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Now that Google's selling Motorola, how much did it overpay in 2011?

Google's (GOOG) Motorola greeted the new year with good news for smartphone customers, cutting the no-contract price of its well-reviewed Moto X to $399 from $549.

Just how much did Google (GOOG) overpay for Motorola Mobility when it agreed to buy the phone maker for $12.5 billion in 2011?

Shareholders will have to figure that out after Google announced on Wednesday that it is unloading the money-losing subsidiary on Chinese electronics maker Lenovo Group (0992.HK) for $2.9 billion.

Sure, Motorola had $3 billion of cash on its balance sheet when it was acquired and Google later sold a set-top box division for $2.4 billion. But that still leaves Google CEO Larry Page left to explain why he’s only getting $3 billion for the remaining net investment of $7 billion. "Patents," he'd likely reply.

Analysts speculated all along that Google made the hasty deal only to get control of Motorola’s vast trove of about 17,000 patents. At the time, Apple (AAPL) and Microsoft (MSFT) appeared to be waging an intellectual property war to beat back the Android challenge. Many of those battles continue and intellectual property attorneys are split over whether the Motorola patents have helped Google much, if at all.

Still, Google said it would retain "the vast majority" of patents from Motorola in the sale to Lenovo.

That would leave the company with a still significant patent stash and a net outlay, after all the wheeling and dealing, of about $4 billion. Of course, Google also reported operating losses for Motorola as its owner, including $645 million in the first nine months of 2013 and $1.1 billion in 2012. A portion of the losses consisted of non-cash charges for stock-based compensation and other items.

Series of agreements

Word of the sale also helps make sense of a series of agreements between Google and Samsung Electronics (005930.KS)  in recent days. The Motorola purchase hurt Google’s relationship with Samsung, the leading seller of phones running Android. At one point, the tensions even prompted speculation that Samsung would try to replace Android on many phones with its in-house Tizen OS.

But just over the past week, the two companies had a major thaw in relations, signing a broad patent cross-licensing deal. Samsung also agreed to minimize its efforts to gunk up Android with software add-ons, according to a report from Recode.

Motorola piled up losses throughout Google’s ownership tenure, despite massive cost cutting. New phones unveiled last year, the Moto X and Moto G, captured solid reviews but few buyers, which may have prompted Page to sour on the unit.

Lenovo has been working hard to become a major player in smartphones. The acquisition strategy mirrors its successful purchase of IBM’s (IBM) PC business back in 2005.

Lenovo ranked fifth in worldwide smartphone sales last year, despite having no major presence in the United States and Western Europe, according to IDC data. It captured 4.5% of the market based on phones shipped, up from 3.3% in 2012. Samsung was first, with a 31% share, and Apple was second with 15%.