FORTUNE — J.C. Penney is an absolute mess.

Its transformative CEO Ron Johnson is history, after failing to convince American grandmothers that “everyday low prices” are superior to “30% off sales.” It proved unable to attract younger demographics by altering its brand to an acronym, perhaps because none of its “stores within a store” sold buckets of fried chicken. Its new CEO Mike Ullman is the guy they previously booted — perhaps explaining why shares spiked upon news of Johnson’s ouster, but sank once Ullman was announced as his replacement. In fact, J.C. Penney stock is trading even lower than it was during the 2008 financial market meltdown.

All of this must make J.C. Penney JCP investors like Bill Ackman want to stick their heads in an oven. And, sadly, I don’t see private equity firms riding to their rescue.

From a surface level, I understand why some folks have been playing with the idea of a J.C. Penney buyout (possibly even signing an NDA or two). It scores well on the generic LBO checklist:

Depressed stock price? Check. Possible leadership vacuum? Check. Known industry sector? Check. Nearly $13 billion in annual revenue to leverage up against? Check. Company-owned real estate? Check. Tons of private equity dry powder seeking U.S. buyouts of between $1 billion and $5 billion (i.e., not consortium deals)? Check.

But the devil is in the details, and J.C. Penney’s catalogs ought to be written by Dante.

For starters, its market cap is barely larger than its existing long-term debt ($3.12 billion vs. $2.87 billion). And those bonds are trading at just 70 cents on the dollar. Even if private equity firms could make the new leverage math work, what type of terms could they get? Forget covenant light. This would be covenant heavy times infinity.

The second big stumbling block is Bill Ackman, who is J.C. Penney’s largest outside shareholder. He previously has lauded retail privatizations, such as what Kohlberg Kravis Roberts KKr did with Dollar General DG . So chances are he’d want in on the possible upside, perhaps via a public equity stub (shares of DELL) — which is not something that private equity firms typically favor. If private equity firms instead tried to buy him out at a guaranteed loss, then they could be setting themselves up for an unwelcome fight.

Finally, there is an argument to be made that Ron Johnson already failed at the type of overhaul that private equity suitors would favor. He kept telling people to ignore the short-term so that the long-term vision could take hold. Perhaps Wall Street just didn’t have adequate patience or maybe there is a viable middle ground between Johnson’s radicalism and status quo, but private equity firms already have seen J.C. Penney’s knife fall through different types of weather. There is little chance that they’ll be eager to catch it this time around.

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