The Company’s stock-based compensation awards are generally granted in the first quarter of the year and consist of stock options, restricted stock units and performance share units. Eligible employees were also granted restricted stock units, during the three month period ended September 30, 2020, that vest ratably over two years, subject to the passage of time and the employee's continued employment during such period. In some instances, such as death, awards may vest concurrently with or following an employee's termination.

Stock-based compensation expense for the six month periods ended June 30, 2022 and 2021 are included in “Cost of sales” and “Selling and administrative expenses” in the Condensed Consolidated Statements of Operations and are as follows.


	For the Three Month Period Ended June 30,				For the Six Month Period Ended June 30,
	2022		2021		2022		2021
Stock-based compensation expense recognized in:
Continuing operations	$	22.4	$	21.5	$	42.2	$	43.1
Discontinued operations	—		8.4		—		10.9
Total stock-based compensation expense	$	22.4	$	29.9	$	42.2	$	54.0

In the six month period ended June 30, 2022, the $42.2 million of stock-based compensation expense included expense for equity awards granted under the 2013 and 2017 Plan of $43.6 million and a decrease in the liability for stock appreciation rights (“SAR”) of $1.4 million. Of the $43.6 million of expense for equity awards granted under the 2013 Plan and 2017 Plan, $25.6 million related to the $150 million equity grant to nearly 16,000 employees worldwide made in the third quarter of 2020 (“All-Employee Equity Grant”).

As of June 30, 2022, there was $85.7 million of total unrecognized compensation expense related to outstanding stock options, restricted stock unit awards and performance stock unit awards.

Stock options are granted to employees with an exercise price equal to the fair value of the Company’s per share common stock on the date of grant. Stock option awards typically vest over four or five years and expire ten years from the date of grant.

A summary of the Company’s stock option (including SARs) activity for the six month period ended June 30, 2022 is presented in the following table (underlying shares in thousands).


	Shares	Weighted-Average Exercise Price (per share)
Stock options outstanding as of December 31, 2021	6,746	$	21.76

Granted	734	53.08
Exercised or settled	(373)	22.94
Forfeited	(103)	36.13
Expired	—	—
Stock options outstanding as of June 30, 2022	7,004	24.77

Vested as of June 30, 2022	4,965	18.24

The following assumptions were used to estimate the fair value of options granted during the six month periods ended June 30, 2022 and 2021 using the Black-Scholes option-pricing model.


	For the Six Month Period Ended June 30,
Assumptions	2022		2021
Expected life of options (in years)	6.3		6.3
Risk-free interest rate	1.9% - 3.1%		0.9% - 1.1%
Assumed volatility	37.1% - 38.3%		39.1% - 39.4%
Expected dividend rate	0.2	%	0.0	%

Restricted stock units are granted to employees and non-employee directors based on the market price of the Company’s common stock on the grant date and recognized in compensation expense over the vesting period. A summary of the Company’s restricted stock unit activity for the six month period ended June 30, 2022 is presented in the following table (underlying shares in thousands).


	Shares	Weighted-Average Grant-Date Fair Value
Non-vested as of December 31, 2021	2,677	$	34.08

Granted	468	53.02
Vested	(454)	31.86
Forfeited	(142)	35.77
Non-vested as of June 30, 2022	2,549	37.86

Performance share units are granted to employees and are subject to a three year performance period. The number of shares issued at the end of the performance period is determined by the Company’s total shareholder return percentile rank versus the S&P 500 index for the three year performance period. The grant date fair value of these awards is determined using a Monte Carlo simulation pricing model and compensation cost is recognized straight-line over a three year period.

A summary of the Company’s performance stock unit activity for the six month period ended June 30, 2022 is presented in the following table (underlying shares in thousands).


	Shares	Weighted-Average Grant-Date Fair Value
Non-vested as of December 31, 2021	393	$	39.89
Granted	175	63.39
Forfeited	(29)	39.61
Non-vested as of June 30, 2022	539	47.54

The following assumptions were used to estimate the fair value of performance share units granted during the six month periods ended June 30, 2022 and 2021 using the Monte Carlo simulation pricing model.


	For the Six Month Period Ended June 30,
Assumptions	2022		2021
Expected term (in years)	2.9		2.9
Risk-free interest rate	1.7	%	0.2	%
Assumed volatility	36.4	%	36.9	%
Expected dividend rate	0.2	%	—	%