Carl Icahn is at it again. After taking a minority position in Apple (AAPL 0.52%), the activist investor has used the social-media megaphone of Twitter to convince Apple to increase its buyback program. In late 2013, Mr. Icahn asked for Apple to buy back $150 billion shares, even though the company had already committed $100 billion to its capital return program -- a figure that includes dividends .

Tim Cook proved a shrewd operator and, by the time it was all over, Carl Icahn essentially gave up on the request. However, not one to take no for an answer, Mr. Icahn is back, imploring Apple to increase the value of its shares with an open letter released Oct. 9. Although the letter doesn't mention specifics in regards to the amount, Mr. Icahn later mentioned $100 billion as the amount of the buyback.

Carl Icahn thinks Apple will release a TV set
Carl Icahn's letter is rather long and values Apple using extremely aggressive assumptions, especially when compared to recent results. However, one thing that stood out was his insistence that Apple will release a TV set:

While Apple has not announced plans for a TV set and may never do so, we believe we have good enough reason to expect the introduction of an UltraHD TV set in FY 2016. We think television represents a large opportunity for Apple, one that reaches far beyond "the hobby" that Apple TV currently represents... Therefore, included in our forecasts, we expect Apple to sell 12 million 55" and 65" TV sets in FY 2016 and 25 million in FY 2017 at an average selling price of $1,500 at gross margins consistent with the overall company.

There's a lot to dive in here, so let's look at Mr. Icahn's assumptions.

A lot can happen, but the UltraHD market currently isn't that big
Before we begin, it's prudent to define UltraHD market. The Consumer Electronics Association announced the term UltraHD would be defined as "any display with a 16 x 9 ratio with at least 1 digital input cable carrying a minimum resolution of 3,840 x 2,160 square pixels," and comes in 4K Ultra HD and 8K Ultra HD. And although sales appear to be growing, IHS estimates UHD TV sales will only total 14.5 million units this year.

Under Mr. Icahn's optimistic assumptions, in less than a year -- Apple started fiscal 2015 on Oct. 1 -- the company is expected to sell the equivalent of 83% of this year's total sales of UHD sets. This is asking a lot, especially from a company like Apple that focuses more on profit than market share. Not only that, Apple finds competition from its archnemeses Samsung, LG Electronics, and Vizio.

Apple can keep its companywide margins in tact at a price point of $1,500?
Next, Icahn discusses margins by noting that Apple can keep its average selling price of 55-inch and 65-inch UHD units at $1,500, and keep margins consistent with the company. During the last 10 quarters, Apple has maintained gross margins of 40.25% led by the high-margin iPhone. In order to keep this gross margin intact, Apple would need to produce the unit for an all-in cost of roughly $900.

Let's look at that price point. Right now, low-margin TV company Vizio's UHD sets are $1,400 for the 55-inch model, and $2,200 for the 65-inch model. Those prices include retail markup. For Mr. Icahn to think Apple can sell UHD TVs for $1,500 and keep a 40% gross margin seems like fiction when compared to this company.

Generally, the television business is considered somewhat commoditized with customers sensitive to price, although Apple should enjoy some level of premium pricing due to its brand cachet. However, it will be tough for Apple to enjoy its current margins from a $1,500 UHD unit.

Final thoughts
Will Apple bring a TV set to market? Who knows. Steve Jobs once famously told biographer Walter Isaascson he had "cracked it," in regards to reinventing the television set.

However, during the three years since Jobs' death, we still haven't seen the unit. And there's probably a reason for that -- it isn't the type of high-margin business that Apple's accustomed to. Investors should just file this away as another one of Mr. Icahn's optimistic assumptions.