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Apple has found an investor that hasn’t lost faith in its prospects: itself.

On Tuesday, the company announced that it plans to more than double its program to return cash to shareholders through stock buybacks and a higher dividend, spending a total of $100 billion in cash on the effort through the end of 2015. Its share repurchases alone will increase to $60 billion from the $10 billion it had previously committed, the largest such plan in history, the company said.

The move to rekindle its relationship with investors came as Apple announced its first profit decline in a decade. The company said its net income fell 18 percent, as one of the most successful technology franchises in recent years, the iPhone, showed signs of slowing and other, less profitable products began to make up more of its sales.

The rarity of Apple’s decline in profit, which was expected, underscores how one of the more remarkable winning streaks in business has come to an end, at least for now. Investors have battered the company’s stock for months, sending its shares down from their peak of more than $700 a share last year as warning signs began to emerge about its growth prospects.

In regular trading Tuesday, Apple shares rose nearly 2 percent to close at $406.13, and they were up to about $425 in after-hours trading as investors reacted to the quarterly earnings news.

One of the biggest questions facing Apple is whether the company can innovate its way out of its funk by delivering a breakthrough new product, perhaps in a category like television, that rekindles growth and the passion of investors with it.

Apple provided no detail about its plans Tuesday, other than the vague hints it often shares about exciting new products to come. “Our teams are hard at work on some amazing new hardware, software, and services and we are very excited about the products in our pipeline,” Tim Cook, the company’s chief executive, said in a statement.

For its fiscal second quarter, which ended March 30, the company said its net income dropped to $9.55 billion, or $10.19 a share, from $11.62 billion, or $12.30 a share, in the same period a year earlier.

Revenue, meanwhile, rose 11 percent to $43.6 billion from $39.19 billion a year before.

Wall Street analysts had expected the company to report earnings of $10.07 a share and revenue of $42.59 billion, according to the average of estimates compiled by Thomson Reuters.

Months ago, Apple sought to brace investors by warning that profit could decline about 20 percent in the quarter. At that time, Apple had forecast revenue of $41 billion to $43 billion.

Sales of iPhones, the company’s biggest business, grew only 3 percent to $22.96 billion in the second quarter. Apple has said the expected decline in profit would be the result of a top-to-bottom overhaul of its product lines, including Macs, iPads and iPhones, all of which tend to be trickier and more expensive to manufacture during their initial months on the market. Eventually, manufacturing costs could fall as kinks are worked out and sales volumes increase.

Apple also has warned, though, that new products like the iPad mini carry lower profit margins than older items like its full-size iPad sibling. That has stirred up worries that Apple’s efforts to cater to more budget-conscious consumers with low-price products, especially in smartphones, could steadily erode its considerable profits.

Apple is widely thought to be preparing a low-cost version of the iPhone to compete more aggressively with smartphones based on Google’s Android operating system. A cheaper device could hold special appeal in huge markets like India and China, where average incomes are far lower than in the West.

Pushing into inexpensive phones could hurt Apple’s much-admired profit margins, though. Last year, the company garnered almost 70 percent of the profit in the mobile handset business, according to estimates by Canaccord Genuity.

Apple said it plans to borrow cash as part of its plan to return cash to shareholders. Even though Apple has far more capital than it needs in its coffers, much of it is held overseas and would be subject to taxes if the company were to bring it back to the United States.

“We believe so strongly that repurchasing our shares represents an attractive use of our capital that we have dedicated the vast majority of the increase in our capital return program to share repurchases,” Cook said in a statement.