(MONEY Magazine) – In the 1970s, Club Med (NYSE, $27) thrived by selling singles, who were seeking adventure and romance, vacations on the cheap in Cancun, Eleuthera, Mauritius and other Third World locales. As the baby boomers matured, earnings growth at Club Med slowed, averaging less than 5% annually for the three years through 1989. To rejuvenate its profits, Club Med has diversified over the past few years by opening new resorts targeted at different kinds of people -- sports enthusiasts, families with children and honeymooners, as well as the usual frisky singles. This year, that mid-life shift has started to pay off. Analyst Caroline Levy at Shearson Lehman Hutton expects earnings at Club Med (1989 revenues: $469 million) to rise by 40%. Among its 110 resorts, Club Med now counts golf academies, tennis clinics ( and family-oriented villages that offer special activities for children ages four months to 11 years supervised by trained staff members. Tots can swim or wade, and older children can scuba dive and race go-carts while their parents are off on their own. This fall, the company's crown jewel will be the 617-foot Club Med 1, a new 442-passenger sailing ship. It's scheduled to begin its first full season of Caribbean jaunts in September. At an average of $2,000 per person, says Levy, ''these cruises will expand the company's appeal to the upscale market.'' Analysts believe that Club Med can sustain annual earnings growth of 15% over the next three years. Levy thinks that the stock, which trades at a relatively low P/E of 12.6, could climb 18% to $32 over the next 12 months.