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Stock-Based Compensation - Valuation Assumptions (Details)
12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Performance Shares      
Stock Based Compensation Activity [Line Items]      
Risk-free interest rate 4.21% 4.04% 0.99%
Expected volatility of the Company’s stock 27.20% 33.50% 30.00%
Employee Stock Option      
Stock Based Compensation Activity [Line Items]      
Expected life of option (years) 5 years 8 months 12 days 5 years 9 months 18 days 6 years
Risk-free interest rate 3.86% 3.59% 1.35%
Expected volatility of the Company’s stock 29.80% 29.40% 27.80%
Expected dividend yield on the Company’s stock 2.77% 2.10% 1.71%