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Stock-Based Compensation (Tables) | 12 Months Ended
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Dec. 31, 2022
Share-Based Payment Arrangement [Abstract] |
Schedule of Equity-Based Compensation Plans | Information related to the Company’s equity-based compensation plans in effect as of December 31, 2022 was as follows:
Plan Category |  | Number of Securities to be Issued Upon Exercise of Outstanding Options or Vesting of Share Awards |  |  | Weighted-Average Exercise Price of Outstanding Options |  |  | Number of Securities Remaining Available for Future Issuance Under Equity Compensation Plans |
Equity compensation plans approved by security holders |  |  | 956,284 |  |  | $ | 79.86 |  |  |  | 2,498,048 |
Equity compensation plans not approved by security holders |  |  | — |  |  |  | — |  |  |  | — |
|  |  | 956,284 |  |  | $ | 79.86 |  |  |  | 2,498,048 |
Schedule of Stock Based Compensation Expense | Total stock-based compensation expense was as follows (in millions):
|  | Year Ended December 31, |  |  | Three Months Ended December 31, (transition period) |  |  | Year Ended September 30, |
|  | 2022 |  |  | 2021 |  |  | 2021 |  |  | 2020 |
Stock options |  | $ | 0.3 |  |  | $ | 0.2 |  |  | $ | 1.8 |  |  | $ | 6.8 |
Stock awards (shares and units) |  |  | 25.7 |  |  |  | 3.5 |  |  |  | 19.3 |  |  |  | 15.8 |
Performance share awards |  |  | 2.6 |  |  |  | 0.5 |  |  |  | 6.1 |  |  |  | 6.7 |
Cash-settled stock appreciation rights |  |  | (0.8 | ) |  |  | 0.3 |  |  |  | 1.1 |  |  |  | 0.2 |
Cash-settled restricted stock unit awards |  |  | 0.9 |  |  |  | 0.4 |  |  |  | 1.5 |  |  |  | 0.7 |
Total stock-based compensation cost |  |  | 28.7 |  |  |  | 4.9 |  |  |  | 29.8 |  |  |  | 30.2 |
Income tax benefit recognized for stock-based compensation |  |  | (4.2 | ) |  |  | (0.8 | ) |  |  | (4.4 | ) |  |  | (3.6 | )
Stock-based compensation cost, net of tax |  | $ | 24.5 |  |  | $ | 4.1 |  |  | $ | 25.4 |  |  | $ | 26.6 |
Schedule of Stock Option Activity | Stock Options — A summary of the Company’s stock option activity is as follows:
|  | Year Ended December 31, |  |  | Three Months Ended December 31, (transition period) |  |  | Year Ended September 30, |
|  | 2022 |  |  | 2021 |  |  | 2021 |  |  | 2020 |
|  | Options |  |  | Weighted- Average Exercise Price |  |  | Options |  |  | Weighted- Average Exercise Price |  |  | Options |  |  | Weighted- Average Exercise Price |  |  | Options |  |  | Weighted- Average Exercise Price |
Outstanding, beginning of period |  |  | 433,026 |  |  | $ | 78.37 |  |  |  | 471,676 |  |  | $ | 77.96 |  |  |  | 1,083,402 |  |  | $ | 74.38 |  |  |  | 1,328,390 |  |  | $ | 62.62 |
Granted |  |  | — |  |  |  | — |  |  |  | — |  |  |  | — |  |  |  | — |  |  |  | — |  |  |  | 301,025 |  |  |  | 90.28 |
Forfeited |  |  | (4,170 | ) |  |  | 90.28 |  |  |  | (2,002 | ) |  |  | 85.04 |  |  |  | (8,065 | ) |  |  | 81.40 |  |  |  | (40,965 | ) |  |  | 79.00 |
Expired |  |  | (4,583 | ) |  |  | 84.67 |  |  |  | — |  |  |  | — |  |  |  | (3,999 | ) |  |  | 86.59 |  |  |  | (5,869 | ) |  |  | 84.25 |
Exercised |  |  | (47,504 | ) |  |  | 64.90 |  |  |  | (36,648 | ) |  |  | 72.69 |  |  |  | (599,662 | ) |  |  | 71.38 |  |  |  | (499,179 | ) |  |  | 52.18 |
Outstanding, end of period |  |  | 376,769 |  |  |  | 79.86 |  |  |  | 433,026 |  |  |  | 78.37 |  |  |  | 471,676 |  |  |  | 77.96 |  |  |  | 1,083,402 |  |  |  | 74.38 |
Exercisable, end of period |  |  | 376,769 |  |  |  | 79.86 |  |  |  | 364,403 |  |  |  | 76.13 |  |  |  | 251,049 |  |  |  | 74.73 |  |  |  | 537,241 |  |  |  | 68.16 |
Schedule of Outstanding Stock Options | Stock options outstanding and exercisable as of December 31, 2022 were as follows (in millions, except share and per share amounts):
|  | Outstanding |  |  | Exercisable |
Exercise Prices |  | Options |  |  | Weighted Average Remaining Contractual Life (in years) |  |  | Weighted Average Exercise Price |  |  | Aggregate Intrinsic Value |  |  | Options |  |  | Weighted Average Remaining Contractual Life (in years) |  |  | Weighted Average Exercise Price |  |  | Aggregate Intrinsic Value |
$60.01 - $80.00 |  |  | 153,431 |  |  |  | 4.7 |  |  |  | 66.29 |  |  |  | 3.4 |  |  |  | 153,431 |  |  |  | 4.7 |  |  |  | 66.29 |  |  |  | 3.4 |
$80.01 - $100.00 |  |  | 223,338 |  |  |  | 6.3 |  |  |  | 89.19 |  |  |  | 0.1 |  |  |  | 223,338 |  |  |  | 6.3 |  |  |  | 89.19 |  |  |  | 0.1 |
|  |  | 376,769 |  |  |  | 5.6 |  |  |  | 79.86 |  |  | $ | 3.5 |  |  |  | 376,769 |  |  |  | 5.6 |  |  |  | 79.86 |  |  | $ | 3.5 |
Schedule of Weighted-Average Assumptions Used to Value Options Granted | The following weighted-average assumptions were used in the Black-Scholes valuation model for stock options granted during the year ended September 30, 2020:
Assumptions: |  |  |
Expected term (in years) |  |  | 5.4 |
Expected volatility |  |  | 34.10 | %
Risk-free interest rate |  |  | 1.63 | %
Expected dividend yield |  |  | 1.37 | %
Schedule of Nonvested Stock Activity | Stock Awards — A summary of the Company’s stock award activity is as follows:
|  | Year Ended December 31, |  |  | Three Months Ended December 31, (transition period) |  |  | Year Ended September 30, |
|  | 2022 |  |  | 2021 |  |  | 2021 |  |  | 2020 |
|  | Number of Shares |  |  | Weighted- Average Grant Date Fair Value |  |  | Number of Shares |  |  | Weighted- Average Grant Date Fair Value |  |  | Number of Shares |  |  | Weighted- Average Grant Date Fair Value |  |  | Number of Shares |  |  | Weighted- Average Grant Date Fair Value |
Nonvested, beginning of period |  |  | 308,941 |  |  | $ | 90.10 |  |  |  | 394,888 |  |  | $ | 81.58 |  |  |  | 346,808 |  |  | $ | 79.44 |  |  |  | 411,510 |  |  | $ | 72.66 |
Granted |  |  | 255,375 |  |  |  | 109.66 |  |  |  | 63,800 |  |  |  | 114.89 |  |  |  | 307,025 |  |  |  | 82.80 |  |  |  | 183,725 |  |  |  | 87.82 |
Forfeited |  |  | (26,020 | ) |  |  | 97.24 |  |  |  | (4,428 | ) |  |  | 86.08 |  |  |  | (36,545 | ) |  |  | 78.81 |  |  |  | (27,076 | ) |  |  | 80.57 |
Vested |  |  | (174,635 | ) |  |  | 88.98 |  |  |  | (145,319 | ) |  |  | 77.97 |  |  |  | (222,400 | ) |  |  | 80.39 |  |  |  | (221,351 | ) |  |  | 73.64 |
Nonvested, end of period |  |  | 363,661 |  |  |  | 103.86 |  |  |  | 308,941 |  |  |  | 90.10 |  |  |  | 394,888 |  |  |  | 81.58 |  |  |  | 346,808 |  |  |  | 79.44 |
Schedule of Nonvested Performance-Based Units Activity | Performance Share Awards — A summary of the Company’s performance share awards activity is as follows. There was no activity related to performance share awards during the three months ended December 31, 2021:
|  | Year Ended December 31, |  |  | Year Ended September 30, |
|  | 2022 |  |  | 2021 |  |  | 2020 |
|  | Number of Shares |  |  | Weighted- Average Grant Date Fair Value |  |  | Number of Shares |  |  | Weighted- Average Grant Date Fair Value |  |  | Number of Shares |  |  | Weighted- Average Grant Date Fair Value |
Nonvested, beginning of period |  |  | 72,475 |  |  | $ | 93.62 |  |  |  | 110,450 |  |  | $ | 89.54 |  |  |  | 124,750 |  |  | $ | 84.10 |
Granted |  |  | 57,250 |  |  |  | 126.60 |  |  |  | 86,550 |  |  |  | 86.09 |  |  |  | 55,325 |  |  |  | 109.09 |
Forfeited |  |  | (3,748 | ) |  |  | 114.83 |  |  |  | (52,099 | ) |  |  | 90.03 |  |  |  | (16,615 | ) |  |  | 92.88 |
Performance adjustments |  |  | 369 |  |  |  | 107.45 |  |  |  | 63,843 |  |  |  | 80.45 |  |  |  | 33,941 |  |  |  | 87.44 |
Vested |  |  | (28,746 | ) |  |  | 103.47 |  |  |  | (136,269 | ) |  |  | 80.73 |  |  |  | (86,951 | ) |  |  | 92.73 |
Nonvested, end of period |  |  | 97,600 |  |  |  | 108.20 |  |  |  | 72,475 |  |  |  | 93.62 |  |  |  | 110,450 |  |  |  | 89.54 |
Schedule of Weighted-Average Assumptions to Estimate Grant Date Fair Values | The grant date fair values of the TSR performance share awards were estimated using a Monte Carlo simulation model utilizing the following weighted-average assumptions:
|  | Year Ended December 31, |  |  | Year Ended September 30, |
Total Shareholder Return Performance Shares Granted During |  | 2022 |  |  | 2021 |  |  | 2020 |
Assumptions: |  |  |  |  |  |  |  |  |
Expected term (in years) |  |  | 2.86 |  |  |  | 2.87 |  |  |  | 2.87 |
Expected volatility |  |  | 38.52 | % |  |  | 40.33 | % |  |  | 31.16 | %
Risk-free interest rate |  |  | 1.64 | % |  |  | 0.23 | % |  |  | 1.59 | %

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