Shares of eBay jumped 2.8 percent Wednesday after analysts at Morgan Stanley "double upgraded" the stock on expectations that a transition away from PayPal will give the online seller a boost.

Analysts at the investment bank raised their rating on eBay to overweight all the way from underweight — skipping equal weight — and hiked their price target to $58 a share from $36. Morgan Stanley's new price target represents a 42.8 percent upside from Tuesday's close. EBay's stock was up 7.6 percent this year as of Tuesday's closing.

"We expect EBAY to start intermediating its own payments (pulling away from PayPal) in '18 as management stated on its 4Q:17 conference call, with a planned full transition in mid-2020," Morgan Stanley analyst Brian Nowak said in a note to clients. "We are bullish about this initiative as we've seen other leading platforms … observe higher user conversion/spend from."

"As a payment intermediator, EBAY will be responsible for collecting funds from buyers and instructing payment processors to disburse funds to merchants, which is currently done by PayPal. EBAY acting as both marketplace and payment intermediator could simplify and reduce costs for merchants, who would pay a single fee to EBAY," he said.

EBay and PayPal were part of the same company until 2015, when they were split into independent stand-alone businesses. Earlier this year, eBay announced it would use Adyen to process its sales.

Nowak said eBay's move away from PayPal should improve the company's ability to grow buyers and gross merchandise value, as well as increase earnings before interest and taxes (EBIT) by 20 percent over the next three years. It will also lead to a 52 percent increase in gross payment margin, he said.

"We could be early, as the market may not give EBAY credit for its 2021 payments business for some time," Nowak said. "That said, we expect the '18/'19 testing/gradual roll-out to act as sign posts for progress."