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Guarantor Financial Information (Condensed Consolidating Statements of Cash Flows) (Details) - USD ($)
$ in Millions
3 Months Ended
Mar. 31, 2018
Mar. 31, 2017
Dec. 31, 2017
Dec. 31, 2016
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities $ (45.8) $ (33.3)    
Net cash provided by (used in) discontinued operating activities (20.4) (10.1)    
Net Cash Provided by (Used in) Operating Activities (66.2) (43.4)    
Cash flows from investing activities:        
Capital expenditures (52.8) (35.2)    
Acquisition of businesses, net of cash acquired (201.6) (9.8)    
Proceeds from sale of property, plant and equipment 0.7 0.4    
Proceeds from Sale of Equity Method Investments (4.0)      
Payments for (Proceeds from) Businesses and Interest in Affiliates 0.0 0.0    
Net cash provided by (used in) continuing investing activities (257.7) (44.6)    
Cash flows from financing activities:        
Net proceeds (repayments) in debt (279.5) 0.0    
Debt issuance costs (8.5) (0.2)    
DividendsPaid 111.6 102.7    
Dividends paid to noncontrolling interests (11.0) (6.9)    
Repurchase of ordinary shares (250.0) (250.1)    
Other, net 5.2 18.4    
Net proceeds (repayments) from debt 0.0 0.0    
Net cash provided by (used in) continuing financing activities (96.4) (341.5)    
Effect of exchange rate changes on cash and cash equivalents 46.0 37.3    
Net increase (decrease) in cash and cash equivalents (374.3) (392.2)    
Cash and cash equivalents 1,175.1 1,322.5 $ 1,549.4 $ 1,714.7
IR Ireland [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities 102.6 21.6    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities 102.6 21.6    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisition of businesses, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment 0.0 0.0    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates 0.0 0.0    
Net cash provided by (used in) continuing investing activities 0.0 0.0    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0      
Debt issuance costs 0.0 0.0    
DividendsPaid 111.6 102.7    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares (250.0) (250.1)    
Other, net 6.6 16.6    
Net proceeds (repayments) from debt 252.4 314.7    
Net cash provided by (used in) continuing financing activities (102.6) (21.5)    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents 0.0 0.1    
Cash and cash equivalents 0.0 0.1 0.0 0.0
IR Irish Holdings [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities 0.0 0.0    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities 0.0 0.0    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisition of businesses, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment 0.0 0.0    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates 0.0 0.0    
Net cash provided by (used in) continuing investing activities 0.0 0.0    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0      
Debt issuance costs 0.0 0.0    
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares 0.0 0.0    
Other, net 0.0 0.0    
Net proceeds (repayments) from debt 0.0 0.0    
Net cash provided by (used in) continuing financing activities 0.0 0.0    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents 0.0 0.0    
Cash and cash equivalents 0.0 0.0 0.0 0.0
IR Lux International [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities 0.0 0.0    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities 0.0 0.0    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisition of businesses, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment 0.0 0.0    
Proceeds from Sale of Equity Method Investments (4.0)      
Payments for (Proceeds from) Businesses and Interest in Affiliates (0.5) 1,153.2    
Net cash provided by (used in) continuing investing activities (4.5) 1,153.2    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0      
Debt issuance costs 0.0 0.0    
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares 0.0 0.0    
Other, net 0.0 0.0    
Net proceeds (repayments) from debt 4.0 (1,153.2)    
Net cash provided by (used in) continuing financing activities 4.0 (1,153.2)    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents (0.5) 0.0    
Cash and cash equivalents 0.1 0.0 0.6 0.0
IR Global [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities (32.2) (72.6)    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities (32.2) (72.6)    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisition of businesses, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment 0.0 0.0    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates 0.0 72.8    
Net cash provided by (used in) continuing investing activities 0.0 72.8    
Cash flows from financing activities:        
Net proceeds (repayments) in debt (31.6)      
Debt issuance costs (8.5) (0.2)    
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares 0.0 0.0    
Other, net 0.0 0.0    
Net proceeds (repayments) from debt 9.1 0.0    
Net cash provided by (used in) continuing financing activities 32.2 (0.2)    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents 0.0 0.0    
Cash and cash equivalents 0.0 0.0 0.0 0.0
IR New Jersey [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities 19.6 27.3    
Net cash provided by (used in) discontinued operating activities (20.3) (17.8)    
Net Cash Provided by (Used in) Operating Activities (0.7) 9.5    
Cash flows from investing activities:        
Capital expenditures (8.8) (10.5)    
Acquisition of businesses, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment 0.0 0.0    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates (208.8) 0.0    
Net cash provided by (used in) continuing investing activities (217.6) (10.5)    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0      
Debt issuance costs 0.0 0.0    
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares 0.0 0.0    
Other, net (0.4) 0.0    
Net proceeds (repayments) from debt (105.0) (69.7)    
Net cash provided by (used in) continuing financing activities (105.4) (69.7)    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents (323.7) (70.7)    
Cash and cash equivalents 35.6 563.9 359.3 634.6
IR Lux Finance [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities (0.3) 0.0    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities (0.3) 0.0    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisition of businesses, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment 0.0 0.0    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates 0.0 11.6    
Net cash provided by (used in) continuing investing activities 0.0 11.6    
Cash flows from financing activities:        
Net proceeds (repayments) in debt (247.9)      
Debt issuance costs 0.0 0.0    
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares 0.0 0.0    
Other, net 0.0 0.0    
Net proceeds (repayments) from debt (247.5) (11.6)    
Net cash provided by (used in) continuing financing activities 0.4 (11.6)    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents 0.1 0.0    
Cash and cash equivalents 0.1 0.0 0.0 0.0
Other Subsidiaries [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities (135.5) (9.6)    
Net cash provided by (used in) discontinued operating activities (0.1) 7.7    
Net Cash Provided by (Used in) Operating Activities (135.6) (1.9)    
Cash flows from investing activities:        
Capital expenditures (44.0) (24.7)    
Acquisition of businesses, net of cash acquired (201.6) (9.8)    
Proceeds from sale of property, plant and equipment 0.7 0.4    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates 287.0 919.7    
Net cash provided by (used in) continuing investing activities 42.1 885.6    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0      
Debt issuance costs 0.0 0.0    
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests (11.0) (6.9)    
Repurchase of ordinary shares 0.0 0.0    
Other, net (1.0) 1.8    
Net proceeds (repayments) from debt 9.3 (1,237.5)    
Net cash provided by (used in) continuing financing activities (2.7) (1,242.6)    
Effect of exchange rate changes on cash and cash equivalents 46.0 37.3    
Net increase (decrease) in cash and cash equivalents (50.2) (321.6)    
Cash and cash equivalents 1,139.3 758.5 1,189.5 1,080.1
Consolidation, Eliminations [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities 0.0 0.0    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities 0.0 0.0    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisition of businesses, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment 0.0 0.0    
Proceeds from Sale of Equity Method Investments 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates (77.7) (2,157.3)    
Net cash provided by (used in) continuing investing activities (77.7) (2,157.3)    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0      
Debt issuance costs 0.0 0.0    
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares 0.0 0.0    
Other, net 0.0 0.0    
Net proceeds (repayments) from debt 77.7 2,157.3    
Net cash provided by (used in) continuing financing activities 77.7 2,157.3    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents 0.0 0.0    
Cash and cash equivalents $ 0.0 $ 0.0 $ 0.0 $ 0.0