Should Apple (AAPL) use some of its growing cash pile to buy back a large number of shares?

Bernstein Research analyst Toni Sacconaghi thinks so. He wrote Wednesday morning that the combination of a depressed P/E multiple, low interest rates and a $24.5 billion cash pile - nearly 30% of its market cap - “make a strong case for Apple to initiate a substantial share repurchase program.” Sacconaghi says the company “could drive meaningful EPS accretion via buybacks” in fiscal 2009.

Sacconaghi notes that the company has not bought back shares in over 5 years; it has repurchased just $217 million of its stock over the last 10 years. But with the company generating more than $8 billion a share in cash, he says the conditions are now “ideal” to start a repurchase program.

Sacconaghi calculates that a $10 billion repurchase program in 2009 would boost EPS by about 4% - and the accretion could be higher if the buybacks were front-loaded. If the company bought back $20 billion of shares in the first quarter, he figures, EPS for the year would be 15% higher, or an extra 75 cents a share.

A share repurchase, Sacconaghi says, would be a more favorable use of cash than either a major acquisition or a big dividend. He notes the company could simply let it pile up, but then the questions of what to do with it would “likely only get louder.” A regular dividend would not put much of a dent in the pile; a 5% yield would only consume half of its cash flow. And he says a big special dividend would not likely be well received, since it would be dilutive to earnings.

As for potential acquisitions, Sacconaghi notes that the company has generally not made large acquisitions - and that there aren’t any large companies that holders would view as complimentary to Apple. He also notes that the company has not paid a dividend since 1995, and has spent only $1 billion on acquisitions in its entire history.

Apple closed Wednesdayup $4.64, or 4.6%, to $104.55.