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Guarantor Financial Information (Condensed Consolidating Statements of Cash Flows) (Details) - USD ($)
$ in Millions
6 Months Ended
Jun. 30, 2018
Jun. 30, 2017
Dec. 31, 2017
Dec. 31, 2016
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities $ 414.5 $ 422.3    
Net cash provided by (used in) discontinued operating activities (36.8) (16.8)    
Net Cash Provided by (Used in) Operating Activities 377.7 405.5    
Cash flows from investing activities:        
Capital expenditures (163.4) (79.5)    
Acquisitions and equity method investments, net of cash acquired (281.5) (39.9)    
Proceeds from sale of property, plant and equipment   0.5    
Proceeds from Equity Method Investment, Distribution 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates 0.0 0.0    
Net cash provided by (used in) continuing investing activities (444.9) (118.9)    
Cash flows from financing activities:        
Net proceeds (repayments) in debt (266.7) 7.6    
Debt issuance costs (11.6) (0.2)    
DividendsPaid 221.8 204.8    
Dividends paid to noncontrolling interests (35.5) (7.0)    
Payments to Noncontrolling Interests 0.0 (6.8)    
Repurchase of ordinary shares (500.1) (575.2)    
Other, net 10.9 34.7    
Net proceeds (repayments) from debt 0.0 0.0    
Net cash provided by (used in) continuing financing activities (491.4) (766.9)    
Effect of exchange rate changes on cash and cash equivalents (21.3) 75.7    
Net increase (decrease) in cash and cash equivalents (579.9) (404.6)    
Cash and cash equivalents 969.5 1,310.1 $ 1,549.4 $ 1,714.7
IR Ireland [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities 80.0 75.4    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities 80.0 75.4    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisitions and equity method investments, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment   0.0    
Proceeds from Equity Method Investment, Distribution 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates 872.3 0.0    
Net cash provided by (used in) continuing investing activities 872.3 0.0    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0 0.0    
Debt issuance costs 0.0 0.0    
DividendsPaid 221.8 204.8    
Dividends paid to noncontrolling interests 0.0 0.0    
Repurchase of ordinary shares (500.1) (575.2)    
Other, net 13.8 35.0    
Net proceeds (repayments) from debt (244.2) 669.6    
Net cash provided by (used in) continuing financing activities (952.3) (75.4)    
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 International [Member]        
Cash flows from investing activities:        
Proceeds from Equity Method Investment, Distribution 0.0      
IR Irish Holdings [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities (2.7) 0.0    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities (2.7) 0.0    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisitions and equity method investments, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment   0.0    
Payments for (Proceeds from) Businesses and Interest in Affiliates (668.1) 0.0    
Net cash provided by (used in) continuing investing activities (668.1) 0.0    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0 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 670.8 0.0    
Net cash provided by (used in) continuing financing activities 670.8 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 17.6 (17.5)    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities 17.6 (17.5)    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisitions and equity method investments, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment   0.0    
Proceeds from Equity Method Investment, Distribution (4.0)      
Payments for (Proceeds from) Businesses and Interest in Affiliates 741.2 1,153.0    
Net cash provided by (used in) continuing investing activities 737.2 1,153.0    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0 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 (754.7) (1,135.4)    
Net cash provided by (used in) continuing financing activities (754.7) (1,135.4)    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents 0.1 0.1    
Cash and cash equivalents 0.7 0.1 0.6 0.0
IR Global [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities (94.4) (142.5)    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities (94.4) (142.5)    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisitions and equity method investments, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment   0.0    
Proceeds from Equity Method Investment, Distribution 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates 0.0 142.7    
Net cash provided by (used in) continuing investing activities 0.0 142.7    
Cash flows from financing activities:        
Net proceeds (repayments) in debt (31.6) 0.0    
Debt issuance costs (11.6) (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 74.4 0.0    
Net cash provided by (used in) continuing financing activities 94.4 (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 439.1 139.0    
Net cash provided by (used in) discontinued operating activities (38.3) (14.5)    
Net Cash Provided by (Used in) Operating Activities 400.8 124.5    
Cash flows from investing activities:        
Capital expenditures (55.4) (25.9)    
Acquisitions and equity method investments, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment   0.0    
Proceeds from Equity Method Investment, Distribution 3.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates (800.5) 0.0    
Net cash provided by (used in) continuing investing activities (852.9) (25.9)    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 7.5 7.5    
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) (1.0)    
Net proceeds (repayments) from debt 100.7 (135.7)    
Net cash provided by (used in) continuing financing activities 92.8 (144.2)    
Effect of exchange rate changes on cash and cash equivalents 0.0 0.0    
Net increase (decrease) in cash and cash equivalents (359.3) (45.6)    
Cash and cash equivalents 0.0 589.0 359.3 634.6
IR Lux Finance [Member]        
Condensed Financial Statements, Captions [Line Items]        
Net cash provided by (used in) continuing operating activities (24.6) (23.7)    
Net cash provided by (used in) discontinued operating activities 0.0 0.0    
Net Cash Provided by (Used in) Operating Activities (24.6) (23.7)    
Cash flows from investing activities:        
Capital expenditures 0.0 0.0    
Acquisitions and equity method investments, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment   0.0    
Proceeds from Equity Method Investment, Distribution 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates 0.0 11.7    
Net cash provided by (used in) continuing investing activities 0.0 11.7    
Cash flows from financing activities:        
Net proceeds (repayments) in debt (249.0) 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 (224.3) 12.0    
Net cash provided by (used in) continuing financing activities 24.7 12.0    
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 (0.5) 391.6    
Net cash provided by (used in) discontinued operating activities 1.5 (2.3)    
Net Cash Provided by (Used in) Operating Activities 1.0 389.3    
Cash flows from investing activities:        
Capital expenditures (108.0) (53.6)    
Acquisitions and equity method investments, net of cash acquired (281.5) (39.9)    
Proceeds from sale of property, plant and equipment   0.5    
Proceeds from Equity Method Investment, Distribution 1.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates 468.2 589.4    
Net cash provided by (used in) continuing investing activities 79.7 496.4    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 6.4 0.1    
Debt issuance costs 0.0 0.0    
DividendsPaid 0.0 0.0    
Dividends paid to noncontrolling interests (35.5) (7.0)    
Repurchase of ordinary shares 0.0 0.0    
Other, net (2.5) 0.7    
Net proceeds (repayments) from debt (235.8) (1,307.3)    
Net cash provided by (used in) continuing financing activities (280.2) (1,320.5)    
Effect of exchange rate changes on cash and cash equivalents (21.3) 75.7    
Net increase (decrease) in cash and cash equivalents (220.8) (359.1)    
Cash and cash equivalents 968.7 721.0 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    
Acquisitions and equity method investments, net of cash acquired 0.0 0.0    
Proceeds from sale of property, plant and equipment   0.0    
Proceeds from Equity Method Investment, Distribution 0.0      
Payments for (Proceeds from) Businesses and Interest in Affiliates (613.1) (1,896.8)    
Net cash provided by (used in) continuing investing activities (613.1) (1,896.8)    
Cash flows from financing activities:        
Net proceeds (repayments) in debt 0.0 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 613.1 1,896.8    
Net cash provided by (used in) continuing financing activities 613.1 1,896.8    
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