Visa Inc., the world’s largest credit-card network, said profit rose 28% in the company’s first earnings report since its record $19 billion initial public offering last month. The shares fell 7% after the results didn’t meet the most optimistic predictions.

Net income climbed to $314 million, or 39 cents a share, in the quarter ended March 31, from $246 million a year earlier, the San Francisco-based company said yesterday in a statement. Adjusted net income was 52 cents a share, beating the 45-cent average estimate of 16 analysts surveyed by Bloomberg.

Visa has advanced about 72% in the six weeks since its IPO as investors clamor for the company handling the most credit and debit transactions. Visa and No. 2-ranked MasterCard Inc., which has surged 522% since its 2006 IPO, are benefiting from consumers’ increasing preference for using plastic over cash and checks.

“Expectations for Visa, because of the overdone run-up in the stock price, were likely beyond what Visa could have reached,” an analyst at New York-based Calyon Securities, Craig Maurer, said in an interview. He rates the company “buy.”

Total operating revenue rose 22% to $1.45 billion. Visa expects earnings a share to grow at least 20% and revenue to grow between 11% and 15% annually for the next three years. It also expects to produce at least $1 billion in extra cash a year.

Credit-card purchases and cash advances rose 21% to $1.1 trillion in the quarter ended December 31, the company said. Total Visa cards in use globally rose 16% to 1.6 billion. The company reports these figures one quarter in arrears.