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Guarantor Financial Information (Condensed Consolidating Statements of Cash Flows) (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Jun. 30, 2016
Sep. 30, 2017
Sep. 30, 2016
Dec. 31, 2016
Dec. 31, 2015
Condensed Financial Statements, Captions [Line Items]          
Net cash provided by (used in) continuing operating activities   $ 890.8 $ 1,022.6    
Net cash provided by (used in) discontinued operating activities   (17.6) 94.1    
Net Cash Provided by (Used in) Operating Activities   873.2 1,116.7    
Cash flows from investing activities:          
Capital expenditures   (149.9) (127.5)    
Acquisition of businesses, net of cash acquired   (60.3) (9.2)    
Proceeds from sale of property, plant and equipment   1.1 2.6    
Proceeds from Divestiture of Businesses, Net of Cash Divested     422.5    
Proceeds from Sale of Equity Method Investments $ 423.0 0.0 423.0    
Payments for (Proceeds from) Businesses and Interest in Affiliates   0.0 0.0    
Net cash provided by (used in) continuing investing activities   (206.4) 288.4    
Cash flows from financing activities:          
Net proceeds (repayments) in debt   11.6 150.6    
Debt issuance costs   (0.2) (2.1)    
DividendsPaid   318.0 245.6    
Dividends paid to noncontrolling interests   (15.5) (13.8)    
Payments to Noncontrolling Interests   (6.8) 0.0    
Repurchase of ordinary shares   (911.1) (250.1)    
Other, net   40.7 16.3    
Short-term borrowings (payments), net   0.0 0.0    
Net cash provided by (used in) continuing financing activities   (1,222.5) (645.9)    
Effect of exchange rate changes on cash and cash equivalents   100.0 8.6    
Net increase (decrease) in cash and cash equivalents   (455.7) 767.8    
Cash and cash equivalents   1,259.0 1,504.6 $ 1,714.7 $ 736.8
IR Ireland [Member]          
Condensed Financial Statements, Captions [Line Items]          
Net cash provided by (used in) continuing operating activities   82.7 (37.0)    
Net cash provided by (used in) discontinued operating activities   0.0 0.0    
Net Cash Provided by (Used in) Operating Activities   82.7 (37.0)    
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 Divestiture of Businesses, Net of Cash Divested     0.0    
Payments for (Proceeds from) Businesses and Interest in Affiliates   0.0 (160.2)    
Net cash provided by (used in) continuing investing activities   0.0 (160.2)    
Cash flows from financing activities:          
Net proceeds (repayments) in debt   0.0 0.0    
Debt issuance costs   0.0 0.0    
DividendsPaid   318.0 245.6    
Dividends paid to noncontrolling interests   0.0 0.0    
Payments to Noncontrolling Interests   0.0      
Repurchase of ordinary shares   (911.1) (250.1)    
Other, net   41.9 16.3    
Short-term borrowings (payments), net   1,104.5 676.6    
Net cash provided by (used in) continuing financing activities   (82.7) 197.2    
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 International [Member]          
Cash flows from investing activities:          
Proceeds from Divestiture of Businesses, Net of Cash Divested     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    
Payments for (Proceeds from) Businesses and Interest in Affiliates   0.0 (19,535.7)    
Net cash provided by (used in) continuing investing activities   0.0 (19,535.7)    
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    
Payments to Noncontrolling Interests   0.0      
Repurchase of ordinary shares   0.0 0.0    
Other, net   0.0 0.0    
Short-term borrowings (payments), net   0.0 19,535.7    
Net cash provided by (used in) continuing financing activities   0.0 19,535.7    
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   (17.5) (11.4)    
Net cash provided by (used in) discontinued operating activities   0.0 0.0    
Net Cash Provided by (Used in) Operating Activities   (17.5) (11.4)    
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 Divestiture of Businesses, Net of Cash Divested     0.0    
Payments for (Proceeds from) Businesses and Interest in Affiliates   1,170.9 (2.4)    
Net cash provided by (used in) continuing investing activities   1,170.9 (2.4)    
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    
Payments to Noncontrolling Interests   0.0      
Repurchase of ordinary shares   0.0 0.0    
Other, net   0.0 0.0    
Short-term borrowings (payments), net   (1,153.4) 13.9    
Net cash provided by (used in) continuing financing activities   (1,153.4) 13.9    
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 Global [Member]          
Condensed Financial Statements, Captions [Line Items]          
Net cash provided by (used in) continuing operating activities   (214.2) (206.7)    
Net cash provided by (used in) discontinued operating activities   0.0 0.0    
Net Cash Provided by (Used in) Operating Activities   (214.2) (206.7)    
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 Divestiture of Businesses, Net of Cash Divested     0.0    
Payments for (Proceeds from) Businesses and Interest in Affiliates   270.1 (242.8)    
Net cash provided by (used in) continuing investing activities   270.1 (242.8)    
Cash flows from financing activities:          
Net proceeds (repayments) in debt   0.0 0.0    
Debt issuance costs   (0.2) (2.1)    
DividendsPaid   0.0 0.0    
Dividends paid to noncontrolling interests   0.0 0.0    
Payments to Noncontrolling Interests   0.0      
Repurchase of ordinary shares   0.0 0.0    
Other, net   0.0 0.0    
Short-term borrowings (payments), net   (55.5) 440.2    
Net cash provided by (used in) continuing financing activities   (55.7) 438.1    
Effect of exchange rate changes on cash and cash equivalents   0.0 0.0    
Net increase (decrease) in cash and cash equivalents   0.2 (11.4)    
Cash and cash equivalents   0.2 0.0 0.0 11.4
IR New Jersey [Member]          
Condensed Financial Statements, Captions [Line Items]          
Net cash provided by (used in) continuing operating activities   228.1 569.4    
Net cash provided by (used in) discontinued operating activities   (15.5) 99.5    
Net Cash Provided by (Used in) Operating Activities   212.6 668.9    
Cash flows from investing activities:          
Capital expenditures   (59.8) (56.3)    
Acquisition of businesses, net of cash acquired   (2.7) (9.2)    
Proceeds from sale of property, plant and equipment   0.0 0.0    
Proceeds from Divestiture of Businesses, Net of Cash Divested     0.0    
Payments for (Proceeds from) Businesses and Interest in Affiliates   (347.0) 65.7    
Net cash provided by (used in) continuing investing activities   (409.5) 0.2    
Cash flows from financing activities:          
Net proceeds (repayments) in debt   7.5 7.6    
Debt issuance costs   0.0 0.0    
DividendsPaid   0.0 0.0    
Dividends paid to noncontrolling interests   0.0 0.0    
Payments to Noncontrolling Interests   0.0      
Repurchase of ordinary shares   0.0 0.0    
Other, net   (1.2) 0.0    
Short-term borrowings (payments), net   35.8 (120.2)    
Net cash provided by (used in) continuing financing activities   27.1 (127.8)    
Effect of exchange rate changes on cash and cash equivalents   0.0 0.0    
Net increase (decrease) in cash and cash equivalents   (169.8) 541.3    
Cash and cash equivalents   464.8 541.3 634.6 0.0
IR Lux Finance [Member]          
Condensed Financial Statements, Captions [Line Items]          
Net cash provided by (used in) continuing operating activities   (23.9) (20.8)    
Net cash provided by (used in) discontinued operating activities   0.0 0.0    
Net Cash Provided by (Used in) Operating Activities   (23.9) (20.8)    
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 Divestiture of Businesses, Net of Cash Divested     0.0    
Payments for (Proceeds from) Businesses and Interest in Affiliates   11.7 243.7    
Net cash provided by (used in) continuing investing activities   11.7 243.7    
Cash flows from financing activities:          
Net proceeds (repayments) in debt   0.0 143.0    
Debt issuance costs   0.0 0.0    
DividendsPaid   0.0 0.0    
Dividends paid to noncontrolling interests   0.0 0.0    
Payments to Noncontrolling Interests   0.0      
Repurchase of ordinary shares   0.0 0.0    
Other, net   0.0 0.0    
Short-term borrowings (payments), net   12.2 (79.9)    
Net cash provided by (used in) continuing financing activities   12.2 (222.9)    
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 0.1 0.0 0.1
Other Subsidiaries [Member]          
Condensed Financial Statements, Captions [Line Items]          
Net cash provided by (used in) continuing operating activities   835.6 729.1    
Net cash provided by (used in) discontinued operating activities   (2.1) (5.4)    
Net Cash Provided by (Used in) Operating Activities   833.5 723.7    
Cash flows from investing activities:          
Capital expenditures   (90.1) (71.2)    
Acquisition of businesses, net of cash acquired   (57.6) 0.0    
Proceeds from sale of property, plant and equipment   1.1 2.6    
Proceeds from Divestiture of Businesses, Net of Cash Divested     422.5    
Payments for (Proceeds from) Businesses and Interest in Affiliates   56.2 (930.4)    
Net cash provided by (used in) continuing investing activities   (87.7) (576.5)    
Cash flows from financing activities:          
Net proceeds (repayments) in debt   4.1 0.0    
Debt issuance costs   0.0 0.0    
DividendsPaid   0.0 0.0    
Dividends paid to noncontrolling interests   (15.5) (13.8)    
Payments to Noncontrolling Interests   (6.8)      
Repurchase of ordinary shares   0.0 0.0    
Other, net   0.0 0.0    
Short-term borrowings (payments), net   (1,105.5) 95.8    
Net cash provided by (used in) continuing financing activities   (1,131.9) 82.0    
Effect of exchange rate changes on cash and cash equivalents   100.0 8.6    
Net increase (decrease) in cash and cash equivalents   (286.1) 237.8    
Cash and cash equivalents   794.0 963.1 1,080.1 725.3
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 Divestiture of Businesses, Net of Cash Divested     0.0    
Payments for (Proceeds from) Businesses and Interest in Affiliates   (1,161.9) 20,562.1    
Net cash provided by (used in) continuing investing activities   (1,161.9) 20,562.1    
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    
Payments to Noncontrolling Interests   0.0      
Repurchase of ordinary shares   0.0 0.0    
Other, net   0.0 0.0    
Short-term borrowings (payments), net   1,161.9 (20,562.1)    
Net cash provided by (used in) continuing financing activities   1,161.9 (20,562.1)    
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