsiCo’s only comment is an official statement that it has met with Peltz and “looks forward to continuing constructive discussions,” but Nooyi is on record opposing big acquisitions or a breakup.

The other complication involves PepsiCo’s U.S. beverage business, which still needs help. PepsiCo’s market share dropped 0.6 point last year, just as it did the year before, reports Beverage Digest. It’s now 26.9%, while Coca-Cola has held steady at 34%. Pepsi needs to arrest that trend, which is one reason Nooyi has invested in research for the industry’s holy grail, a low- or no-calorie all-natural sweetener that can make soft drinks taste just like today’s full-calorie versions.

In February she told investors for the first time that the FDA is now reviewing PepsiCo products that “once commercialized could potentially alter the trajectory of our cola business in a meaningful way.” Then, while discussing beverages in April, she told analysts that she was exploring “sensible opportunities to unlock incremental value through meaningful structural alternatives” but would say no more about it “until early next year.” Translation: Either Pepsi disrupts the industry with a breakthrough sweetener, or the company sells, spins off, or otherwise jettisons its North American bottlers. Maybe both. Investors would applaud.

The directors made Nooyi CEO because they wanted her to shake up the company. She has done that — and contrary to the appearances of a year ago, she may not be finished.

This story is from the July 1, 2013 issue of Fortune.

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