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Stock-Based Compensation (Tables)

12 Months Ended

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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