Shares of Time Warner (TWX) have been among the largest gainers in the early days of 2016 as speculation mounts that it could be forced to sell all or part of the company.

The NY Post's Claire Atkinson, who was the first to report about activist investors led by Corvex Capital circling the company, is reporting that some of Time Warner's largest institutional investors want to see a sale or partial sale of the company. In her latest story, Atkinson mentioned potential interest from Amazon (AMZN - Get Report) , which has been gobbling up content at a rapid pace to better compete against Netflix (NFLX - Get Report) and other streaming services.

Though investors want to see the share prices of media companies, particularly Time Warner, rise after getting destroyed in 2015, does it make sense to sell the company, particularly to Amazon?

Probably not, but a stake or an enhanced strategic partnership in Time Warner does make sense.

Amazon is spending an unknown-but-reported enormous amount of money on content in 2016 (it spent $1.3 billion in 2014 according to the company's 2014 fourth quarter results), both new and original to bolster its Amazon Prime service, which is reported to have roughly 44 million subscribers.

The company also spent a reported $250 million in 2015 on former Top Gear hosts Jeremy Clarkson, James May, and Richard Hammond to launch a new car show that will run three years and 36 episodes.

Seattle-based Amazon already has a deal with Time Warner's HBO to buy older content from the service, including shows such as The Sopranos, The Wire, Boardwalk Empire and others, but not new shows such as Game of Thrones, Veep, Silicon Valley or others. In a way, Time Warner's HBO is monetizing its library of older shows, a strategy that hurt the major networks -- CBS, FOX, NBC, ABC when they did deals with Netflix. HBO, however, has been more strategic about what which programs it licenses to Amazon Instant Video.

Amazon doesn't need to purchase Time Warner, which would likely cost AT LEAST $80 a share (based on a sum-of-the-parts analysis which I'll explain later) to keep getting access to HBO's shows, as well as other shows from Time Warner's networks, including TNT, Cartoon Network and TBS.

"It's an intriguing possibility," said Chief Analyst of Jackdaw Research Jan Dawson via email, who likened it to AOL buying Time Warner in the day. "The logic was flawed back then and I'd argue the logic would still be flawed now. It's a very expensive acquisition just to beef up Prime Video. I'm not convinced either that this acquisition makes sense or that Amazon would pursue it."

A strategic stake, perhaps becoming one of, if not the largest, shareholder, would, however, make more sense for a number of reasons:

1. It would keep HBO, perhaps the most valuable subscription business ever built, away from competition unless the competition, such as Apple (AAPL - Get Report) , Alphabet's Google (GOOGL - Get Report) (GOOG - Get Report) or other cash-rich tech companies compensated Amazon.

2. Amazon doesn't need the corporate overhead of businesses such as TNT and TBS, particularly since both heavily invest in original content themselves.

3. It would get a stake in Warner Bros. Television, the largest and most prolific producer of content in Hollywood. (Warners produces such hit series as The Big Bang Theory, Person of Interest, Two Broke Girls, Blacklist, Arrow and Gotham just to name a few. A more complete list can be found here.)

4. It could also get the next viewing rights to Seinfeld and Friends, which were recently sold to Hulu and Netflix, respectively, as WBTV owns the production rights to both of those hit 90's series as well.

5. It could get access to Warner's upcoming slate of films, assuming HBO decided they were less valuable sitting on HBO or HBO Now for eternity. Warner's upcoming slate includes such expected hits as Batman v. Superman: Dawn of Justice, Suicide Squad, the Fantastic Beasts and Where to Find Them franchise, Wonder Woman, The Lego Movie franchise, as well as upcoming movies from A-list actors such as The Rock (who also is the star of a hit show on HBO, entitled Ballers).

6. It would get a stake in Warner Bros. Interactive Entertainment, perhaps the most unsung portion of Warner's business.

Putting my analyst hat on, it's pretty clear that on a sum-of-the parts basis, Time Warner is considerably undervalued, perhaps by 25% or more.

For the purposes of this article, I'll keep the math rough and simple, but know there's more detail behind these valuations.

-HBO: $43 billion
-CNN: $7 billion
-Warner Bros. film business: $5 billion
-Warner Bros. Television Production: $4 billion
-Warner Bros. Interactive Entertainment: $4 billion
-Consumer Products business (merchandise based off Time Warner properties, including toys, clothes and the like): $2 billion
-TNT, TBS and Cartoon Network: $0

Market value of the company: $65 billion or $80 a share (excluding the value of TNT, TBS and Cartoon Network)

HBO is valued at roughly 90% of Netflix since HBO is in profit maximization mode, while Netflix is in subscriber acquisition/revenue growth mode, so a 10% discount seemed fairly reasonable, with HBO having nearly 120 million subscribers around the world, plus whatever it is able to garner from HBO Now, its over-the-top streaming service, which recently broke through the top 10 of top grossing apps in the App Store.

In the case of CNN, there were reports in 2015 that CBS and Time Warner would merge and as a result of that merger, Time Warner would have to sell off CNN. Such a sale was speculated to generate $6 billion. In 2014, Fox had reportedly valued CNN at $8 billion, according to a Bloomberg report, so a $7 billion valuation is smack dab in the middle.

I assigned a 25% premium for Warners' film business over its most closely associated competition, Lionsgate (LGF) , due to the quality of film slate, library and name recognition of talent.

Warner's Television Production business is still the backbone of Hollywood, despite more and more shows being owned and operated by networks. The upcoming Hulu mini-series, 11.22.63, about the assassination of JFK, is produced by Warner's as are the aforementioned shows. Even Netflix is somewhat reliant on WBTV, with Warner Horizon Television (a subsidiary of WBTV) being the distributor for the upcoming show Fuller House, a sequel series to the hit 90's comedy Full House, which was not coincidentally, produced by WBTV. That doesn't even account for countless other shows currently on the air and still in production.

Warner's CEO Kevin Tsujihara has continued to tout the Time Warner unit's leadership advantage in moving the production business into new areas, including international and unscripted series as well as producing shows for sister companies HBO, TNT and TBS.

Perhaps the crown jewel of Warner Bros. that gets little to no attention from the market is its games business, Warner Bros. Interactive Entertainment.

It produces a long list of hit video: anything Lego related, games from its DC arm, including one of the best of 2015, Batman: Arkham Knight, to name but a few. In 2015, the unit generated $727 million in revenue and with publicly traded video game companies such as Activision (ATVI - Get Report) or EA (EA - Get Report) trading for about five times revenue. But growing from a much larger base, a rough valuation of 5.5 times revenue doesn't seem overly pricey, especially for a unit which grew revenue 54% year over year.

A consumer products business at half the valuation of a similar business, such as Hasbro (HAS - Get Report) or Mattel (MAT - Get Report) seem reasonable, especially if, as Time Warner CEO Jeff Bewkes and Tsujihara have stated in the past, it could add an additional $150 million to Time Warner's bottom line if it can become HALF as good as Disney's (DIS - Get Report) .

I gave little to no value to TNT, TBS and Cartoon Network as it's unclear what the business model for these networks will be in 2-3 years. Sure these networks helped to generate $2.398 billion for Time Warner in revenue in the third quarter of 2015, but that was down slightly from the third quarter of 2014 when they accounted for $2.446 billion in revenue.

Yes, those networks will continue to generate subscriber fees and ad revenue but with TNT and TBS recently being "reinvented," according to network boss Kevin Reilly, how the pay-TV business shakes out is anyone's guess.

There are other businesses Time Warner owns or partly owns, including Bleacher Report, its joint venture deals in China to provide HBO content to Tencent Holdings. But I assigned no value to those even though they're clearly worth something.

Ultimately, at a VERY conservative $80 a share, Amazon would have to spend a great deal of cash (or cash and stock) to acquire Time Warner, when it may not want all of what Time Warner has to offer. An enhanced strategic partnership, or a sizable investment by Amazon, seems to make much more sense than an outright purchase.