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Employee Equity and Profit Participation Program - Additional Information (Detail) (Trust for Benefit of Employees [Member], USD $)
In Millions, unless otherwise specified
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Trust for Benefit of Employees [Member]
     
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Amount borrowed from company to purchase common shares maximum $ 63mga_AmountBorrowedFromCompanyToPurchaseCommonSharesMaximum
/ us-gaap_StatementScenarioAxis
= us-gaap_TrustForBenefitOfEmployeesMember
$ 39mga_AmountBorrowedFromCompanyToPurchaseCommonSharesMaximum
/ us-gaap_StatementScenarioAxis
= us-gaap_TrustForBenefitOfEmployeesMember
$ 18mga_AmountBorrowedFromCompanyToPurchaseCommonSharesMaximum
/ us-gaap_StatementScenarioAxis
= us-gaap_TrustForBenefitOfEmployeesMember
Amount included in accounts receivable $ 63mga_TrustIndebtednessReceivable
/ us-gaap_StatementScenarioAxis
= us-gaap_TrustForBenefitOfEmployeesMember
$ 39mga_TrustIndebtednessReceivable
/ us-gaap_StatementScenarioAxis
= us-gaap_TrustForBenefitOfEmployeesMember