Apple CEO Tim Cook will ignore Carl Icahn's $100 billion share repurchase request. Source: Wikimedia

On Thursday, activist investor Carl Icahn released another open letter to Apple (AAPL -1.22%). The letter was mostly complimentary of CEO Tim Cook, but yet again asked Apple to accelerate its share repurchase program. And although it appears Cook accelerated the timing of the company's existing stock repurchase program after the last letter, he generally ignored Icahn's request for a $150 billion buyback. And Cook could ignore Icahn's advice this time, too.

In the latest letter, Icahn avoided mentioning specific numbers regarding to the size of his desired buyback (although he mentioned $100 billion in a later interview). Instead, he highlighted the value of such a move:

We are simply asking you to help us convince the board to repurchase a lot more, and sooner. We feel compelled to do so because we forecast such impressive earnings growth over the next few years, and therefore we believe Apple is dramatically undervalued in today's market, and the more shares repurchased now, the more each remaining shareholder will benefit from that earnings growth.

In the letter, he mentioned Apple's "persistent liquidity of $133 billion," but failed to note that most of that money isn't domestically held and cannot be used to repurchase shares. Simply put, under current conditions, Apple cannot comply with Icahn's request without paying taxes to bring the cash state side.

Apple's legendary cash pile has a few strings attached
For anybody following Apple, its cash pile has become the stuff of legend. Coming in at nearly $165 billion as of the tech giant's last quarterly report, Apple's huge cash pile is nearly 30% of the market value of the company. And with cash come options to pay dividends, buy back shares, or to acquire other businesses. Strictly for perspective, Apple could buy Nike, Starbucks, and Chipotle, combined, at current prices with cash to spare.

However, Apple is estimated to only hold $27 billion in cash in the U.S., and that's the only type of cash it can use to repurchase shares and pay dividends without paying taxes. That money is needed to fund Apple's near-$3 billion quarterly dividend outlay. 

Apple could repatriate its foreign cash to fund the large buyback that Icahn wants, but the company is reticent to pay the 35% tax rate that would come with such a move. One way to sidestep repatriation taxes and still access cash (and historically low interest rates) would be to turn to the debt markets. Apple has done that by recently issuing $29 billion in debt -- $17 billion in April 2013 and an additional $12 billion in April 2014. Astute readers would have noticed Carl Icahn's $133 billion total did not match Apple's nearly $165 billion cash pile, the $29 billion long-term debt (among other short term borrowings) partly reconciles the two figures.

Should Apple follow Icahn's advice?
Still, Icahn's advice seems rather sound initially; if you feel your shares are undervalued by the market you should take advantage of Wall Street's myopia by buying your shares back at a discount. Once the market wises up and prices your company accordingly, each shareholder profits from not only higher valuations, but also from lower shares outstanding.

The question for investors to understand Icahn's proposition is this: Should Apple repatriate cash and pay taxes and/or continue to tap the debt markets to lower its share count? Icahn included some of the numbers he used to come to his $203 per share value for Apple stock.  First, he assumes Apple will increase earnings per share by 30% in both fiscal 2016 and 2017, and that's on top of a massive 44% earnings growth in the quickly approaching 2015 fiscal year.

Apple's EPS was $5.72 in fiscal 2013, which was actually down from $6.38 in 2012 (figures are split-adjusted). In addition, on a trailing-12 month basis, Apple's reported $6.23 in total EPS over the last four reporting periods. When comparing the last four fiscal quarters with the prior year's corresponding quarter, the 30% growth looks like it will be hard to achieve.

Fiscal QuarterFQ 3FQ 2FQ 1FQ 4
Most Recent EPS $1.29 $1.67 $2.08 $1.19
Prior Year EPS $1.07 $1.45 $1.99 $1.25
Percentage Gain 20.5% 15.1% 4.5% (4.8%)

Source: Apple 10Qs

Final thoughts
Even stranger, Mr. Icahn's letter appears to assume that Mr. Market will "get it" soon and reverse Apple's P/E multiple of 8 times (ex cash) and presumably bid it up to a double its current valuation to 19 times their optimistic 2015 earnings estimate. It is extremely hard to estimate earnings and revenue growth figures, but almost impossible to predict massive sentiment shifts in valuation. To be fair, Mr. Icahn states "[the valuation of 8 times earnings ex cash] will not last for long," stopping short of providing a direct price point target for the stock instead opting for his $203 value estimate.

In the end, Apple's Tim Cook will be gracious but could likely ignore this request. And while the idea is interesting, Apple investors can rest assured that Tim Cook is continuously looking for ways to continue enriching shareholders. Repatriating or tapping the debt markets to reach Icahn's $100 billion may not be in shareholders' best interests. Apple still has nearly $40 million left in its existing share repurchase program. Look for Apple to utilize that  cash and Carl Icahn may back down from his lofty demands.