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Income Taxes (Narrative) (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended 12 Months Ended
Apr. 17, 2018
Dec. 31, 2017
Sep. 30, 2018
Jun. 30, 2017
Sep. 30, 2018
Sep. 30, 2017
Sep. 30, 2016
Sep. 30, 2015
Income Taxes [Line Items]                
U.S. federal statutory tax rate   35.00% 21.00%   24.50% 35.00% 35.00%  
Discrete net tax expense related to Tax Act         $ 180.6      
Reduction in equity affiliate income for impacts of the Tax Act         28.5      
Provisional tax expense for deemed repatriation tax and additional foreign taxes on repatriation of earnings         392.4      
Provisional tax expense for deemed repatriation tax         322.1      
Provisional tax expense for additional foreign taxes on repatriation of earnings         70.3      
Provisional tax benefit for re-measurement of net U.S. deferred tax liabilities at lower corporate tax rate         211.8      
Non-recurring benefit related to U.S. taxation of deemed foreign dividends         56.2      
Deemed repatriation tax obligation after application of foreign tax credits     $ 203.2   203.2      
Deemed repatriation tax obligation in noncurrent liabilities     184.4   184.4 $ 0.0    
Cash paid for taxes (net of cash refunds)         372.0 1,348.8 $ 440.8  
Tax benefit from restructuring of foreign subsidiaries         (35.7)      
Excess tax benefits from share-based compensation         $ 21.5 $ 17.6    
Effective tax rate         26.00% 18.40% 27.80%  
Income tax benefit on tax losses from foreign holding company           $ (111.4)    
Goodwill impairment charge           145.3    
Goodwill impairment charge deductible for tax purposes           0.0    
Business separation additional income tax expense             $ 51.8  
Foreign earnings repatriated             443.8  
Deferred tax assets, valuation allowance     105.0   $ 105.0 107.7    
Previously undistributed earnings of foreign subsidiaries and corporate joint ventures         5,800.0      
Cumulative undistributed earnings     3,200.0   3,200.0      
US Income and foreign withholding taxes estimate     420.4   420.4      
Unrecognized tax benefits     233.6   233.6 146.4 90.2 $ 83.8
Unrecognized tax benefits that would impact effective tax rate     88.6   88.6 73.8    
Interest and penalties related to unrecognized tax benefits         (2.4) 3.7 1.8  
Accrued interest and penalties     8.4   8.4 12.1    
Additions for tax positions of prior years         119.2 16.1 2.9  
Additions for tax positions of the current year         26.4 47.5 12.5  
Settlement of uncertainties related to unrecognized tax benefits $ 43.1       14.2 2.0 $ 5.6  
Discontinued Operations, Held-for-sale or Disposed of by Sale | Performance Materials Division (PMD)                
Income Taxes [Line Items]                
Gain on sale           2,870.0    
Industrial Gases - Americas                
Income Taxes [Line Items]                
Goodwill impairment charge       $ 145.3   $ 145.3    
Foreign Loss Carryforwards                
Income Taxes [Line Items]                
Deferred tax assets, valuation allowance     56.0   56.0      
Foreign Capital Losses                
Income Taxes [Line Items]                
Deferred tax assets, valuation allowance     47.9   47.9      
Discontinued Operations                
Income Taxes [Line Items]                
Tax benefit related to settlement and release of reserves         25.6      
Continuing Operations                
Income Taxes [Line Items]                
Tax benefit related to settlement and release of reserves         9.1      
State                
Income Taxes [Line Items]                
Operating loss carryforwards     324.9   324.9      
Tax credit carryforwards     1.9   1.9      
Foreign                
Income Taxes [Line Items]                
Operating loss carryforwards     340.6   340.6      
Operating loss carryforwards not subject to expiration     121.8   121.8      
Tax credit carryforwards     21.6   21.6      
Indefinite tax credit carryforwards     $ 16.4   $ 16.4