MIAMI — The world’s largest cruise line has suffered through a number of high-profile mishaps. Yet passengers continue to book vacations thanks to discounts, albeit at a slower pace, its earnings report shows.

Carnival Corp. offered more sales to attract wary passengers after an engine fire last month crippled the Carnival Triumph, leaving 4,200 people stranded for five days without working toilets or power. This week, two more of its ships had mechanical problems, ruining the vacations of thousands more travelers.

Carnival said Friday that it earned $37 million, or 5 cents per share, in the first quarter ended Feb. 28. That compares with a loss of $139 million, or 18 cents per share, a year earlier. But its forecast for the year came in below analysts’ predictions. Its shares fell more than 2 percent.

On Thursday, the company ended the voyage of the Carnival Dream after the ship’s backup emergency diesel generator failed, causing problems with some elevators and toilets. Instead of continuing back to Florida, Carnival was forced to charter airplanes to fly home the ship’s 4,300 passengers.

The Dream’s next trip, which was supposed to start Sunday, was canceled. All of the passengers scheduled for that voyage will receive a refund for the cruise and airfare.

The company also said that another ship — the Legend — was having mechanical problems and would skip its stop at the Cayman Islands, heading straight to its final port in Tampa, Fla., instead.

Carnival runs cruises under 10 brands including Holland America, Princess, Cunard and its namesake line.

Vacationers have been wary about booking cruises ever since the Costa Concordia — also owned by Carnival — sank off the coast of Italy in January 2012. Passengers have returned to the seas, but many needed to be coaxed by deep discounts.

Asked if they would like to share how deep the discounts have been for the various lines, Carnival executives replied, “Not particularly.”

In its earnings release Friday, the Miami-based company said advance bookings for 2013 are behind the same point a year earlier.

The company blamed Europe’s economic problems for its inability to raise prices. North American prices are up slightly but those in Europe and Asia are lagging. Passengers in Europe are booking vacations much closer to the date of departure, Carnival said.

Carnival’s rivals have also been hurt by the lagging European economy.

The company now expects revenue to be flat for the year, compared with a previous forecast for growth of 1 to 2 percent.

That outlook worried investors.

Carnival shares dropped 83 cents, or 2.3 percent, to $34.90.

Executives said Carnival is doing an assessment of emergency power and redundancies across its entire fleet following the Triumph mishap.

Howard S. Frank, the company’s chief operating officer, didn’t estimate the possible cost of improvements for analysts during a conference call Friday. “I don’t see it as being enormous,” Frank said.

The company refused to tell analysts how much it spent each year on safety and training.