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An $18 billion liability figure attached itself on Friday to Volkswagen's diesel disaster. Tuesday morning brought news that the German carmaker has set aside $7.3 billion (€6.5 billion) to cover a scandal spreading worldwide. How to make sense of these impressive-sounding numbers?

As we all know, Volkswagen has apologized for selling hundreds of thousands of diesel cars in the U.S. with software specifically designed to evade government pollution tests. That's bad, but it gets worse. As regulators in multiple countries have weighed in to say they would also investigate VW imports, the company disclosed that the irregularities on diesel-emission readings extend to some 11 million vehicles globally.

At this early stage, putting a precise price tag on the ultimate cost of pollution penalties, criminal fines, private settlements, and the like is virtually impossible. But we can begin to break down some likely elements of the pecuniary damage VW faces.

The EPA's big, discounted fine

The $18 billion liability figure reflects the maximum per-car clean-air penalty the Environmental Protection Agency could, in theory, assess. For those who like to see the math: Some 482,000 four-cylinder VW and Audi cars, sold in the U.S. since 2008, multiplied by $37,500 for each non-compliant vehicle.

Volkswagen Chief Executive Officer Winterkorn (left) and Michael Horn, president and chief executive officer of Volkswagen Group of America (right), with two other VW executives at the the 2015 North American International Auto Show. Photographer: Andrew Harrer

That's the way a very angry American judge might calculate civil damages, if there were a trial. But there won't be a trial. Volkswagen Chief Executive Officer Martin Winterkorn said on Sunday that his company is “deeply sorry” for the emissions-cheating scandal and will do “everything necessary in order to reverse the damage this has caused.” On Monday night, Michael Horn, head of the brand in the U.S., elaborated at an ill-timed promotional event in New York. “Our company was dishonest with the EPA, and the California Air Resources Board, and with all of you,” Horn told reporters. “And in my German words: We have totally screwed up.”

Horn's German words can also be translated as: We will settle this fiasco as rapidly as possible. In exchange for sending their lawyers promptly to the negotiation table, Volkswagen will probably get a significant discount from the EPA on the maximum statutory pollution penalty. Just how much of a discount, though, will turn in part on the criminal investigation.

The criminal probe: a further $1 billion?

Prosecutors from the the Justice Department’s Environment and Natural Resources Division will look for evidence of knowing fraud by VW engineers and executives. Since the company has admitted that it rigged diesel vehicles to pass lab tests, even though they emitted as much as 40 times the legal limit of pollutants on the road, it seems highly likely that investigators will find fraud.

That will probably lead to three results: a corporate criminal plea by Volkswagen, a criminal fine assessed by the Justice Department, and criminal charges against individuals. The VW case will become a test for the Obama administration's newly stated commitment to holding particular corporate employees and officials responsible for wrongdoing attributed to their employer. That's bad timing for VW diesel-emissions team members. Earlier this month, the Justice Department announced with some fanfare that companies that want credit for cooperating with investigators must name individuals that they allege are responsible for misconduct. Look for VW to acknowledge collective guilt and point the finger at offending individuals whom the company will accuse of betraying its otherwise supposedly high-minded values.

A satellite image of the 2010 Gulf of Mexico oil spill. Photographer: DigitalGlobe via Getty Images

We have some potentially helpful comparison points. Just a few days ago, General Motors agreed to pay $900 million to resolve a federal criminal investigation of ignition-switch flaws linked to at least 124 crash deaths and the recall of 2.59 million cars. So far, no individuals have been criminally charged in the GM case, but prosecutors have said the probe is continuing. In an earlier case concerning cars that allegedly accelerated spontaneously, Toyota reached a $1.2 billion settlement with the Justice Department, the largest-ever U.S. criminal penalty for a car company. (GM and Toyota didn't face the kind of civil pollution liability VW has all but conceded; on the other hand, the deceptively dirty diesel engines didn't kill anyone—at least, not in an immediate sense.)

Let's say VW is willing to pony up $1 billion or so in criminal penalties and to make examples of some of its soon-to-be-former employees associated with the emissions manipulation ...

Then there's civil liability and private plaintiffs

I'd wager that to make the clean-air infractions go away, the company would have to at least double that amount on the civil side, for a grand total of $3 billion to $4 billion of U.S. government liability. The key to such a deal will be time. VW will seek to pay over a period of years. The government will probably go along with that. In July, BP agreed to settle its government environmental liability related to the 2010 Gulf of Mexico oil spill for $18.7 billion. BP's deal allows it to pay over 18 years, which makes the arrangement far more feasible for the British energy giant.

Satisfying the EPA and Justice Department is not the end of the liability story for VW. State attorneys general are going to want in on the money grab. And some of the most potent private plaintiffs' law firms in the country are already filing or assembling lawsuits seeking compensatory and punitive damages for hundreds of thousands of car owners whose vehicles are worth thousands of dollars less today than they were last week. Yet another category of suits will seek compensation for shareholders who have seen the value of their VW stock shrink by more than a third since the scandal broke last week.

Given what VW has already conceded, these private suits will have what the trial lawyers politely call "settlement value." When the suits get bundled together into class actions—at least one for economic tort damages and a second for securities fraud—that value will climb from the hundreds of millions of dollars Ainto the billions (again, with the likelihood of some time delay in terms of actual check-cutting.)

An early estimate of VW's total liability

For a first cut at VW's total U.S. liability, I'd start with something in the neighborhood of $6 billion. That doesn't address the penalties the company faces in Germany and numerous other countries, none of which have liability systems as expansive as that of the U.S. but all of which are going to want to teach VW a lesson. In this light, the company's $7.3 billion set-aside starts to look overly optimistic.

And then there's the dent to Volkswagen's credibility in consumers' eyes—a form of damage that could prove incalculable.