For BlackBerry investors cheering the prospect of a sale of its BBM messaging service after last week’s $19 billion deal for WhatsApp, the waiting may be the hardest part.

BlackBerry shares have rallied 18 percent since Facebook agreed to pay $42 per user for WhatsApp’s mobile-messaging application, implying a valuation of as much as $3.6 billion for BBM. The messaging service isn’t likely to find a buyer willing to pay close to that much because it lacks the scale of WhatsApp with a user base one-fifth the size, BGC Partners Inc. said.