Johnson Controls Inc. of Milwaukee has plans to desert the United States by combining with a previous corporate deserter, Tyco International PLC, and setting up a headquarters in Ireland. (Mauritz Antin/EPA)

This column has been updated.

If you want an example of how bizarre U.S. tax laws can be — and how companies can game the system — look no further than the recently announced deal for Johnson Controls Inc. of Milwaukee to desert our country by combining with a previous corporate deserter, Tyco International PLC.

Tyco is run out of Princeton, N.J., but for tax purposes it is based in Ireland, where the combined Johnson Controls PLC will be based.

This isn’t your standard “corporate inversion,” as polite people call these kinds of tax-avoiding deals. Technically, it’s not even an inversion. Rather, it’s an especially aggressive transaction that, among other things, will let Johnson game the tax system by handing its shareholders about $3.9 billion in cash in order to get tax-free access to $8.1 billion in cash currently held overseas.

You don’t believe that even our absurd tax system will let Johnson PLC do this? Let me take you through the numbers and show you how it works.

A brief aside: Normally, I spare you as many numbers as possible, and don’t use Inc. or PLC after corporate names. But today, I’m departing from that form, because you need to see the details in order to understand the transaction.

Back to the main event. Under our tax laws, if a U.S. company combines with a foreign company (or a nominally foreign company such as Tyco), it can play a variety of tax games, provided that the shareholders of the U.S. company own more than 60 percent but less than
80 percent of the stock in the new, combined company.

However, the company can play far more games — and avoid certain kinds of embarrassment that there’s no space to discuss today — if the shareholders of the U.S. company own more than 50 percent of the combined company but less than 60 percent.

This is where the $3.9 billion in cash comes in.

Under terms of the Johnson-Tyco transaction — which involves Tyco buying Johnson, although Johnson’s management will run the combined company — Tyco will have about 404 million shares outstanding when the deal is consummated. (Tyco has more shares than that, but each current Tyco share will become 0.955 of a Johnson PLC share.)

Johnson has about 647 million shares outstanding. If the companies just combined without playing the cash game I’m about to describe, Johnson holders would own about 61.5 percent of the combined company — 647 million of the 1.051 billion shares.

But Johnson will use the $3.9 billion of cash to buy in about 112 million of its shares. That way, Johnson Inc. holders end up with 535 million Johnson PLC shares, about 57 percent of the 939 million shares that will be outstanding.

When I emailed my math, which is based on public filings, to Johnson spokesman Fraser Engerman, he answered, “Not going to dispute your numbers.”

By being in the more-than-50-less-than-60 percent sweet spot, Johnson PLC can get its hands on its offshore cash directly, instead of having to leap through various hoops as less-aggressive deserters do.

I have no idea why it’s legal for Johnson to buy in a chunk of its shares to make the numbers work — but apparently, it is.

I also have no idea why on Earth more-than-50-less-than-60 percent deals are treated so much more favorably for companies (and unfavorably to those of us who pick up the tab for the taxes they avoid) than more-than-60-less-than-80 percent transactions are.

I asked tax expert Ed Kleinbard of the University of Southern California’s Gould School of Law about this. He said it’s because of the way Congress wrote Section 7874 of the Internal Revenue Code, which it passed about 10 years ago to try to plug loopholes through which companies squeezed in order to invert.

“Congress drew the 60 percent line when it enacted the statute,” Kleinbard said in an email. “There’s no fundamental economic explanation for that decision. . . . I am not aware of any history that explains why Congress drew the inversion line at 60 percent.”

Pfizer Inc. of New York, which is part of the biggest corporate desertion in history by combining with Allergan PLC of Parsippany, N.J., is also doing a stock buyback and a more-than-50-less-than-60 percent deal. But the arithmetic there isn’t as clear cut as in the Johnson-Tyco deal.

So there you have it. Johnson, a vendor to the taxpayer-rescued U.S. auto industry, repays us by doing not only a desertion but a mega-desertion.

Thanks, guys. If U.S. vehicle makers hit the skids again, maybe Johnson PLC can ask Irish taxpayers for help.

Addendum: Although I included far more technical material than usual in this column, I left out some things I should have included — one of which I didn’t know.

As I said, technically, Tyco PLC is buying Johnson Controls Inc., and the combined company will be Johnson Controls PLC. What I didn’t realize is that the $3.9 billion of cash that will be used to buy Johnson stock is coming from Tyco, not from Johnson. And in this case, that makes all the difference.

The fact that Tyco rather than Johnson is buying Johnson shares for cash is why this transaction doesn’t violate rules the Treasury has adopted to stop U.S. companies from “skinnying down” by buying in their own shares in order to make transactions like this one fit into the necessary parameters.

No-skinny down would apply if Johnson were buying Johnson stock for cash. It doesn’t apply here because Tyco is buying Johnson stock for cash. It’s a loophole that the Treasury — inadvertently, I’m sure — left when it wrote its no-skinny down rule.

Of course, money is fungible, and after the transaction closes, the combined company can use Johnson’s offshore cash to replenish the $3.9 billion that Tyco laid out.

My bet is that after seeing Johnson-Tyco, the Treasury will try to tighten up no-skinny down. What this whole thing shows is how hard it is to write rules to stop big companies from doing what they want to do.