CUPERTINO, Calif. — Apple’s next big thing will likely be a large dividend increase financed by a tax cut on its overseas profits, but the famously secretive company isn’t giving any clues about how big it might be.

CEO Tim Cook had an opportunity to address the issue Tuesday at Apple’s annual meeting, when a shareholder asked if the iPhone maker might double its current quarterly dividend of 63 cents per share.

Not surprisingly, Cook dodged the question, rising from his seat because he said it suddenly felt “a little hot.” He all but guaranteed that Apple’s board will raise the dividend in April, as it has done each year since the company reinstated the shareholder payments in 2012. But didn’t giving any other specifics.

Apple’s annual dividend increases have ranged from 8 percent to 15 percent since the payment was reinstated at a split-adjusted 38 cents per share nearly six years ago.

Cook dismissed the possibility of a one-time payment known as a special dividend, saying he didn’t think that form of distribution “really helps the company or shareholders.”

Before fielding eight shareholder questions during the 75-minute meeting, Cook also disclosed that Apple’s music streaming service now has 36 million subscribers as it nears the third anniversary of its debut. Spotify, the music streaming pioneer that Apple is trying to upstage, has more than 70 million subscribers.

Apple is hoping to gain more ground on Spotify with an internet-connected speaker called the HomePod. The device is being touted as a high-fidelity speaker that can also serve as a digital disc jockey that learns listeners’ tastes so it can automatically play songs that they will like from Apple’s vast music-streaming library.

Investors have been anticipating a substantial increase in Apple’s dividend since the company announced plans to take advantage of a temporary tax break championed by President Trump to bring an estimated $245 billion in overseas cash back to the U.S. That represents most of the $285 billion in cash that Apple held at the end of last year.

The hopes for a large dividend increase and a coinciding commitment to buy back large amounts of Apple stock has helped buoy the company’s shares. That despite a disappointing revenue forecast for the current quarter ending in March that stoked concerns about waning demand for the company’s marquee product, the iPhone X.

None of the shareholders at the meeting pressed Cook about how the iPhone X is faring or about Apple’s handling of software updates that secretly slowed down older iPhones, triggering customer complaints and government inquiries inside and outside the U.S.

The sweeping tax reforms passed by Congress in late December included a provision lowering the rate on companies’ overseas cash to 15.5 percent, below the 21 percent paid on profits made in the U.S. Before those changes, corporate profits held outside the U.S. were taxed at a 35 percent rate when brought back into the country.

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