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Carl Icahn thinks Apple (NASDAQ:AAPL) stock could soar to $1,250 in the next three years, giving investors who own Apple at $525 a 33.5% annualized return. He laid out the scenario in his open letter to Apple CEO Tim Cook, made public this morning. As he has previously suggested, it would take a $150 billion buyback. This prompts two questions:

  1. Is the proposed buyback realistic?
  2. If the buyback were executed, could shares really appreciate to $1,250 in three years?

Let's dig in.

The buyback
Icahn suggests the buyback should be executed at $525 per share, approximately where Apple shares traded at market open this morning. Is it realistic to expect Apple to be able to repurchase $150 billion in shares at $525? Probably not.

Here's why. The buyback, Icahn suggests, should be in the form of a tender offer. In a tender offer, Apple would offer to purchase investors' shares at a given price. Typically, however, tender offers must tender a price at a premium to the market price in order to incentivize shareholders to sell. That being said, how would Apple get $150 billion worth of shares at $525 per share if the stock is currently trading slightly above that price? For instance, If a current shareholder is already holding shares at $525, why would he or she decide to sell at $525 just because Apple makes a tender offer that would offer zero upside? Even more, how would Apple find enough investors to get a whopping $150 billion worth of shares? With Apple trading at or above $525, it wouldn't.

In a conversation I had this morning with Fool contributor Adam Levine-Weinberg, who follows Apple's story closely, he suggested $525 may be far too low:

Short of reporting a terrible December quarter forecast, there's no way Apple could get shareholders to tender $150 billion worth of stock for $525. It would probably have to offer $600-$650 to get that much interest, at which point the economics are not quite so favorable.

In other words, Icahn should have struck hard back in June when Apple was still at $400.

Would a tender offer at $600 to $650 per share be good use of Apple's cash? Maybe, but that's certainly far more difficult to argue than a tender offer at $525.

Sure, Icahn did say that he believes the tender offer would still be compelling at $550 or $575 per share in an interview with MoneyBeat on CNBC this afternoon. But even this sounds wishful. A tender offer at $575 would give investors about an 8% return at today's price, hardly meaningful for current investors who obviously feel comfortable holding at $530. Even more, Apple reports fourth-quarter earnings and first quarter guidance on Oct. 28; if Apple beats analyst estimates, shares could easily jump to $575, once again increasing the amount Apple would have to tender in order to incentivize shareholders to sell.

Apple to $1,250?
The shares are irrationally undervalued, Icahn argues. In the letter to Cook, he calls Apple his "most compelling investment" and says its undervalued state is a "short-term anomaly." He illustrates his reasoning by comparing shares to the S&P 500.

The S&P 500 trades at roughly 14x forward earnings. After backing off net cash, Apple trades at just 9x (not factoring into account that the company has a significantly lower cash tax rate than the rate Wall Street analysts use). This discount (cash adjusted) becomes even more compelling given our confidence that Apple will grow earnings per share at a rate well in excess of the S&P 500 for the foreseeable future. 

With a position valued at about $2.5 billion, Icahn has put his money where his mouth is. In fact, he has recently increased his position from approximately 3.9 million shares to approximately 4.7 million shares (22% increase). Is Icahn right about Apple shares?

He's not generally a tech guy, however, so his confidence in Apple stock should be taken with a grain of salt. And the underlying premise for shares reaching $1,250 in three years is based on the unrealistic assumption that Apple could actually execute the proposed tender offer at $525 for $150 billion. The math goes like this:

... if the company decided to borrow the full $150 billion at a 3% interest rate to commence a tender at $525 per share, the result would be an immediate 33% boost to earnings per share, translating into a 33% increase in the value of the shares, which significantly assumes no multiple expansion. Longer term (in three years) if you execute this buyback as proposed, we expect the share price to appreciate to $1,250, assuming the market rewards EBIT growth of 7.5% per year with a more normal market multiple of 11x EBIT.

Sounds great. But unfortunately the tender offer is downright unrealistic unless a significant sell-off occurs. Even Warren Buffett recently suggested Apple's board should ignore Icahn's request.

What can we take away from Icahn's proposal?
It's difficult to say whether or not anything could come of this letter. At this point, the biggest takeaway for investors from Icahn's proposal is an interesting angle for Apple as an undervalued stock. The theoretical possibility of the buyback and the fact that Apple's balance sheet is in such a position that the company could feasibly execute such a large tender offer provides a convincing case for Apple stock around $525.

Fool contributor Daniel Sparks owns shares of Apple. The Motley Fool recommends Apple. The Motley Fool owns shares of Apple. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.