The first tranche will vest on June 1 2014 and is worth $9.8 million at Monday's closing price of $600.96. She will receive 85 per cent of the stock award as long as she remains at Apple for four years, regardless of performance.
The remaining 17,303 shares, worth $10.3 million on Monday, are tied to performance measured by Apple's relative total shareholder return.
The Apple stores' performance has waned in the absence of a permanent chief, with average revenue per store dipping from $29.4 million in the first half of 2013 to $29.1 million in the first half of its current fiscal year.
More than half of Apple's 423 stores are in the US, in spite of just 31 percent of the company's revenues in the past quarter coming from the Americas. By contrast, Burberry said last year that more than three-quarters of its stores were in emerging markets such as China.
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Apple has already said it expects to open 30 new retail stores this year, of which two-thirds will be outside the US. Recent openings in Brazil and Turkey have brought Apple's retail network to 15 countries, attracting footfall in the tens of millions every quarter.
About 11 percent of Apple's total revenue comes from its retail stores, which employ more than half of Apple's more than 80,000 full-time staff.
Ms Ahrendts is used to such challenges. At Burberry, Ms Ahrendts tripled the luxury company's share price and dragged the ageing brand into the digital world.
The Indiana-born executive was appointed Burberry's chief in July 2006 after long stints at more mass-market brands such Liz Claiborne and Donna Karan. In 2012, a survey by corporate governance group Manifest and pay consultancy MM&K found that she was the best-paid chief executive in the FTSE 350, taking home a total of £16.9 million in salary and stock awards.