The Costco cobrand card was a huge win for Visa, but nevertheless the card network's chief executive, Charlie Scharf, found himself defending the terms of the partnership.

As part of the deal between Costco, Visa and Citigroup, the warehouse store's acceptance cost will reportedly be around zero, compared to the 0.6% of each transaction that Costco paid American Express. American Express and Costco are ending their cobranded relationship, partly because American Express could not agree to financial terms with the retailer.

During April 30's conference call to discuss Visa's quarterly earnings,  investors asked Scharf about the cost of the Costco deal, and whether it could support loyalty or rewards programs given the reportedly low interchange rates  and the overall competitiveness of the cobranded card market.

"We view Costco as extremely unique," Scharf said during the call. "This is an industry where it's amazing with the gossip. Everyone likes to talk about what happens in terms of pricing and who did what to whom."

Visa's CEO did not discuss the financial terms of the deal with Costco or the negotiation process, but he repeatedly stressed warehouse chain's size and the opportunity to gain new card users that Visa would not have otherwise reached. He also suggested the Costco deal would not affect cobrand terms with other merchants.

"What we and issuers were willing to do for Costco is very specific to a unique opportunity to gain credit card acceptance," Scharf said.

During his prepared remarks at the beginning of the earnings call, Scharf said the Costco win is good for Visa and even better for the card network's issuers. "They're one of the largest and best retailers in the world," he said, noting Costco is the third largest merchant in the U.S. "[Costco] historically did not accept our credit product and how we have an opportunity to gain acceptance where MasterCard and American Express are not accepted."

The Costco pact creates the opportunity for additional consumer payments volume, Scharf said. He did not reference Amex, but Amex reported that 70% of Costco Amex card spending took place outside of the merchant chain.

"It's a great opportunity to drive incremental usage," Scharf said. "It should help all Visa issuers drive their cardholder acquisition opportunities."

Visa did not approach Costco as a "one off" deal, said Richard Crone, a payments consultant, adding there are other factors such as the value for branding and the new card account holders.

"Visa, as a payment network, looks to a major merchant cobrand deal to create a network effect," Crone said.

Visa is also bracing for a tough fight for other cobrand relationships, given Amex's Costco loss.

"Cobranding is very competitive, as is the issuing business," Scharf said. "I think when people lose a relationship like this, they need to figure out what they are going to look at, so things will continue to be competitive."

Overall, Visa reported quarterly profits that beat analysts' estimates. Net income for the quarter ending March 31 fell 3% to $1.55 billion, or 63 cents per share, from $1.6 billion, or 63 cents per share, from a year earlier, adjusted for a stock split. The average estimate of 34 Bloomberg-surveyed analysts was 62 cents a share.

Visa reported financial headwinds from lower gas prices, Russian economic weakness and the strong U.S. dollar. 

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