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Income Taxes - Narrative (Details) - USD ($)
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2020
Aug. 31, 2019
Income Tax Contingency [Line Items]        
Undistributed earnings and original investments in foreign subsidiaries $ 204,000,000      
Deferred income tax liability for certain foreign withholding taxes and U.S. state taxes 3,200,000      
Unrecognized tax benefits 19,500,000 $ 17,700,000 $ 17,200,000 $ 16,600,000
Unrecognized tax benefits that if recognized would affect annual effective tax rate 18,800,000 17,100,000    
Total accrued interest 2,100,000 $ 2,000,000 $ 1,700,000  
Accruals related to income tax penalties 0      
Internal Revenue Service (IRS)        
Income Tax Contingency [Line Items]        
Federal tax credit carryforwards, subject to expiration 4,900,000      
Operating loss carryforwards 13,600,000      
State and Local Jurisdiction        
Income Tax Contingency [Line Items]        
Federal tax credit carryforwards, subject to expiration 100,000      
Operating loss carryforwards 33,900,000      
Foreign Tax Authority        
Income Tax Contingency [Line Items]        
Operating loss carryforwards $ 7,100,000