It's one thing for an activist investor to be unhappy with how a company is running its business, particularly if that company is facing serious difficulties. But it's entirely different when an activist becomes obsessed with the company's capital-allocation strategy.

That seems to be the case with Carl Icahn -- a man who's become famous for being able to move Apple's (AAPL 0.06%) share price with a tweet or two. Icahn wants Apple to buy back a ton of stock with the cash that it has on hand. Why is he obsessing over this?

Do buybacks really add value?
A share buyback takes from cash that would otherwise sit on the balance sheet, likely in low-yield bonds and marked as "cash and marketable securities." It would earn modest interest, at best, and since much of it is held overseas for tax purposes, it would likely be discounted by investors valuing the business at the rate that the company would need to pay to repatriate it. This may seem unattractive, but the bright side to all of this is that the company has a massive war chest when it needs it.

So, the question, then, is whether a buyback -- particularly of the magnitude Icahn is proposing -- adds value or not. The answer to this hotly debated and highly controversial question is, "It depends."

What does it depend on?
When a company's stock is at a pretty low point, perhaps driven by some temporary setbacks or snags in the business, or simply due to macroeconomic and technical factors, then a buyback makes perfect sense. Picking up shares when they're dirt cheap and when the business is on the cusp of an inflection makes good sense. It legitimately creates value for shareholders, since the company can get real share-count reduction mileage out of each dollar spent.

Unfortunately, many companies often buy back shares at/near highs. The idea here is that the company begins buying back stock when cash flow is ample and, therefore, when the stock price reflects the strength of the business. If things just keep getting better and the share price rockets in perpetuity, then in theory the best time to buy is "now." But things are rarely so simple. Many companies have destroyed a ton of shareholder value by trying to buy back shares to boost EPS today, only to not have the cash handy to buy back stock when the shares really need that support.

Apple's shares are well off their lows
Apple's shares are "cheap" in the sense that they trade for a fairly low price-to-earnings multiple, ex-cash. However, on a discounted-cash-flow basis, the shares seem to be pretty fairly valued if one assumes that Apple can grow in the high single digits over the next decade before leveling off to mid-single-digit growth. Further, given the risk that smartphones and tablets become commoditized by large, vertically integrated players like Samsung, any assumptions of very long-term growth should be discounted commensurate with that risk.

Buybacks should be opportunistic
With that in mind, it makes sense for Apple to use its buyback strategically. When the shares become too cheap for non-company-specific things, then a powerful buyback can be used to buoy the shares and, ultimately, shrink the share count at nearly optimal points. Of course, timing the market is as much an art as it is a science, but the point is that such a buyback needs to be handled in a way that maximizes shareholder value.

Foolish bottom line
Icahn's roughly $3 billion stake in Apple is not enough to really move the needle for a company with a market capitalization pushing $500 billion. So Apple is likely to do what Apple feels is best. Frankly, Apple shouldn't focus on trying to manipulate the stock price or earnings with buybacks, and should instead keep its focus on making the world's best computers. If it keeps doing so, then the stock price will fall naturally into place.