Stock-based Compensation (Tables)

12 Months Ended

Dec. 31, 2023

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									PSOs
	2023			2022			2021			2021
Expected term to exercise (years)		4.0			4.0			4.0			4.0
Expected volatility		34.6	%		35.3	%		36.4	%		36.3	%
Risk-free interest rate		4.4	%		4.0	%		1.1	%		1.0	%
Expected dividend yield		1.4	%		1.6	%		1.0	%		1.0	%

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, 2023, 2022 and 2021 was as follows (in millions):

	Year Ended December 31,
	2023						2022							2021
Consolidated Statements of Comprehensive Income Classification	Options		RSUs, PSUs		Total		Options, SARs		RSUs, PSUs			Total		Options, SARs		RSUs, PSUs		Total
Cost of software-enabled services	$	34.4	$	22.6	$	57.0	$	47.2	$	(1.1	)	$	46.1	$	39.1	$	3.7	$	42.8
Cost of license, maintenance and other related		4.5	2.3			6.8		5.6		(0.1	)		5.5		5.2	0.1			5.3
Total cost of revenues		38.9		24.9		63.8		52.8		(1.2	)		51.6		44.3		3.8		48.1
Selling and marketing	19.7		9.3			29.0	24.2			(1.3	)		22.9	19.1		1.5			20.6
Research and development	13.9		7.5			21.4	17.2			(0.6	)		16.6	14.2		0.8			15.0
General and administrative	28.1		17.1			45.2	35.1			(1.4	)		33.7	28.4		1.9			30.3
Total operating expenses		61.7		33.9		95.6		76.5		(3.3	)		73.2		61.7		4.2		65.9
Total stock-based compensation expense	$	100.6	$	58.8	$	159.4	$	129.3	$	(4.5	)	$	124.8	$	106.0	$	8.0	$	114.0

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, 2023, 2022 and 2021 (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, 2020		42.7		$	48.16		0.2		$	44.96
Granted	9.5			$	80.24	0.4			$	75.03
Cancelled/forfeited		(2.1	)	$	61.90		—		$	—
Vested		—		$	—		(0.2	)	$	45.59
Exercised		(5.2	)	$	39.23		—		$	—
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

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, 2023:

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)

28.4

$

52.22

$

337.2

5.04

37.8

$

56.76

$

360.0

5.80

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
	2023
Expected life (years)	2.8
Expected volatility		27.4	%
Risk-free interest rate		4.6	%
Expected dividend yield		1.4	%