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Debt (Details)
12 Months Ended
Sep. 30, 2019
USD ($)
Sep. 30, 2018
USD ($)
Sep. 30, 2017
USD ($)
bank
Nov. 15, 2019
USD ($)
Sep. 13, 2018
USD ($)
May 31, 2016
Debt Instrument [Line Items]            
Senior Notes $ 500,000,000 $ 500,000,000        
Long-term Debt, Gross 673,125,000 648,125,000        
Unamortized Debt Issuance Expense (3,991,000) (4,857,000)        
Long-term debt 669,134,000 643,268,000        
Debt Instrument, Interest Rate, Stated Percentage           6.00%
Debt Instrument, Fair Value Disclosure $ 526,300,000          
Voting interest in domestic subsidiaries pledged against credit facility 100.00%          
Voting interest in foreign subsidiaries pledged against credit facility 65.00%          
Investment limit in foreign subsidiaries $ 100,000,000          
Cash investment limit for acquisition of business $ 200,000,000          
Minimum fixed charge coverage ratio allowed under debt covenant 3.00          
Leverage ratio, actual 1.73          
Debt Instrument, Covenant Compliance, Senior Debt Leverage Ratio, actual 0.47          
Fixed charge coverage ratio, actual 9.76          
Credit facility, origination costs $ 2,900,000   $ 6,900,000      
Credit facility, periodic interest payment $ 40,800,000 $ 39,800,000 $ 38,900,000      
Credit facility, average interest rate during period 5.40% 5.20% 4.90%      
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      
Line of Credit [Member]            
Debt Instrument [Line Items]            
Credit facility, borrowings outstanding $ 173,125,000 $ 148,125,000        
Credit facility, current maximum amount       $ 1,000,000,000 $ 700,000,000  
Credit facility, revolving loan, basis spread on federal funds effective rate 0.50%          
Credit facility, revolving loan, basis spread on adjusted LIBOR 1.00%          
Maximum leverage ratio allowed under debt covenant 4.50          
Debt Instrument, Covenant Compliance, Senior Debt Leverage Ratio 3.00          
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%          
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 3.44%          
Forecast [Member]            
Debt Instrument [Line Items]            
Debt Instrument, Redemption Price, Percentage 101.00%          
Other Noncurrent Assets [Member] | Line of Credit [Member]            
Debt Instrument [Line Items]            
Unamortized Debt Issuance Expense $ (3,100,000) $ (3,800,000)        
Subsequent Event [Member]            
Debt Instrument [Line Items]            
Long-term Debt, Gross       1,100,000,000    
Subsequent Event [Member] | Line of Credit [Member]            
Debt Instrument [Line Items]            
Credit facility, current maximum amount       1,000,000,000    
Subsequent Event [Member] | Foreign Subsidiary [Member] | Line of Credit [Member]            
Debt Instrument [Line Items]            
Credit facility, borrowings outstanding       $ 0