Apple Inc. (Nasdaq: AAPL) climbed the most in two months Tuesday after Sanford C. Bernstein & Co. said the company is considering a stock split, which could prompt it to be added to the Dow Jones Industrial Average.

Apple, the world’s largest company by market value, climbed 2.5 percent to $609.61 at 11:18 a.m. in New York, and earlier touched $611.27 for the biggest gain since May 23. The shares of the Cupertino, California-based company have risen 47 percent this year through yesterday.

Shares finished the day up $15.73, or 2.6 percent, at $610.76.

The company’s decision in March to pay its first dividend in 17 years makes it more likely the stock could be added to the Dow index after a split, said Toni Sacconaghi, an analyst at Bernstein who rates the shares outperform, in a report today.

“We see the timing as ripe,” Sacconaghi said. “Apple’s initiation of a dividend brings the company in line with all other Dow components. We note that Apple is currently the only company above $215 billion in market cap that pays a dividend and is not included in the Dow.”

Steve Dowling, an Apple spokesman, declined to comment. Apple said in March that it didn’t see a stock split as in the best interest of shareholders, though the company continues to review the possibility. Sacconaghi couldn’t be reached for comment, and the Bernstein report didn’t indicate the basis for its stock split prediction.

There are five technology companies in the 30-member Dow index: International Business Machines Corp., Hewlett-Packard Co., Intel Corp., Cisco Systems Inc. and Microsoft Corp.

Dow Reshuffle

Dow membership was last reshuffled in June 2009, when Cisco and Travelers Cos. replaced General Motors Corp., which filed for bankruptcy protection, and Citigroup Inc., the recipient of $45 billion in taxpayer aid.

Apple and Google Inc. have been passed over for inclusion because the shares would command the biggest weightings in the index, which ranks stocks by price. With both stocks trading above $600, they would have three times the influence of IBM, which has the largest weight in the index.

“Excluding IBM, tech’s weighting in the Dow is only 5.3 percent,” Sacconaghi said. Compared to the Standard & Poor’s 500 index, which is weighted by market value, technology stocks are underweight by 370 basis points in the Dow, he said. Apple has a 4.55 percent weighting in the S&P.

“This disparity between tech weighting in the Dow and S&P 500 leads us to believe Dow is likely to add more tech stocks, and that Apple would be a primary candidate if the company split its stock.”

Nine companies in the Standard & Poor’s 500 Index have announced stock splits this year and 16 did in 2011, according to S&P. That compares with an average of 35 from 2004 through 2007 and represents a fraction of the 102 in 1997, the data show. Splits are designed to attract investors by making stocks more affordable.

Historic Splits

While the bull market that began in March 2009 has pushed the benchmark gauge for U.S. equities within 10 percent of its record high this year, the lack of splits helped send the average price of shares in the S&P 500 to a record $58.52 apiece on April 30, more than two decades of data compiled by Bloomberg show. That’s 9.1 percent higher than when the index reached its all-time high of 1,565.15 in October 2007 and 31 percent above the index peak in 2000.

The Dow average was devised by Charles H. Dow, co-founder of Wall Street Journal publisher Dow Jones & Co. Originally containing 12 stocks, it expanded to 20 companies in 1916 and to 30 in 1928. Members must have an “excellent” reputation, show sustained growth and “be of interest to a large number of investors,” according to the S&P Dow Jones Indices website.

Kraft Decision

The average’s new owners will face their first decision on how the 116-year-old gauge should be composed when Kraft Foods Inc. splits itself in two later this year. Kraft’s $70 billion market value is ranked 21th in the 30-stock gauge and will shrink with the spinoff of its of its U.S. grocery business.

Past spinoffs have led to deletions. Altria Group Inc. was dropped in February 2008, one month before the divestiture of its overseas tobacco unit and almost one year after its spinoff of Kraft. Westinghouse Electric Corp.’s split into separate manufacturing and media companies led to its removal in 1997.

The Dow, which began in 1896 with General Electric Co., American Tobacco and 10 other companies, was taken over in July by S&P Dow Jones Indices, a joint venture of McGraw-Hill Cos. and CME Group Inc. About $28 billion in products such as exchanged-traded funds are linked to the index, and changes prompt money managers to buy or sell stocks to match the adjustments.

Changes in the composition of the average “are rare, and generally occur only after corporate acquisitions or other dramatic shifts in a component’s core business,” according to the S&P Dow Jones Indices website. “When such an event necessitates that one component be replaced, the entire index is reviewed,” and “multiple component changes are often implemented simultaneously.”