Imagine this. You're onboard, settled in, and now you have to listen to a flight attendant's credit card sales pitch.

It drones on forever. Maybe you already even have the credit card. And you find yourself asking: Is this airline in the credit card business or the travel business?

An exaggeration? Maybe not.

A new report by an airline industry analyst suggests airlines are making billions by selling frequent flyer points to banks, so they can use the points to entice customers to use credit cards--an amount that potentially rivals what they make from the traditional travel part of their business.

What's more, he thinks the airlines ought to spin off their frequent flyer programs into separate companies.

Here's the theory, the calculations behind it, and the literally billions of dollars that airlines are making from a business that most people don't even know they're in.

$3.8 billion

Meet Joseph DeNardi, managing director of Stifel Nicolaus. He's been pushing the notion for a long time that airlines' frequent flyer programs are worth more than the airlines themselves, and pushing the airlines to spin off the programs.

The airlines resist that, as you might imagine. In fact, they don't make it easy to break down exactly how much of their revenue comes from these programs.

But now, DeNardi says he's figured it out. In fact, looking at just seven airlines, he says it added up to about $3.8 billion in the first half of 2018 alone. Here's DeNardi's breakdown:

American Airlines: $1.15 billion

United Airlines: $962 million

Delta Air Lines: $805 million

Southwest Airlines: $563 million

Alaska Airlines: $215 million

JetBlue Airways: $80 million

Hawaiian Airlines: $34 million

His assessment is based on what "marketing revenue," which is basically the difference between what a single airplane mile costs them, versus what they sell it to the banks for.

Those are big numbers, and they're going up quickly; American is up 10 percent year over year against the first half of 2017; Hawaiian is up 53 percent. Compare those numbers to the total 2017 pretax profit that American Airlines reported, $3.1 billion, and you can begin to see DeNardi's point.

May I have your attention, please?

DeNardi's report was dissected by both Gary Neff at View From the Wing and Brian Sumers at Skift.

As Sumers points out, DeNardi shared some of his calculations with American Airlines CEO Doug Parker and argued that more than half of American's total margin could be coming from the loyalty programs.

Parker disputes it.

But the fact remains: Both American and United Airlines trot their flight attendants out, reportedly on every flight, with credit card pitches that "can go on for as long as three minutes, often interrupting in-flight entertainment and waking up passengers midflight."

United even pays flight attendants a $100 bonus for each passenger who signs up for a credit card. Southwest just launched a credit card, but promises it won't do in-flight pitches.

Passengers utterly hate these pitches. They post about them on social media, and they wonder why an airline would so annoyingly alienate its core customers.

I have to say, DiNardi's theory offers a pretty compelling explanation for them. Because what if his analysis is right, and the airlines actually have a more efficient business in credit cards and frequent flyer programs than in the labor- and capital-intensive air travel business?