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Debt (Details)
12 Months Ended
May 15, 2019
Sep. 30, 2016
USD ($)
Sep. 30, 2015
USD ($)
bank
Sep. 30, 2014
USD ($)
Jul. 02, 2016
USD ($)
May 31, 2016
USD ($)
Apr. 02, 2016
USD ($)
Debt Instrument [Line Items]              
Senior Notes   $ 500,000,000 $ 0     $ 500,000,000  
Debt Instrument, Interest Rate, Stated Percentage           6.00%  
Debt Instrument, Fair Value Disclosure   $ 536,300,000          
Additional borrowing capacity on credit facility if agreed to by lenders         $ 500,000,000    
Voting interest in domestic subsidiaries pledged against credit facility   100.00%          
Credit facility, borrowings outstanding   $ 758,125,000 618,125,000        
Voting interest in foreign subsidiaries pledged against credit facility   65.00%          
Investment limit in foreign subsidiaries   $ 75,000,000          
Cash investment limit for acquisition of business   $ 200,000,000          
Maximum leverage ratio allowed under debt covenant   4.00          
Minimum fixed charge coverage ratio allowed under debt covenant   3.50          
Leverage ratio, actual   3.55          
Debt Instrument, Covenant Compliance, Senior Debt Leverage Ratio, actual   1.18          
Fixed charge coverage ratio, actual   7.14          
Credit facility, origination costs   $ 6,900,000   $ 7,900,000      
Credit facility, periodic interest payment   $ 13,300,000 $ 10,100,000 $ 5,700,000      
Credit facility, average interest rate during period   3.00% 1.70% 1.60%      
Long-term Debt, Gross   $ 758,125,000 $ 668,125,000        
Unamortized Debt Issuance Expense   (10,709,000) (7,587,000)        
debt net of unamortized debt issuance cost   747,416,000 660,538,000        
Current portion of long term debt   $ 0 $ 50,000,000        
Maximum [Member]              
Debt Instrument [Line Items]              
Credit facility, variable interest rate, length of time between updates   180 days          
Minimum [Member]              
Debt Instrument [Line Items]              
Credit facility, variable interest rate, length of time between updates   30 days          
Term Loan [Member]              
Debt Instrument [Line Items]              
Number of banks in credit agreement | bank     16        
Credit facility, borrowings outstanding   $ 0 $ 475,000,000        
Line of Credit [Member]              
Debt Instrument [Line Items]              
Credit facility, current maximum amount             $ 1,000,000,000
Credit facility, borrowings outstanding   $ 258,125,000 $ 193,125,000        
Credit facility, revolving loan, basis spread on federal funds effective rate   0.50%          
Credit facility, revolving loan, basis spread on adjusted LIBOR   1.00%          
Debt Instrument, Covenant Compliance, Senior Debt Leverage Ratio   3.0          
Line of Credit [Member] | Maximum [Member]              
Debt Instrument [Line Items]              
Credit facility, revolving loan, commitment fees percentage   0.30%          
Line of Credit [Member] | Minimum [Member]              
Debt Instrument [Line Items]              
Credit facility, revolving loan, commitment fees percentage   0.175%          
Revolving Credit Facility [Member]              
Debt Instrument [Line Items]              
Credit facility, current maximum amount         $ 900,000,000    
LIBOR for Eurodollar-Based Borrowings [Member] | Line of Credit [Member] | Maximum [Member]              
Debt Instrument [Line Items]              
Debt Instrument, Basis Spread on Variable Rate   1.75%          
LIBOR for Eurodollar-Based Borrowings [Member] | Line of Credit [Member] | Minimum [Member]              
Debt Instrument [Line Items]              
Debt Instrument, Basis Spread on Variable Rate   1.25%          
Base Rate [Member] | Line of Credit [Member] | Maximum [Member]              
Debt Instrument [Line Items]              
Debt Instrument, Basis Spread on Variable Rate   0.75%          
Base Rate [Member] | Line of Credit [Member] | Minimum [Member]              
Debt Instrument [Line Items]              
Debt Instrument, Basis Spread on Variable Rate   0.25%          
Revolving Loan, Reset December 17, 2015 | Term Loan [Member]              
Debt Instrument [Line Items]              
Credit facility, term loan, interest rate at period end   2.56%          
Scenario, Forecast [Member]              
Debt Instrument [Line Items]              
Debt Instrument, Redemption Price, Percentage 101.00%