Five years ago PayPal was a Wall Street favorite and a leader in digital payments. Since then the stock has plunged, Apple Pay dominates payment services in the U.S. and PayPal is facing a takeover bid it does not like. What happens next?

The company synonymous with digital payments this past week got a US$53 billion offer to be taken private by upstart rival Stripe and buyout shop Advent International. PayPal’s board is discussing the bid but believes US$60.50 a share is not enough, people familiar with the company said.

It is a comedown for a company that helped to pioneer e-commerce and email-based payments, launching the careers of tech titans Elon Musk and Peter Thiel in the process. Founded in 1998, the San Jose, California, firm…