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Retirement Benefits - Pension Plans and Defined Contribution Plans (Details) - USD ($)
$ in Millions
3 Months Ended 12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Estimated Future Benefit Payments          
Employer's contribution to defined contribution plans (as a percent)     4.00%    
Contribution vesting period     3 years    
Expenses related to defined contribution plans     $ 10.4 $ 10.4 $ 9.0
Minimum          
Estimated Future Benefit Payments          
Contribution vesting period     0 years    
Maximum          
Estimated Future Benefit Payments          
Employer's matching contribution to defined contribution plans (as a percent)     6.00%    
Contribution vesting period     3 years    
Pension Plans Defined Benefit          
Cash Flows          
Cash contribution to defined benefit retirement plans     $ 10.6 $ 10.3 $ 10.0
Pension Plans Defined Benefit | Minimum          
Cash Flows          
Estimated cash contribution to defined benefit retirement plans $ 11.8   $ 11.8    
Foreign Plan          
Fair Value Measurements          
Defined Benefit Plan, Assumptions Used Calculating Net Periodic Benefit Cost, Discount Rate     3.50% 3.90% 1.10%
Defined Benefit Plan, Benefit Obligation, Actuarial Gain (Loss)     $ (12.5) $ (1.5)  
Employee and employer contributions     $ 10.3 $ 9.8  
Defined Benefit Plan, Assumptions Used Calculating Net Periodic Benefit Cost, Rate of Compensation Increase     2.00% 2.00% 2.00%
Fair value of plan assets 56.6 $ 49.0 $ 56.6 $ 49.0 $ 41.5
Estimated Future Benefit Payments          
2025   9.8   9.8  
2026   10.0   10.0  
2027   10.2   10.2  
2028   9.7   9.7  
2029   9.6   9.6  
2030-2034   45.1   45.1  
Defined Benefit Plan, Benefit Obligation, Business Combination     0.0 2.7  
Defined Benefit Plan, Plan Assets, Payment for Settlement     (5.0) (3.7)  
Foreign Plan | Cash equivalents | Level 1          
Fair Value Measurements          
Fair value of plan assets 7.5 5.4 7.5 5.4  
Foreign Plan | Cash equivalents | Level 2          
Fair Value Measurements          
Fair value of plan assets 0.0 0.0 0.0 0.0  
Foreign Plan | Cash equivalents | Level 3          
Fair Value Measurements          
Fair value of plan assets 0.0 0.0 0.0 0.0  
Foreign Plan | Estimate of Fair Value Measurement [Member]          
Fair Value Measurements          
Fair value of plan assets 56.6 49.0 56.6 49.0  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Level 1          
Fair Value Measurements          
Fair value of plan assets 22.9 22.5 22.9 22.5  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Level 2          
Fair Value Measurements          
Fair value of plan assets 30.3 20.0 30.3 20.0  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Level 3          
Fair Value Measurements          
Fair value of plan assets 3.4 6.5 3.4 6.5  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Cash equivalents          
Fair Value Measurements          
Fair value of plan assets 7.5 5.4 7.5 5.4  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Equity securities          
Fair Value Measurements          
Fair value of plan assets 12.0 9.8 12.0 9.8  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Equity securities | Level 1          
Fair Value Measurements          
Fair value of plan assets 12.0 9.8 12.0 9.8  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Equity securities | Level 2          
Fair Value Measurements          
Fair value of plan assets 0.0 0.0 0.0 0.0  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Equity securities | Level 3          
Fair Value Measurements          
Fair value of plan assets 0.0 0.0 0.0 0.0  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Government bonds          
Fair Value Measurements          
Fair value of plan assets 3.4 7.3 3.4 7.3  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Government bonds | Level 1          
Fair Value Measurements          
Fair value of plan assets 3.4 7.3 3.4 7.3  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Government bonds | Level 2          
Fair Value Measurements          
Fair value of plan assets 0.0 0.0 0.0 0.0  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Government bonds | Level 3          
Fair Value Measurements          
Fair value of plan assets 0.0 0.0 0.0 0.0  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Corporate bonds          
Fair Value Measurements          
Fair value of plan assets 27.8 18.6 27.8 18.6  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Corporate bonds | Level 1          
Fair Value Measurements          
Fair value of plan assets 0.0 0.0 0.0 0.0  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Corporate bonds | Level 2          
Fair Value Measurements          
Fair value of plan assets 27.8 18.6 27.8 18.6  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Corporate bonds | Level 3          
Fair Value Measurements          
Fair value of plan assets 0.0 0.0 0.0 0.0  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Real estate and real estate funds          
Fair Value Measurements          
Fair value of plan assets 3.4 6.5 3.4 6.5  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Real estate and real estate funds | Level 1          
Fair Value Measurements          
Fair value of plan assets 0.0 0.0 0.0 0.0  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Real estate and real estate funds | Level 2          
Fair Value Measurements          
Fair value of plan assets 0.0 0.0 0.0 0.0  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Real estate and real estate funds | Level 3          
Fair Value Measurements          
Fair value of plan assets 3.4 6.5 3.4 6.5  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Other          
Fair Value Measurements          
Fair value of plan assets 2.5 1.4 2.5 1.4  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Other | Level 1          
Fair Value Measurements          
Fair value of plan assets 0.0 0.0 0.0 0.0  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Other | Level 2          
Fair Value Measurements          
Fair value of plan assets 2.5 1.4 2.5 1.4  
Foreign Plan | Estimate of Fair Value Measurement [Member] | Other | Level 3          
Fair Value Measurements          
Fair value of plan assets 0.0 0.0 $ 0.0 $ 0.0  
United States          
Fair Value Measurements          
Defined Benefit Plan, Assumptions Used Calculating Net Periodic Benefit Cost, Discount Rate     5.40% 5.40% 3.00%
Defined Benefit Plan, Benefit Obligation, Actuarial Gain (Loss)     $ (1.5) $ 9.1  
Employee and employer contributions     1.7 2.0  
Defined Benefit Plan, Assumptions Used Calculating Net Periodic Benefit Cost, Rate of Compensation Increase         3.00%
Fair value of plan assets 0.0 219.2 0.0 219.2 $ 225.4
Estimated Future Benefit Payments          
2025 1.7   1.7    
2026 1.7   1.7    
2027 1.7   1.7    
2028 1.6   1.6    
2029 1.6   1.6    
2030-2034 7.1   7.1    
Defined Benefit Plan, Benefit Obligation, Business Combination     0.0 0.0  
Defined Benefit Plan, Plan Assets, Payment for Settlement 0.0 0.0      
United States | Common Collective Trusts          
Fair Value Measurements          
Fair value of plan assets 0.0 144.5 0.0 144.5  
United States | Cash equivalents          
Fair Value Measurements          
Fair value of plan assets $ 0.0 $ 74.7 $ 0.0 $ 74.7