Zoetis Inc., the animal-health products maker at the center of the latest round of pharmaceutical deal talk, said Tuesday that its board has approved a $500 million share-buyback program. The announcement comes a day after the company disclosed a deal to buy Abbott Laboratories’s ABT, -0.23% animal-health business for $255 million and about a week after the disclosure that activist investor William Ackman had taken a stake of about $2 billion in Zoetis.