Trian, which is led by Nelson Peltz, held 1.19 percent stake in PepsiCo as of Dec. 31, according to Thomson Reuters data.
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Peltz has urged PepsiCo to split its more successful snack division from its beverage business, arguing that the move would reduce costs and unlock value for shareholders. PepsiCo's chief executive Indra Nooyi has said that the company's current strategy is working.
In July, Peltz said a proxy fight was a possibility. Johnson's election to the board marks a settlement between Pepsi and Trian.
In a statement Friday afternoon, Peltz said, "We support Indra's commitment to operational excellence, which has resulted in improved performance of the company. We are confident that Bill will be a strong and complementary addition to the PepsiCo Board.''
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PepsiCo shares were down about 1 percent in after-hours trading on Friday.