Amtrak, the federally subsidized passenger railroad, is planning by the end of this year to re-establish train service carrying people and their automobiles between Washington and Florida.

The Amtrak board yesterday gave all but final approval to its planned "auto-ferry," which will be similar to the service offered by Auto-Train Corp. before it went out of business in May 1981.

Auto-Train had accumulated about $25 million in debts when it filed for bankruptcy, but Amtrak is confident, spokesman Cliff Black said, that's its version will make money and partially offset the annual Amtrak subsidy, estimated at $700 million for the current fiscal year.

"Our projections show that the gross revenues would exceed the cost to operate it by approximately $4 million per annum," Black said.

The auto-ferry service can probably be run profitably by Amtrak, said Murray Drabkin of the law firm Cadwalader, Wickersham and Taft, who was appointed by the bankruptcy court as trustee for Auto-Train Corp.

Amtrak already has much of the equipment that would be needed, plus ticketing and reservation systems and track rights, Black said. The auto-ferry is expected to serve 140,000 passengers annually.

Fares have not been determined, he said. Auto-Train was charging $149 for cars and $99 for each accompanying passenger. Like Auto-Train, the Amtrak auto-ferry will require passengers and cars to travel together.

Amtrak currently operates two daily round-trip trains between New York and Florida, all of which pass through Washington. The auto-ferry would be an additional train that would run nonstop on a daily schedule during peak periods and three times a week during off-peak periods.

It is possible the auto-ferry would use the same terminals the old Auto-Train used--near Interstate 95 at Lorton and in Sanford, Fla. The Sanford terminal, adjacent to Amtrak's station, is still owned by Auto-Train and Drabkin said he is negotiating for Amtrak to use the facility.

Amtrak will need to spend about $4.4 million to buy equipment before it can run the service, Black said, and most of that money will be for auto-carrying rail cars. Amtrak already has adequate coaches, dining cars and sleeping cars.

Amtrak's announcement ends an attempt by a group of investors headed by Washington attorney Carl Shipley to start a similar service. Shipley said yesterday that he had talked with Amtrak about a privately financed venture about a year ago.

"We had concluded that we could run a succesful, modestly profitable rail operation," Shipley said. Amtrak, he said, "has crowded us out. We are disappointed" but "glad the service is going to be started again."