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Income Taxes (Deferred Assets and Liabilities) (Details) (USD $)
In Thousands, unless otherwise specified
Dec. 31, 2014
Dec. 31, 2013
Deferred tax assets:    
Allowance for uncollectible accounts $ 1,096us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAllowanceForDoubtfulAccounts $ 897us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAllowanceForDoubtfulAccounts
Accrued assets and other 27,537us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsOther 5,292us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsOther
Valuation allowances (3,736)us-gaap_DeferredTaxAssetsValuationAllowanceCurrent (2,021)us-gaap_DeferredTaxAssetsValuationAllowanceCurrent
Total current deferred tax assets 24,897us-gaap_DeferredTaxAssetsNetCurrent 4,168us-gaap_DeferredTaxAssetsNetCurrent
Share-based compensation 7,719us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsShareBasedCompensationCost 7,635us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsShareBasedCompensationCost
Interest on unrecognized tax benefits 245us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsContingencies 230us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsContingencies
Accrued liabilities and other 3,931us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAccruedLiabilities 3,629us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAccruedLiabilities
Medical malpractice 16,240us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsSelfInsurance 0us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsSelfInsurance
Operating and capital loss carryforwards 22,709amsg_DeferredTaxAssetsOperatingAndCapitalLossCarryforwards 9,185amsg_DeferredTaxAssetsOperatingAndCapitalLossCarryforwards
Valuation allowances (13,721)us-gaap_DeferredTaxAssetsValuationAllowanceNoncurrent (7,665)us-gaap_DeferredTaxAssetsValuationAllowanceNoncurrent
Total non-current deferred tax assets 37,123us-gaap_DeferredTaxAssetsNetNoncurrent 13,014us-gaap_DeferredTaxAssetsNetNoncurrent
Total deferred tax assets 62,020us-gaap_DeferredTaxAssetsNet 17,182us-gaap_DeferredTaxAssetsNet
Deferred tax liabilities:    
Prepaid expenses 2,435us-gaap_DeferredTaxLiabilitiesOther 1,071us-gaap_DeferredTaxLiabilitiesOther
Property and equipment, principally due to differences in depreciation 15,235us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment 4,137us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment
Goodwill, intangible assets and other, principally due to differences in amortization 655,368us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssets 184,897us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssets
Total deferred tax liabilities 673,038us-gaap_DeferredIncomeTaxLiabilities 190,105us-gaap_DeferredIncomeTaxLiabilities
Net deferred tax liabilities $ 611,018us-gaap_DeferredTaxLiabilities $ 172,923us-gaap_DeferredTaxLiabilities