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Long-Term Debt (Details) (USD $)
12 Months Ended
Dec. 31, 2014
Dec. 31, 2012
Dec. 31, 2003
Dec. 31, 2013
Line of Credit Facility [Line Items]        
Line of Credit Facility, Current Borrowing Capacity $ 1,500,000,000us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity      
Line of Credit Facility, Borrowing Capacity, Term 5 years      
Additional borrowings available 350,000,000us-gaap_DebtInstrumentUnusedBorrowingCapacityAmount      
Line of Credit Facility, Initiation Date Jul. 27, 2012      
Line of Credit Facility, Expiration Date Jul. 27, 2017      
Line of Credit Facility, Amount Outstanding 0us-gaap_LineOfCredit      
Non-cash debt extinguishment charge   1,000,000us-gaap_ExtinguishmentOfDebtAmount    
Outstanding letters of credit 48,900,000rop_LettersOfCreditOutstanding      
Debt covenant compliance 3.5us-gaap_RatioOfIndebtednessToNetCapital1      
Debt Instrument [Line Items]        
Total Debt 2,214,123,000us-gaap_LongTermDebt     2,464,852,000us-gaap_LongTermDebt
Current Portion 11,092,000us-gaap_LongTermDebtCurrent     11,016,000us-gaap_LongTermDebtCurrent
Long-term debt, net of current portion 2,203,031,000us-gaap_LongTermDebtNoncurrent     2,453,836,000us-gaap_LongTermDebtNoncurrent
Principal amount 2,200,000us-gaap_DebtInstrumentFaceAmount      
Future maturities of long term debt [Abstract]        
2015 11,092,000us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths      
2016 2,332,000us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo      
2017 400,630,000us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree      
2018 800,066,000us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour      
2019 500,003,000us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive      
Thereafter 500,000,000us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive      
Total 2,214,123,000us-gaap_LongTermDebt     2,464,852,000us-gaap_LongTermDebt
Credit Facility Member 2012 [Member]        
Debt Instrument [Line Items]        
Principal amount 0us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= rop_CreditFacilityMember2012Member
    250,000,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= rop_CreditFacilityMember2012Member
Senior Notes 2017 [Member]        
Debt Instrument [Line Items]        
Issuance Date Nov. 21, 2012      
Interest rate (in hundredths) 1.85%us-gaap_DebtInstrumentInterestRateStatedPercentage
/ us-gaap_DebtInstrumentAxis
= rop_SeniorNotes2017Member
     
Principal amount 400,000,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= rop_SeniorNotes2017Member
    400,000,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= rop_SeniorNotes2017Member
Periodic interest payments semi-annually      
Periodic interest payments, start May 15, 2013      
Maturity Date Nov. 15, 2017      
Senior Notes 2018 [Member]        
Debt Instrument [Line Items]        
Issuance Date Jun. 06, 2013      
Interest rate (in hundredths) 2.05%us-gaap_DebtInstrumentInterestRateStatedPercentage
/ us-gaap_DebtInstrumentAxis
= rop_SeniorNotes2018Member
     
Principal amount 800,000,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= rop_SeniorNotes2018Member
    800,000,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= rop_SeniorNotes2018Member
Periodic interest payments semi-annually      
Periodic interest payments, start October 1, 2013      
Maturity Date Oct. 01, 2018      
Senior Notes 2019 [Member]        
Debt Instrument [Line Items]        
Issuance Date Nov. 21, 2012      
Interest rate (in hundredths) 3.125%us-gaap_DebtInstrumentInterestRateStatedPercentage
/ us-gaap_DebtInstrumentAxis
= rop_SeniorNotes2019Member
     
Principal amount 500,000,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= rop_SeniorNotes2019Member
    500,000,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= rop_SeniorNotes2019Member
Periodic interest payments semi-annually      
Periodic interest payments, start May 15, 2013      
Maturity Date Nov. 15, 2022      
Senior Notes 2022 [Member]        
Debt Instrument [Line Items]        
Issuance Date Aug. 15, 2009      
Interest rate (in hundredths) 6.25%us-gaap_DebtInstrumentInterestRateStatedPercentage
/ us-gaap_DebtInstrumentAxis
= rop_SeniorNotes2022Member
     
Principal amount 500,000,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= rop_SeniorNotes2022Member
    500,000,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= rop_SeniorNotes2022Member
Periodic interest payments semi-annually      
Periodic interest payments, start March 1, 2010      
Maturity Date Sep. 30, 2019      
Convertible Notes [Member]        
Debt Instrument [Line Items]        
Interest rate (in hundredths) 3.75%us-gaap_DebtInstrumentInterestRateStatedPercentage
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleSubordinatedDebtMember
     
Principal issuance percentage (in hundredths)     60.498%rop_PrincipalIssuancePercentageInHundredths
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleSubordinatedDebtMember
 
Principal amount 8,003,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleSubordinatedDebtMember
  230,000,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleSubordinatedDebtMember
8,270,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_ConvertibleSubordinatedDebtMember
Capital Lease Obligations And Foreign Letter Of Credit Issuance [Member]        
Debt Instrument [Line Items]        
Principal amount 6,120,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= rop_CapitalLeaseObligationsAndForeignLetterOfCreditIssuanceMember
    6,582,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= rop_CapitalLeaseObligationsAndForeignLetterOfCreditIssuanceMember
Senior Subordinated Notes [Member]        
Debt Instrument [Line Items]        
Interest rate (in hundredths) 3.75%us-gaap_DebtInstrumentInterestRateStatedPercentage
/ us-gaap_DebtInstrumentAxis
= us-gaap_SeniorSubordinatedNotesMember
     
Principal amount 8,000,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_SeniorSubordinatedNotesMember
     
Maturity Date Dec. 31, 2034      
Subordinated Convertible Notes        
Subordinated convertible notes, original public offering amount 230,000,000rop_SeniorNotesOffering
/ us-gaap_DebtInstrumentAxis
= us-gaap_SeniorSubordinatedNotesMember
     
Original issue discount (in hundredths) 60.498%rop_SubordinatedConvertibleNotesIssueDiscountPercentage
/ us-gaap_DebtInstrumentAxis
= us-gaap_SeniorSubordinatedNotesMember
     
Subordinated convertible note holding period for contingent cash interest 180      
Trading days the average price of subordinated convertible note must meet threshold within six months measurement period 5      
Commencement date for measurement of average trading price on a subordinated convertible note Jan. 15, 2009      
Contingent cash interest payable annual rate if threshold is met (in hundredths) 0.25%rop_SubordinatedConvertibleNotesContingentCashInterestPercentage
/ us-gaap_DebtInstrumentAxis
= us-gaap_SeniorSubordinatedNotesMember
     
Debt Instrument Convertible Price Next Conversion Date $ 572.76rop_DebtInstrumentConvertibleConversionPriceFirstConversionDate
/ us-gaap_DebtInstrumentAxis
= us-gaap_SeniorSubordinatedNotesMember
     
Next conversion date 1/15/2019      
Convertible notes purchase price on January 15, 2019 (third conversion date) $ 689.68rop_DebtInstrumentConvertibleConversionPriceThirdConversionDate
/ us-gaap_DebtInstrumentAxis
= us-gaap_SeniorSubordinatedNotesMember
     
Third conversion date 1/15/2024      
Convertible notes purchase price on January 15, 2024 (fourth conversion date) $ 830.47rop_DebtInstrumentConvertibleConversionPriceFourthConversionDate
/ us-gaap_DebtInstrumentAxis
= us-gaap_SeniorSubordinatedNotesMember
     
Fourth conversion date 1/15/2029      
Minimum number of trading days in the consecutive trading period that the common stock sale price above threshold to trigger conversion (in days) 20rop_MinimumNumberOfTradingDaysToTriggerConversionPrice
/ us-gaap_DebtInstrumentAxis
= us-gaap_SeniorSubordinatedNotesMember
     
Number of consecutive trading days in the preceding quarter the minimum trading days must occur in for the sale price to reach threshold to trigger conversion (in days) 30rop_NumberOfConsecutiveTradingDaysInQuarterToTriggerConversionPrice
/ us-gaap_DebtInstrumentAxis
= us-gaap_SeniorSubordinatedNotesMember
     
Conversion price, end of period $ 488.37us-gaap_DebtInstrumentConvertibleConversionPrice1
/ us-gaap_DebtInstrumentAxis
= us-gaap_SeniorSubordinatedNotesMember
     
If converted, the value exceeding principal amount outstanding at end of period 25,000,000us-gaap_DebtInstrumentConvertibleIfConvertedValueInExcessOfPrincipal
/ us-gaap_DebtInstrumentAxis
= us-gaap_SeniorSubordinatedNotesMember
     
If converted, issuance of common stock shares 155,980us-gaap_DebtInstrumentConvertibleNumberOfEquityInstruments
/ us-gaap_DebtInstrumentAxis
= us-gaap_SeniorSubordinatedNotesMember
     
Letters of credit [Member]        
Debt Instrument [Line Items]        
Principal amount $ 49,000,000us-gaap_DebtInstrumentFaceAmount
/ us-gaap_DebtInstrumentAxis
= us-gaap_StandbyLettersOfCreditMember