Discover Financial Services Inc. gave one of the first glimpses of how major new loan loss accounting rules will affect credit card companies. The bottom line: a lot.

The company’s CEO Roger Hochschild told analysts April 25 that if the company had to apply the new current expected credit losses (CECL) rules to calculate total losses this quarter, it would have to boost reserves by 55 to 65 percent.

“The ultimate impact won’t really be determinable until the date of adoption because it’s really heavily dependent on both the composition and trends in our portfolio as well as our forward-looking...