DETROIT—A trust fund set up by the United Auto Workers union is hoping to raise at least $1.3 billion to help pay retiree health care costs by selling rights to an 11 percent ownership stake in Ford Motor Co.

The trust will auction warrants to buy 362 million shares, which were issued in December 2009, starting at 8 a. m. today. The automaker and union agreed to set up the trust to help Ford remove retiree health care costs from its books while it was in financial trouble in 2007.

In January, the trust began paying health care costs for about 200,000 Ford blue-collar retirees and their spouses nationwide, and Ford said it is saving the company roughly $500 million per year.

The trust set a minimum price for each warrant at $3.50. Each warrant gives the holder the right to buy a Ford share at $9.20. At the minimum price, the trust would get $1.3 billion, $100 million more than the value Ford placed on the warrants in December.

Shelly Lombard, credit analyst at the New York bond research firm GimmeCredit, said the trust is wise to sell the warrants now, since Ford’s stock has been on the rise.

“The economy’s improving and Toyota’s on the ropes, so the sense is that things will only go up from here,” she said. “But having said that, it just makes perfect financial sense to take some money off the table. You never know what the market’s going to do.”

In the past 16 months, Ford shares have grown more than 10 times in value as the company avoided bankruptcy protection and government aid, won accolades for its car quality and reported a full-year profit for 2009.

The automaker’s shares closed as low as $1.26 on Nov. 19, 2008, the lowest price in more than 27 years. But on March 18 they hit an intraday price of $14.54, the highest level since January of 2005.

The combined $12.70 that a buyer would pay for both the warrant and a share of Ford stock is 8 percent below Ford’s closing stock price on Friday of $13.86 a share.

Ford shares fell 29 cents, or 2 percent, to $13.57 in Monday trading.

The UAW trust, called a voluntary employees beneficiary association, has received $2.5 billion in cash from Ford. It already had $3.5 billion mainly from previous trusts set up by the company.

Ford still owes the trust two notes that were worth a total of $7 billion as of Dec. 31, and the company can pay up to half of that obligation in stock.

In exchange for all the payments, Ford unloaded a retiree health care liability from its books valued at $13.6 billion over the lives of all 200,000 retirees and spouses.

Ford’s trust is far healthier than similar ones the union negotiated with General Motors Co. and Chrysler Group LLC. The GM and Chrysler trusts are dependent on the two automakers selling stock to the public.

GM’s trust covers around 700,000 retirees and spouses, while Chrysler’s covers 120,000.