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Debt (Details)
3 Months Ended 6 Months Ended
May 15, 2019
Apr. 01, 2017
USD ($)
Apr. 02, 2016
USD ($)
Apr. 01, 2017
USD ($)
Apr. 02, 2016
USD ($)
Sep. 30, 2016
USD ($)
Jul. 02, 2016
USD ($)
May 31, 2016
USD ($)
Sep. 30, 2015
bank
Debt Instrument [Line Items]                  
Senior Notes   $ 500,000,000   $ 500,000,000   $ 500,000,000   $ 500,000,000  
Long-term Debt, Gross   718,125,000   718,125,000   758,125,000      
debt net of unamortized debt issuance cost   $ 711,976,000   $ 711,976,000   751,601,000      
Debt Instrument, Interest Rate, Stated Percentage               6.00%  
Voting interest in domestic subsidiaries pledged against credit facility       100.00%          
Voting interest in foreign subsidiaries pledged against credit facility       65.00%          
Leverage Ratio, Actual   3.25   3.25          
Debt Instrument, Covenant Compliance, Senior Debt Leverage Ratio, actual   0.98   0.98          
Fixed charge coverage ratio, actual   5.23   5.23          
Current portion of long term debt   $ 0   $ 0   0      
Line of Credit [Member]                  
Debt Instrument [Line Items]                  
Long-term portion of long term debt   218,125,000   218,125,000   258,125,000      
Credit facility amount   $ 600,000,000 $ 1,000,000,000 $ 600,000,000 $ 1,000,000,000   $ 900,000,000    
Additional borrowing capacity on credit facility if agreed to by lenders             $ 500,000,000    
Line of Credit Facility, Interest Rate at Period End   2.82%   2.82%          
Component of Base Rate, Basis Spread on Federal Reserve Bank of New York (FRBNY) rate   0.50%   0.50%          
Component of Base Rate, Basis Spread on Adjusted LIBOR       1.00%          
Investment limit in foreign subsidiaries   $ 75,000,000   $ 75,000,000          
Cash investment limit for acquisition of business   $ 200,000,000   $ 200,000,000          
Debt Instrument, Covenant Compliance, Leverage Ratio Four   4.50   4.50          
Minimum fixed charge coverage ratio allowed under debt covenant   3.50   3.50          
Maximum total leverage ratio allowed under debt covenant after covenant modification trigger event   4.00   4.00          
Debt Instrument, Covenant Compliance, maximum Senior Debt Leverage Ratio after covenant modification trigger event   3.0   3.0          
Line of Credit [Member] | Minimum                  
Debt Instrument [Line Items]                  
Line of Credit Facility, Variable Interest Rate, Length of Time Between Updates       30 days          
Credit facility commitment fees percentage       0.175%          
Line of Credit [Member] | Maximum                  
Debt Instrument [Line Items]                  
Line of Credit Facility, Variable Interest Rate, Length of Time Between Updates       180 days          
Credit facility commitment fees percentage       0.30%          
Secured Debt [Member]                  
Debt Instrument [Line Items]                  
Debt Instrument, Number of Banks in Credit Facility | bank                 16
London Interbank Offered Rate (LIBOR) [Member] | Line of Credit [Member] | Minimum                  
Debt Instrument [Line Items]                  
Debt Instrument, Basis Spread on Variable Rate       1.25%          
London Interbank Offered Rate (LIBOR) [Member] | Line of Credit [Member] | Maximum                  
Debt Instrument [Line Items]                  
Debt Instrument, Basis Spread on Variable Rate       1.75%          
Base Rate [Member] | Line of Credit [Member] | Minimum                  
Debt Instrument [Line Items]                  
Debt Instrument, Basis Spread on Variable Rate       0.25%          
Base Rate [Member] | Line of Credit [Member] | Maximum                  
Debt Instrument [Line Items]                  
Debt Instrument, Basis Spread on Variable Rate       0.75%          
Scenario, Forecast [Member]                  
Debt Instrument [Line Items]                  
Debt Instrument, Redemption Price, Percentage 101.00%                
Other Assets [Member] | Line of Credit [Member]                  
Debt Instrument [Line Items]                  
Unamortized Debt Issuance Expense   $ (2,500,000)   $ (2,500,000)   (4,200,000)      
Nonoperating Income (Expense) [Member]                  
Debt Instrument [Line Items]                  
Interest Expense, Debt   11,700,000 $ 4,800,000 22,000,000 $ 11,300,000        
Senior Notes [Member]                  
Debt Instrument [Line Items]                  
Unamortized Debt Issuance Expense   (6,149,000)   (6,149,000)   $ (6,524,000)      
Debt Instrument, Fair Value Disclosure   $ 528,300,000   $ 528,300,000