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TAXES BASED ON INCOME (Details 2) (USD $)
In Millions, unless otherwise specified
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Taxes Based on Income      
Computed tax at 35% of income before taxes $ 127.5us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate $ 127.1us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate $ 83.1us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate
U.S statutory rate 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate    
Increase (decrease) in taxes resulting from:      
State taxes, net of federal tax benefit 1.4us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes 2.4us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes 1.1us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes
Foreign earnings taxed at different rates (15.9)us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential (14.7)us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential 11.8us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential
Valuation allowance 16.0us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance (4.3)us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance (23.6)us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance
Corporate owned life insurance (4.2)us-gaap_IncomeTaxReconciliationNondeductibleExpenseLifeInsurance (6.9)us-gaap_IncomeTaxReconciliationNondeductibleExpenseLifeInsurance (5.5)us-gaap_IncomeTaxReconciliationNondeductibleExpenseLifeInsurance
U.S. federal research and development tax credits (1.6)us-gaap_IncomeTaxReconciliationTaxCreditsOther (7.0)us-gaap_IncomeTaxReconciliationTaxCreditsOther  
Tax contingencies and audit settlements (2.7)avy_IncomeTaxReconciliationTaxContingenciesAndAuditSettlements 23.1avy_IncomeTaxReconciliationTaxContingenciesAndAuditSettlements 9.4avy_IncomeTaxReconciliationTaxContingenciesAndAuditSettlements
Expiration of carryforward items 1.4avy_IncomeTaxReconciliationExpirationOfCarryforwardItems 2.5avy_IncomeTaxReconciliationExpirationOfCarryforwardItems 4.8avy_IncomeTaxReconciliationExpirationOfCarryforwardItems
Other items, net (8.6)us-gaap_IncomeTaxReconciliationOtherAdjustments (3.4)us-gaap_IncomeTaxReconciliationOtherAdjustments (1.1)us-gaap_IncomeTaxReconciliationOtherAdjustments
Provision for income taxes 113.3us-gaap_IncomeTaxExpenseBenefit 118.8us-gaap_IncomeTaxExpenseBenefit 80.0us-gaap_IncomeTaxExpenseBenefit
Expense related to accrual of U.S. taxes on certain foreign earnings   $ 12.1us-gaap_IncomeTaxReconciliationRepatriationOfForeignEarnings $ 11.2us-gaap_IncomeTaxReconciliationRepatriationOfForeignEarnings