Without such tactics, Apple’s federal tax bill in the United States most likely would have been $2.4 billion higher last year, according to a recent study by a former Treasury Department economist, Martin A. Sullivan. As it stands, the company paid cash taxes of $3.3 billion around the world on its reported profits of $34.2 billion last year, a tax rate of 9.8 percent. (Apple does not disclose what portion of those payments was in the United States, or what portion is assigned to previous or future years.)

By comparison, Wal-Mart last year paid worldwide cash taxes of $5.9 billion on its booked profits of $24.4 billion, a tax rate of 24 percent, which is about average for non-tech companies.

Apple’s domestic tax bill has piqued particular curiosity among corporate tax experts because although the company is based in the United States, its profits — on paper, at least — are largely foreign. While Apple contracts out much of the manufacturing and assembly of its products to other companies overseas, the majority of Apple’s executives, product designers, marketers, employees, research and development, and retail stores are in the United States. Tax experts say it is therefore reasonable to expect that most of Apple’s profits would be American as well. The nation’s tax code is based on the concept that a company “earns” income where value is created, rather than where products are sold.

However, Apple’s accountants have found legal ways to allocate about 70 percent of its profits overseas, where tax rates are often much lower, according to corporate filings.

Neither the government nor corporations make tax returns public, and a company’s taxable income often differs from the profits disclosed in annual reports. Companies report their cash outlays for income taxes in their annual Form 10-K, but it is impossible from those numbers to determine precisely how much, in total, corporations pay to governments. In Apple’s last annual disclosure, the company listed its worldwide taxes — which includes cash taxes paid as well as deferred taxes and other charges — at $8.3 billion, an effective tax rate of almost a quarter of profits.

However, tax analysts and scholars said that figure most likely overstated how much the company would hand to governments because it included sums that might never be paid. “The information on 10-Ks is fiction for most companies,” said Kimberly Clausing, an economist at Reed College who specializes in multinational taxation. “But for tech companies it goes from fiction to farcical.”

Apple, in a statement, said it “has conducted all of its business with the highest of ethical standards, complying with applicable laws and accounting rules.” It added, “We are incredibly proud of all of Apple’s contributions.”