The latest contribution to the speculation about a possible Apple TV comes from a survey commissioned by Morgan Stanley which quizzed 1,568 heads of households in the U.S. in September. It found that 47% were at least “somewhat interested” in buying a TV from Apple, analyst Katy Huberty reports. That’s impressive: Only 23% were as interested in the iPhone when the investment firm conducted a similar survey in February 2007, and 21% were interested in the iPad in April 2010. And the findings about an Apple TV may be conservative: “the survey was conducted ahead of an actual product announcement,” Huberty says. Still, respondents on average said that they’d be willing to pay $1,060 for an Apple TV, which is 20% more than they paid for their current sets. (About 46% were willing to go over $1,000 and 10% would cough up more than $2,000.) That’s “an incremental $13B revenue opportunity” for Apple. But consumers might have to pay more than $1,300 for a 45-inch set in order for Apple to generate a gross profit margin of 40% — below its current 44% — the analyst says. Does Apple need to control all aspects of the TV offering, the way it does with, say, music and the iPod? Not necessarily. “Apple is most likely to sell a TV with an integrated digital media receiver and Apple operating system,” says Huberty. “Ease-of-use and searchability of content are key areas in which Apple can differentiate according to our survey.”