Three months after a new rule capped debit card swipe fees, Visa Inc. is weathering a slowdown in its U.S. debit business, though it has so far avoided the doomsday scenarios once predicted.

Starting Oct. 1, regulations capped debit card interchange fees at about 24 cents per transaction, or about half of what retailers previously paid banks on average. The Federal Reserve Board restricted those fees as part of the so-called Durbin amendment of the 2010 Dodd-Frank Act.

The rules appeared to crimp some business at Visa, which has long dominated the U.S. debit market. Its U.S. debit payments volume grew about 5% in its fiscal first quarter from a year earlier, markedly more sluggish than the 16% growth of the previous year.

Analysts largely shrugged off the slowdown, although they acknowledged that Visa and rival MasterCard Inc. have yet to feel the new regulations' full effects. Another restriction on the debit-card industry does not go into effect until April 1.

"The impacts from Durbin so far have been muted. … The caveat is we haven't seen it fully implemented yet and haven't seen responses fully played out," says Gil Luria, a managing director at Wedbush Securities.

Chief executive Joseph Saunders conceded Wednesday that Visa is feeling the effects of the new debit card rules.

"The deceleration of our U.S. debit volume growth during the first quarter was an early sign of this impact, driven by slower growth in PIN transaction and an expected de-emphasis by issuers of debit card, marketing and debit rewards programs," Saunders told analysts during a conference call to discuss Visa's earnings for the quarter ended December 31.

He noted that "a key driver of this slower growth was one major financial institution's decision to remove [Visa debit network] Interlink from the back of their cards, which began in the fall as part of their own plan to comply with the regulation."

Another part of the Durbin amendment requires banks to sign up at least two networks to process every debit card transaction by April 1, thus giving merchants a choice — and theoretically generating competition, and lower prices, between the networks. Many banks have in the past signed exclusive processing contracts with networks.

In response Visa last year announced that it would be rolling out an incentives plan to sway merchants to process transactions using Visa's network.

Saunders reiterated on a call with analysts Wednesday evening that Visa is moving forward with that strategy.

"As a next step in our implementation plan, we will share specifics with acquirers and merchants later in the month," Saunders said

He emphasized that Visa expects to suffer the most from the debit rules over the rest of this year.

"We expect that 2012 will take the brunt of the impact related to U.S. debit regulation, and we still expect growth in 2013 to accelerate off of the 2012 levels," he said.

Some analysts speculate that Visa could offset its slower debit card growth by processing more credit card transactions. Many banks have discontinued debit card reward programs and in some cases have tried to encourage their customers to switch to credit cards, which bring in higher — and unregulated — interchange fees.

"The mix shift is going to higher credit card volumes, which is a much more profitable business," says Darrin Peller, an analyst with Barclays.

But Saunders was far from enthusiastic about a broad shift from debit to credit cards. In response to an analyst question, he said that some movement was likely, though it was to too early to predict "exactly what kind of switch there may be."

He added, "Anecdotally, of course, you know that rewards have been removed from debit cards and rewards exist on credit cards. So they've probably … just logically, you'd have to assume that there's some movement in that regard."

While the networks are currently finding relief in unregulated credit card interchange rates, those fees are also under assault in a long-running court battle. Retailers including Safeway Inc., Collective Brands Inc.'s Payless ShoeSource and Kroger Co. have sued the networks and some large banks, arguing that they violated antitrust laws in setting credit card interchange rates.

Saunders discussed ongoing settlement negotiations in the lawsuits on the Wednesday analyst call, following similar statements by MasterCard chief executive Ajay Banga last week. MasterCard said then that it was setting aside $495 million after tax for a potential settlement of the merchants' consolidated lawsuits.

On Wednesday, Saunders reiterated that Visa now has $4.3 billion set aside in a litigation escrow account, which he says is "consistent with our view of the current status of mediation discussions."

He echoed Banga in adding that Visa would not accept a settlement that requires the networks to make major, permanent changes to its interchange system.

"Visa is unwilling to agree to any significant or long-term credit interchange rate reductions or any settlement agreement that doesn't provide a full resolution to that and other key issues," Saunders said.

Despite the debit headwinds, Visa still posted a profit of $1.03 billion, or $1.49 per share, up 16.4% from a year earlier. Revenue rose 13.8% to $2.55 billion.

The total volume of transactions it processed rose 8% to 13.6 billion.

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