It wasn’t faltering profits or sagging U.S. market share that led DaimlerChrysler AG to agree to sell Chrysler to Cerberus Capital Management LP over the weekend.

Both did figure in the German automaker’s decision. No, the German parent’s ardor for its American partner was poisoned fatally by $16 billion, the number representing the present value of DaimlerChrysler’s health-care liability covering Chrysler’s present and future retirees.

Nine years ago, when Daimler-Benz AG bought Chrysler Corp., no one other than a Cassandra or two from Daimler’s accounting department fretted over the ticking bomb of unfunded health benefits.

Juergen Schrempp, Daimler’s chief executive officer at the time, waved it away with his big cigar. Last September, when asked to consider shrinking health benefits and heading off an explosion, the United Auto Workers union told Mr. Schremmp’s successor, Dieter Zetsche, to take a hike.

The UAW’s obstinacy helped push Mr. Zetsche to his tipping point. He decided to heed German shareholders who had been urging him to unload Chrysler. Now the UAW will have to deal with Cerberus, which like many private-equity investors, can be hard-nosed when whittling down costly liabilities.

The pension fund covering Chrysler workers is over-funded by about $2 billion and thus no worry for Cerberus or the UAW. Retiree health-care obligations, by contrast, aren’t funded at all, meaning the automaker must pay medical bills from increasingly scarce cash.

Why did Chrysler executives from years and decades past promise workers budget-busting health care? A couple of reasons: First, generous health care for retirees served to pacify a bellicose UAW, and it cost little in terms of current cash. Besides, those magnanimous executives — Lee Iacocca, Mr. Schrempp, and others of their ilk — knew the bill would come due when they were gone.

Having forged similar union contracts, General Motors Corp. and Ford Motor Co. also are burdened by giant unfunded health-care liabilities. GM’s liability has climbed to $65 billion, rendering the automaker’s shareholder equity a negative $4.25 billion. Likewise, Ford’s shareholder equity has sunk to a negative $3.7 billion.

Little wonder that some Ford family members in recent weeks have discussed hiring investment bankers, with an eye toward selling some Class-B super voting shares while they still retain some market value.

Most of the $7.4 billion price tag Cerberus is paying for Chrysler will be invested into the automaker’s operations, with the aim of improving its competitiveness. It’s a pittance next to the $36 billion in stock Daimler paid for Chrysler in 1998. In essence, Daimler-Chrysler is paying Cerberus to take Chrysler off its hands — while keeping a 19.9% minority stake — mainly to divest the health-care liability that Mr. Schrempp left for Mr. Zetsche to fix.

Cerberus has several opportunities to profit from Chrysler. The first is to introduce efficiencies between Chrysler’s financing operations and those from Cerberus’s 51% stake in GMAC, GM’s finance unit. Second, Cerberus can improve the basic vehicle manufacturing and sales.

Finally, Cerberus will try to renegotiate the $16 billion liability lower by several billion dollars. The UAW despises that idea, of course, yet the union has figured out by now that it may get nothing if an impasse lands the company in bankruptcy court.

Goodyear Tire & Rubber Co. in February attracted attention by agreeing with the United Steel Workers union to terminate retirement health-care benefits, which had a present value of $1.3 billion. In return, Goodyear agreed to contribute $1 billion, or about 77 cents on the dollar, to a trust the USW controls and uses to pay benefits.

Better some level of guaranteed health care, the USW concluded, than a greater level of benefits that might evaporate if Goodyear failed. Chrysler has started discussing a similar arrangement with the UAW. Presumably Cerberus will be keen as well. Assuming the same discount as at Goodyear, Cerberus might be able to reduce the $16 billion liability by $3 billion to $4 billion, thus justifying its $7.4 billion investment.

GM and Ford are interested as well, and already may be broaching the idea with the UAW. This summer’s labor negotiations are sure to be dominated by ideas for reducing health-care costs and liabilities.

None of the financial engineering, as clever as it is, will mean much for Chrysler unless the automaker can repair fundamental problems, starting with Dodge, Chrysler and Jeep models that lag on motorists’ shopping lists.

Since the late 1970s, Chrysler has survived one crisis after another. By accepting private-equity financing — albeit involuntarily — it’s getting one more chance to show viability, perhaps its last.

Mr. Levin is a Bloomberg News columnist.