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You want your multinational corporation to be seen as a good corporate citizen. But you also feel obliged to your company's shareholders to keep it from paying a cent more in taxes than it is required to.

So what's the dividing line beyond which responsible tax management turns into poor citizenship? Well, for the moment it appears to be somewhere between this:

"Apple set up their sales operations in Europe in such a way that customers were contractually buying products from Apple Sales International in Ireland rather than from the shops that physically sold the products to customers. In this way Apple recorded all sales, and the profits stemming from these sales, directly in Ireland."

And this:

"Under the agreed method, most profits were internally allocated away from Ireland to a 'head office' within Apple Sales International. This 'head office' was not based in any country and did not have any employees or own premises. Its activities consisted solely of occasional board meetings. Only a fraction of the profits of Apple Sales International were allocated to its Irish branch and subject to tax in Ireland. The remaining vast majority of profits were allocated to the 'head office,' where they remained untaxed."

Those passages are both from the news release issued Tuesday by the European Commission announcing that it was ordering Apple to pay $14.5 billion (13 billion euros) in back taxes plus interest.

The decision will surely be fought over for a while yet; U.S. officials have already been complaining that the EU is unfairly targeting American companies in its tax crackdown. But it seems pretty clear that the devices used by U.S. tech giants to shift their European income to not just low-tax jurisdictions but nonexistent ones are proving to be a step too far.

As a single market with a lot of different tax systems, Europe already provided ample opportunity for corporations with operations in multiple countries to reduce their taxes. The initial setup described above shifted Apple's income from big, relatively high-tax markets such as France (33.3 percent corporate tax rate) and Germany (a 15 percent official rate with a bunch of surcharges and municipal taxes that bring the effective rate somewhere between 30 percent and 33 percent) to low-tax Ireland (12.5 percent).

But that wasn't enough for Apple and other U.S. multinationals. Google famously used something called a "Double Irish" with a "Dutch Sandwich" to reduce its overseas tax rate to 2.4 percent. Starbucks avoided corporate income tax in the U.K. for several years by paying royalties to a Dutch subsidiary, buying coffee beans in Switzerland and other tactics. This "stateless income," University of Southern California law professor Edward D. Kleinbard argued in a 2011 article, was becoming a "pervasive presence" that "changes everything" about corporate taxes.

Since then, the Organization for Economic Cooperation and Development (the club of the world's wealthy nations) has started a "base erosion and profit shifting" project meant to curtail such practices. And the EU and individual European countries have been using various tactics to get companies to pay up.

A big hurdle in collecting back taxes is that the past tax avoidance was generally allowed by the letter of European countries' various laws. And so in Apple's case, the EU's charge is that Ireland gave it a sweetheart deal that it did not offer to other companies. It's an alleged violation of EU competition rules, not strictly a tax case.

Still, I do think there's a lesson in it for corporate executives deciding how far to push their tax avoidance. When the corporate structures you devise cross the line from frugality into utter absurdity — and a "head office" with no employees or premises is pretty absurd — you are asking for trouble. Or, to put it another way, when tax planning transmutes your corporation into a citizen of no country at all, you're not being a good corporate citizen.

- — Justin Fox is a Bloomberg View columnist writing about business.