A central challenge is slowing sales of the iPhone, Apple's best-selling and most-profitable product that accounts for 56 percent of revenue. Samsung Electronics Co., HTC Corp. and other rivals are introducing cheaper and feature-laden smartphones and tablets based on Google Inc.'s Android software.

Steve Dowling, a spokesman at Apple, declined to comment.

Apple rose less than 1 percent to the equivalent of $478.91 in German trading at 11:09 a.m. Frankfurt time after closing at $474.98 on Feb. 8 in New York.

One product with the potential to be profitable enough to slow the margin slide could be an Apple-branded watch that also makes phone calls, accesses the Web and provides location- tracking services, said Poonam Goyal, an analyst at Bloomberg Industries. A watch with these features might retail for much less than $200, keeping it within the price range that is the fastest-growing portion of the time-piece market and also the most profitable, she said.

Apple could sell millions of the watches, and generate a margin of about 50 percent, she said. That's about twice the margin Apple might earn by making a TV or selling an inexpensive phone for less-affluent shoppers, said Michael Morgan, an analyst at ABI Research.

The company is developing a wristwatch-like device using curved glass, the New York Times reported yesterday, citing unidentified people familiar with the situation. Natalie Kerris, an Apple spokeswoman, declined to comment on the plans.

Projected Decline

Apple is also seeking new customers in China, where it will be harder to charge premium prices. New products such as the iPad mini are also being priced at relatively lower points, eating into margins.

Gross margin, or how much Apple earns after paying for raw materials, labor and production to build iPhones, iPads, Macs and other products, is projected to decline in fiscal 2013, according to the company's Jan. 24 filing with the U.S. Securities and Exchange Commission.

It predicted gross margins for this quarter would be 37.5 percent to 38.5 percent, down from 47 percent a year earlier. The two new products that Apple will probably introduce this year, a television and a lower-priced iPhone, will be much less profitable and drag down margins, according to Morgan.

Cash Plan

After Apple on Jan. 23 reported its slowest profit growth since 2003, more than 20 analysts lowered their price targets. While Cook made it clear on the earnings call that he's not considering any major strategic shifts, he promised that Apple was developing several new products.

“We're working on some incredible stuff, and the pipeline is chock full,” Cook said. “We feel great about what we have in store.”

Apple said on Feb. 7 that the board and management are considering Greenlight's proposal and are actively discussing disbursing more money.

Apple's cash balance includes $16.2 billion of cash and $23.7 billion in short-term investments. The rest is invested in long-term marketable securities.

“We remain committed to having an ongoing dialogue with our shareholders to get perspectives around return of capital and driving shareholder value,” Apple said in a statement.

That suggests Apple is softening its stance on the preferred shares, after previously saying in its annual proxy that there aren't any plans to issue them.

Apple may also be considering a payments system that would let it keep an extra cut of every device, song and software application sold that might otherwise go to credit-card firms, said Anand Srinivasan, a senior analyst at Bloomberg Industries.

Another approach that Apple may take is to introduce more fully loaded configurations of existing products. An iPad with 128 gigabytes of storage went on sale this month. Since the cost of doubling memory is less than the $100 extra charged for the device, the profit margin is higher, said Srinivasan.

Brisk sales of older models are also causing some investor concern. Last quarter, the new iPhone 5 made up only half the iPhones sold by Verizon Communications. The rest were the 16- month-old iPhone 4S and its predecessor, the iPhone 4. While older models contain cheaper parts and lift margins, they also hamper Apple's ability to realize maximum economies of scale on newer ones.

After commanding a premium for most of the past decade, Apple is trading at a discount of 28 percent to the Standard & Poor's 500 Index on a price-earnings basis, according to data compiled by Bloomberg.

Profit Trade-Off

“They need to do something eye-opening, but nothing is going to have as high a margin as the iPhone,” said Erick Maronak, chief investment officer at Victory Management Inc. Apple's gross margin could easily shrink to 35 percent, he said.

Rather than milk its position for every last dollar, Apple should accept lower profits to keep growing revenue and market share, said Yoffie. Since its 2007 introduction, the average selling price of an iPhone has remained above $600, twice that of rival devices. A slimmer margin on a $300 iPhone sold to hundreds of millions of price-conscious shoppers would bring in more cash than a 50 percent margin on current models, he said.

“If they want to maintain or build market share, they can't sustain prices that are in the neighborhood of 100 percent higher than rival products,” Yoffie said.

Apple may also be speeding up the frequency as well as the variety of its product introductions, to prevent Samsung and others from grabbing share while Apple plans its next blockbuster annual announcement, according to Walter Piecyk, an analyst at BTIG LLC. That may explain Apple's decision to revamp all of its main products — iPhones, iPads, Macs and iPods — in the second half of 2012.

More frequent product introductions and a longer service life for older devices will complicate Apple's formula of selling a handful of products in massive volumes, and churning out profits over time by driving down costs. The shorter the gadget's life, the less time to maximize income, said Piecyk.

Apple is also finding it more difficult to forecast demand and prepare its supply chain as the variety of devices expands. Apple uncharacteristically produced too few iPad minis, iPhone 4s and iMacs during the last quarter, according to Ben Reitzes, an analyst at Barclays Capital Inc.

“Manufacturing issues seem to be occurring in so many products these days,” Reitzes wrote in a research note.

With revenue projected to rise 17 percent to $182.9 billion in the current fiscal year, the trick for Cook will be to refocus investors' attention to dollar profit instead of margins, said Yoffie. At that rate of growth, Apple would reach $400 billion in annual revenue by 2020 — more than $1 billion a day — and be able to churn out far more actual dollars of profit, even if margins decline.

“Apple's goal should not be to maintain their margins, but to increase sales and increase profits,” said Yoffie. “Apple allowed expectations to get way out of line. They let people think it could grow as it has in the past.”

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