The numbers are slightly higher at online retailer's website, but not dramatically so (2.67% for major credit card, compared to 0.84% for either debit card of store issued credit card), the report found.

Aufseeser said the study was aimed at evaluating payment types across a variety of retailers in ways analysts and economists can use to make valid comparisons.

Aufseeser said she considered it especially important to collect data on handling cash since so little data on this cost element exists. “A surprising number of retailers have never really looked into what it costs them each year to accept payments in cash,” she said.

Examples of costs she sought to identify included armored car services, cash registers not balancing and cash lost to employee theft.

Aufseeser found that in convenience stores, on average, cash costs almost three times what debit cards cost and even two-thirds more than credit cards, the highest cost payment method in the two other retails sectors.

Aufseeser attributed the difference to both the much higher average ticket size when consumers use credit or debit cards and the percentage of cash transactions in convenience stores that pay for very small ticket items such as gum, candy and individual sodas.

On average, Aufseeser found debit transactions cost convenience stores $0.43 per transaction, credit cards cost $0.67 per transaction, and cash cost $1.06.

“We found abundant evidence that even if they send what feels like a large check off each month to cover debit interchange, convenience stores are still better off if they promote card use over cash,” Aufseeser said. “It only feels like cash costs less because no one has spent the time and gathered the data to quantify the costs of cash and because of how they pay the interchange.”

The research looked at the costs of debit interchange after the Durbin amendment capped debit interchange for issuers of more than $10 billion in assets.

“We thought about [looking at pre-Durbin interchange], but then thought 'what would be the point,'” Aufseeser said. “The cap is in place now and it would almost surely been very difficult to find data from before the cap.”

Retailers lost the most recent round in their legal battle to force the Federal Reserve to re-issue its regulation mandating a lower debit interchange cap, but have appealed to the Supreme Court.

The different sides of the debit interchange fight had their own reactions to the report.

Read more: Merchants respond …

“Merchants have always tried to avoid the topic of the value of card acceptance in their lobbying efforts, because they know it hurts their push for government price controls,” said Sam Fabens, spokesman for the Electronic Payments Coalition, an organization of credit union and other card issuers and payment processors formed to defend interchange.

“They always point to cash as their favorite method of payment, but maybe they should actually do the math and realize that it costs far more in time and money to accept cash than other forms such as debit. This report is another important piece of evidence that the value of acceptance far outweighs the cost.”

But the National Retail Federation and National Association of Convenience Stores attacked the report for its scope and missing the point.

“There's less to this study than meets the eye,” said Mallory Duncan, general counsel for the NRF. “It only looks at three narrow slices of the retail industry rather than taking a comprehensive approach. It mixes apples and oranges on the size of transactions and amount of costs, and it tries to perpetuate disproven myths about cards letting people spend more or being quicker in the checkout line. This is really just another example of card-focused individuals trying to convince merchants and consumers to give up cold, hard cash in favor of the illusory benefits of plastic.”

Duncan also suggested the only reason the study found debit cheaper than cash was because debit is used more often in some venues and so would have a less expensive per-transaction cost.

“If the numbers here say anything, it isn't that cash is inherently more expensive but that the per-transaction costs of any form of payment go up when it is used less often and its fixed costs are divided over a smaller number of transactions,” Duncan added.

Lyle Beckwith, SVP for government relations for the National Association of Convenience Stores, said, “Even if card usage saved some cash-handling expenses, that does not mean price-fixing on card swipe fees should be allowed. Buying that argument would be akin to saying phone companies should be able to price-fix because using phones saves us all money on building our own carrier-pigeon networks.”

But Leon Majors, SVP at Phoenix Marketing International, a research and consulting firm for card issuers and merchants, said the report's author and critics had missed some of the point.

Majors criticized the report for not having interviewed enough sources but said its conclusions were roughly similar to those he had found in his own research. And even if cash transactions are more expensive than debit cards, whether or not their customers use them is out of the control of most retailers, especially convenience store owners, he argued.

“Who use conveniences stores? All sorts of people,” Majors said. “But very many of those customers come from among the underbanked and unbanked and these people use cash almost always.”

Even if convenience store owners were to figure out debit cards were much cheaper than credit, they would not necessarily have much ability to move most of their customers in that direction, Majors added. They are having some luck with prepaid cards, but that sort of payment change takes years and years, if not decades, to bring about, he said.