The Company has established various plans under which it is authorized to grant restricted stock, restricted stock units, stock options, and stock appreciation rights. The Company may also grant cash awards that can be notionally invested in one or more specified measurement funds, including the Company’s common stock. Awards granted under the Company’s share-based incentive plans typically participate in any dividends declared, but such amounts are deferred until delivery of the shares and are forfeitable if the requisite service is not satisfied. Dividends may accrue in cash or may be reinvested in the Company’s common stock.

The excess tax (deficiency) benefit recognized from share-based incentive plans was $(3.9) million, $(0.2) million, and $1.8 million, for the years ended December 31, 2020, 2021, and 2022, respectively.

As of December 31, 2021, the Company had unrecognized share-based compensation expense of $70.9 million. As of December 31, 2022, the Company had unrecognized share-based compensation of $64.7 million, which will be recognized over a weighted average period of approximately two years (assuming no forfeitures).

The following table summarizes transactions in the Company’s restricted stock units:


	Restricted Stock Units		Weighted Average Grant Date Value
Unvested units—December 31, 2021	1.1		$	95.03
Units granted	0.4		129.46
Units vested	(0.4)		99.38
Units forfeited	(0.0	)	103.77
Performance condition changes	0.0		132.03
Unvested units—December 31, 2022	1.1		$	106.88

The Company granted restricted stock units with fair values of $31.8 million, $32.3 million, and $47.1 million for the years ended December 31, 2020, 2021, and 2022, respectively. These restricted stock units were valued based on the closing price of the Company’s common stock on the grant date and the number of shares expected to vest. Restricted stock units containing vesting conditions generally require service over a period of three years to four years and may also require the satisfaction of certain performance conditions. For awards with performance conditions, the number of restricted stock units expected to vest may change over time depending upon the performance level achieved.

The total fair value of shares vested was $24.1 million, $51.7 million, and $54.6 million during the years ended December 31, 2020, 2021, and 2022, respectively. As of December 31, 2022, the Company had 2.7 million shares available for grant under its plans.

The following table summarizes transactions in the Company’s stock options:


	Stock Options		Weighted Average Exercise Price		Weighted Average Remaining Contractual Life (Years)
Unexercised options outstanding—December 31, 2021	3.2		$	77.39
Options granted	0.0		129.17
Options exercised	(0.0	)	114.09
Options forfeited	(0.0	)	166.15
Options expired	(0.0	)	207.63
Performance condition changes	0.0		131.07
Unexercised options outstanding—December 31, 2022	3.2		$	76.81	3.7
Exercisable at December 31, 2022	0.0		$	121.12	3.0

The Company granted stock options with fair values of $4.4 million, $2.0 million, and $1.8 million for the years ended December 31, 2020, 2021, and 2022, respectively. Stock options generally vest over a period of three years to five years and expire seven years after the grant date. All stock options have been granted with exercise prices equal to the closing price of the Company’s common stock on the grant date. Substantially all of the Company’s outstanding stock options contain both service and performance conditions. For awards with performance conditions, the number of stock options expected to vest may change over time depending upon the performance level achieved.

The Company generally uses treasury stock to settle stock option exercises. The total intrinsic value of stock options exercised during the years ended December 31, 2020, 2021, and 2022 was $0.0 million, $13.4 million, and $1.2 million, respectively. The cash received for stock options exercised was zero, $3.6 million, and $2.6 million during the years ended December 31, 2020, 2021, and 2022, respectively. As of December 31, 2022, the intrinsic value of exercisable stock options outstanding was $1.6 million, and 1.1 million options were available for grant under the Company’s option plans.

The weighted average fair value of stock options was $18.33, $54.19, and $47.84 per option for the years ended December 31, 2020, 2021, and 2022, respectively. The Company uses the Black-Scholes option pricing model to determine the fair value of options. The weighted average grant date assumptions used to estimate the fair value of stock options granted were as follows:


	For the Years Ended December 31,
	2020		2021		2022
Dividend yield	1.6	%	0.0	%	0.0	%
Expected volatility(1)	30.5	%	37.1	%	36.8	%
Risk-free interest rate(2)	0.9	%	1.0	%	1.7	%
Expected life of stock options (in years)(3)	5.7		5.7		5.7
Forfeiture rate	0.0	%	0.0	%	0.0	%

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