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Income Taxes (Schedule of Effective Income Tax Rate Reconciliation) (Details) (USD $)
In Thousands, unless otherwise specified
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Income Tax Disclosure [Abstract]      
Tax expense at statutory rates $ 270,961us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate $ 205,819us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate $ 205,698us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate
State income tax, net of federal benefit 15,715us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes 17,502us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes 13,856us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes
Tax credits (20,986)us-gaap_IncomeTaxReconciliationTaxCredits (18,683)us-gaap_IncomeTaxReconciliationTaxCredits (1,510)us-gaap_IncomeTaxReconciliationTaxCredits
Unrecognized tax benefit (including interest) 5,538us-gaap_IncomeTaxReconciliationTaxContingencies (20)us-gaap_IncomeTaxReconciliationTaxContingencies (12,832)us-gaap_IncomeTaxReconciliationTaxContingencies
Permanent differences (12,253)cern_IncomeTaxReconciliationPermanentDifferences (14,760)cern_IncomeTaxReconciliationPermanentDifferences (19,900)cern_IncomeTaxReconciliationPermanentDifferences
Other, net (10,234)us-gaap_IncomeTaxReconciliationOtherAdjustments (158)us-gaap_IncomeTaxReconciliationOtherAdjustments 5,164us-gaap_IncomeTaxReconciliationOtherAdjustments
Total income tax expense $ 248,741us-gaap_IncomeTaxExpenseBenefit $ 189,700us-gaap_IncomeTaxExpenseBenefit $ 190,476us-gaap_IncomeTaxExpenseBenefit