Stock-Based Compensation (Tables)

12 Months Ended

Dec. 31, 2022

Share-based Compensation Arrangement by Share-based Payment Award

Schedule of Compensation Cost for Share-based Payment Arrangements

Compensation expense for the stock based plans, as reported in our consolidated statements of income, is as follows:

	Year Ended December 31
	2022		2021		2020
	(in millions of dollars)
Performance Share Units	$	5.7	$	3.3	$	5.6
Cash Incentive Units	12.8		3.2		—
Restricted Stock Units and Cash-Settled Restricted Stock Units	32.7		25.5		23.9
Stock Success Units	0.9		2.8		0.4
Other	0.6		0.6		0.5
Total Compensation Expense, Before Income Tax	$	52.7	$	35.4	$	30.4
Total Compensation Expense, Net of Income Tax	$	47.3	$	31.1	$	26.1

Performance Share Units

Share-based Compensation Arrangement by Share-based Payment Award

Valuation Assumptions on PSU Grants

The fair value of PSUs is estimated on the date of initial grant using the Monte-Carlo simulation model. Key assumptions used to value PSUs granted during 2020 are as follows:

	Year Ended December 31, 2020
Expected Volatility (based on our and our peer group historical daily stock prices)	23	%
Expected Life (equals the performance period)	3 years
Risk Free Interest Rate (based on U.S. Treasury yields at the date of grant)	0.85	%

Cash Incentive Units (CIUs)

Share-based Compensation Arrangement by Share-based Payment Award

Activity for CIUs

Activity for CIUs classified as a liability is as follows:

		Weighted Average
	Units	Grant Date
	(000s)	Fair Value
Outstanding at December 31, 2021	7,223	$	1.07
Granted	8,024	1.09
Outstanding at December 31, 2022	15,247	1.08

Schedule of Cash-based Payment Award, Cash-incentive Units, Valuation Assumptions

The fair value of CIUs is estimated at each reporting period using the Monte-Carlo simulation model. Key assumptions used to value CIUs granted during current year are as follows:

	Year Ended December 31
	2022		2021
Expected Volatility (based on our and our peer group historical daily stock prices)	30	%	50	%
Expected Life (equals the performance period)	3 years		3 years
Risk Free Interest Rate (based on U.S. Treasury yields at the date of grant)	4.26	%	0.71	%

Restricted Stock Units (RSUs)

Share-based Compensation Arrangement by Share-based Payment Award

Activity for Restricted Stock Units

Activity for RSUs classified as equity is as follows:

		Weighted Average
	Shares	Grant Date
	(000s)	Fair Value
Outstanding at December 31, 2021	2,016	$	26.63
Granted	1,323	28.21
Vested	(1,018)	27.51
Forfeited	(139)	26.19
Outstanding at December 31, 2022	2,182	27.20

Cash Settled RSUs

Share-based Compensation Arrangement by Share-based Payment Award

Share-based Payment Arrangement, Cash-Settled Restricted Stock Units, Activity

Activity for cash-settled RSUs classified as a liability is as follows:

		Weighted Average
	Shares	Grant Date
	(000s)	Fair Value
Outstanding at December 31, 2021	46	$	23.31
Vested	(23)	23.31
Outstanding at December 31, 2022	23	23.31