When eBay bought PayPal in 2002 for $1.5bn, it was largely as a more efficient way of processing payments through its rapidly expanding online auction site. Now, 13 years later and after a period of slowing growth – and against a raucous cacophony of calls for it to do so – eBay has finally spun off the e-commerce payments platform. Last year, eBay’s revenues grew by 6%, compared to PayPal’s 19% growth to $7.9bn. Following the spin-out, PayPal seems likely to go on to become the bigger company on the Nasdaq exchange – valued at some $47bn, compared to eBay’s current $35bn. In the second quarter, too, PayPal’s performance was far stronger than its parent’s, enjoying a 20% year-on-year rise…