San Francisco ? Catapulted by the biggest IPO in U.S. history, Visa Inc. shares soared more than 30 percent in their stock market debut Wednesday as investors bet an accelerating shift to electronic payments will enrich the world’s largest processor of credit and debit cards.

After being priced above expectations at $44 per share in an initial public offering that raised nearly $18 billion, Visa shares climbed to $58.98 in afternoon trading on the New York Stock Exchange. The run-up gives the San Francisco-based company a market value of about $50 billion.

The fervor reflects investors’ view that Visa is in a lucrative position as more people rely on its electronic network to make payments instead of using cash and checks. Visa is expected to milk the phenomenon to become an even bigger cash cow than it already is.

Visa generated $5.2 billion in annual revenue last year as it handled more than more than 44 billion transactions totaling more than $3.2 trillion. The volume puts Visa far ahead of its main rival MasterCard Inc., whose own shares have more than quintupled from their May 2006 IPO price of $39.