Apple is tight-lipped about whether, let alone how, it might sell TV sets and an online video service that would compete with cable and satellite. But Carl Icahn still has high hopes for the businesses — as well a potential Apple entree into auto sales — he says today in an open letter to CEO Tim Cook that gave a modest lift to the company’s shares.

The billionaire investor made his forecasts as part of a case positing that Apple shares are “dramatically undervalued” and would be helped by a “much larger” buyback on top of the $80 billion it already spent. Apple’s stock, which now trades for about $130 a share, is worth $240, he says.

Image (1) apple-logo__120825004237-200x218.jpg for post 338550The Street doesn’t appreciate that by 2020 the company “is poised to enter and in our view dominate two new categories” — TV and cars. “Combined, these two new markets represent $2.2 trillion, three times the size of Apple’s existing markets (if we exclude Apple Watch).” If Icahn’s right, then the iPhone “sits at the epicenter of this mega-ecosystem.”

Apple will sell 55-inch and 65-inch ultra-HD TV sets beginning in the fiscal year that ends in September 2016, he predicts. The sets will sell for an average of $1,500 apiece, Icahn calculates; Apple should sell 10 million in 2016, and 25 million the following year. He also believes the company will introduce an online video service offering a so-called skinny bundle of TV channels.

Not including ad sales, “the addressable market for television is approximately $575 billion, which is larger than the smartphone market,” Ichan writes. “Also, given that people spend an average of 12% of the day watching TV (equating to 25% of their free time), we view television’s role in the living room as a strategically compelling bolt-on to the Apple ecosystem.”

Packages of TV channels can be sold as “multiple products at various price points across the demographic spectrum” the way Netflix does by charging a higher monthly fee to subscribers who want 4K, Ultra-HD-quality video streams.

That could help “other devices and services in the Apple ecosystem.” For example, “the Apple Watch could perhaps be used as a remote control,” or the company could sell a larger iPad that would serve as “an improved ‘second screen.'”

Analysts who follow Apple also are curious to see what Cook has in mind for TV. But they recognize that the company will have a harder time cracking the market than it had with phones, tablets, and — most recently — digital watches.

TV set manufacturing is a low-margin business; Apple’s profits could take a hit if it sells sets at competitive prices.

Apple’s also struggling to come up with programming deals that would enable it to offer a compelling alternative to cable and satellite — or streaming services offered by Dish Network’s Sling TV, Sony’s PlayStation Vue and coming offerings from Verizon and AT&T among others. Network owners are eager to keep the pay TV bundle intact and have agreements with cable and satellite companies that guarantee them the lowest prices for their channels.