Stock-based Compensation (Tables)

12 Months Ended

Dec. 31, 2024

Share-based Compensation Arrangement by Share-based Payment Award [Line Items]

Summary of Weighted-Average Assumptions using Monte Carlo simulation model

For the stock-options valued using the Black-Scholes option-pricing model, we used the following weighted-average assumptions:

	Time-based stock options
	2024			2023			2022
Expected term to exercise (years)		4.0			4.0			4.0
Expected volatility		29.5	%		34.6	%		35.3	%
Risk-free interest rate		4.3	%		4.4	%		4.0	%
Expected dividend yield		1.5	%		1.4	%		1.6	%

Schedule of Stock-Based Compensation Expense Recognized

The amount of stock-based compensation expense recognized in our Consolidated Statements of Comprehensive Income for the years ended December 31, 2024, 2023 and 2022 was as follows (in millions):

	Year Ended December 31,
	2024						2023						2022
Consolidated Statements of Comprehensive Income Classification	Options		RSUs, PSUs		Total		Options		RSUs, PSUs		Total		Options		RSUs, PSUs			Total
Cost of software-enabled services	$	27.8	$	43.1	$	70.9	$	34.4	$	22.6	$	57.0	$	47.2	$	(1.1	)	$	46.1
Cost of license, maintenance and other related		3.2	4.8			8.0		4.5		2.3		6.8		5.6		(0.1	)		5.5
Total cost of revenues		31.0		47.9		78.9		38.9		24.9		63.8		52.8		(1.2	)		51.6
Selling and marketing	17.1		18.3			35.4	19.7			9.3		29.0	24.2			(1.3	)		22.9
Research and development	12.2		17.6			29.8	13.9			7.5		21.4	17.2			(0.6	)		16.6
General and administrative		24.0	35.2			59.2	28.1			17.1		45.2	35.1			(1.4	)		33.7
Total operating expenses		53.3		71.1		124.4		61.7		33.9		95.6		76.5		(3.3	)		73.2
Total stock-based compensation expense	$	84.3	$	119.0	$	203.3	$	100.6	$	58.8	$	159.4	$	129.3	$	(4.5	)	$	124.8

Summary of Stock Option and SAR Activity as well as RSU Activity

The following table summarizes stock option and SAR activity as well as RSU and PSU activity as of and for the years ended December 31, 2024, 2023 and 2022 (share data in millions):

	Stock Options and SARs					PSUs and RSUs
	Shares			Weighted-Average Exercise Price		Shares			Weighted-Average Grant Date Fair Value
Outstanding at December 31, 2021		44.9		$	55.31		0.4		$	75.03
Granted		3.2		$	51.45		3.1		$	55.61
Cancelled/forfeited		(1.6	)	$	71.50		(0.1	)	$	72.47
Exercised		(2.9	)	$	32.60		—		$	—
Outstanding at December 31, 2022		43.6		$	55.91		3.4		$	58.71
Granted		0.6		$	58.75		1.4		$	58.54
Cancelled/forfeited		(1.9	)	$	68.89		(0.6	)	$	66.09
Exercised		(3.5	)	$	33.49		—		$	—
Vested		—		$	—		(0.7	)	$	52.72
Outstanding at December 31, 2023		38.8		$	57.38		3.5		$	59.04
Granted		2.0		$	65.83		3.5		$	65.04
Cancelled/forfeited		(1.6	)	$	71.97		(1.1	)	$	67.61
Exercised		(7.9	)	$	45.36		—		$	—
Vested		—		$	—		(1.1	)	$	54.77
Outstanding at December 31, 2024		31.3		$	60.22		4.8		$	62.69

Summary of Vested Stock Options and SARs Outstanding that are Currently Exercisable and Stock Options and SARs Outstanding that are Expected to Vest

The following table summarizes information about vested stock options and SARs outstanding that are currently exercisable and stock options and SARs outstanding that are exercisable and expected to vest at December 31, 2024:

Outstanding, Vested Stock Options and SARs Currently Exercisable

Outstanding Stock Options and SARs Exercisable and Expected to Vest

Weighted-

Weighted-

Weighted-

Average

Weighted-

Average

Average

Aggregate

Remaining

Average

Aggregate

Remaining

Exercise

Intrinsic

Contractual

Exercise

Intrinsic

Contractual

Shares

Price

Value

Term

Shares

Price

Value

Term

(In millions)

(In millions)

(Years)

(In millions)

(In millions)

(Years)

23.5

$

56.53

$

466.4

4.70

30.7

$

59.65

$

524.5

5.43

Performance Based Stock Units [Member]

Share-based Compensation Arrangement by Share-based Payment Award [Line Items]

Summary of Weighted-Average Assumptions using Monte Carlo simulation model

For the PSUs with a market condition valued using the Monte Carlo simulation model, we used the following weighted-average assumptions:

	PSUs
	2024			2023
Expected life (years)		2.9		2.8
Expected volatility		23.9	%		27.4	%
Risk-free interest rate		4.5	%		4.6	%
Expected dividend yield		1.5	%		1.4	%