We may grant restricted stock units, non-qualified stock options and other stock awards to eligible employees. All stock-based awards are approved by the Executive Compensation Committee of the Board of Directors. We settle stock awards with treasury shares. At December 31, 2022, there were 17,217,552 shares available for future grants.

Restricted stock units (RSUs) typically vest ratably over a three-year service period and entitle the holder to shares of common stock as the units vest. The following table summarizes information about RSUs:


	2022			2021
	Shares	Weighted average fair value		Shares	Weighted average fair value
Outstanding - beginning of the year	5,738,293	$	6.95	6,560,372	$	6.27
Granted	5,280,429	4.82		2,100,126	8.36

Vested	(2,221,027)	6.10		(2,504,189)	6.72
Forfeited	(1,599,940)	4.69		(418,016)	6.61
Outstanding - end of the year	7,197,755	$	6.09	5,738,293	$	6.95

The fair value of RSUs is determined based on the stock price on the grant date less the present value of expected dividends. At December 31, 2022, there was $11 million of unrecognized compensation cost related to RSUs that is expected to be recognized over a weighted-average period of 1.6 years. The intrinsic value of RSUs outstanding at December 31, 2022 was $27 million. The fair value of RSUs vested during 2022, 2021 and 2020 was $11 million, $22 million and $6 million, respectively. During 2020, we granted 4,123,544 RSUs at a weighted average fair value of $3.92.

In 2022 and 2021, we granted 158,416 and 121,455 RSUs, respectively, to non-employee directors. These RSUs vest one year from the grant date.

Performance stock units (PSUs) are stock awards where the number of shares ultimately received by the employee is conditional upon the attainment of certain performance targets and total shareholder return relative to peer companies. PSUs vest at the end of a three-year service period. There were no PSU awards granted since 2020 and the award period for the final award granted in 2019 closed in 2022. Awards outstanding at December 31, 2022 represent awards that have been deferred and will be issued at a later date.


	2022			2021
	Shares	Weighted average fair value		Shares	Weighted average fair value
Outstanding - beginning of the year	1,009,091	$	6.60	1,730,002	$	9.31

Vested	(197,471)	6.73		(287,109)	9.33
Forfeited	—	—		(433,802)	9.33

Outstanding - end of the year	811,620	$	9.57	1,009,091	$	6.60

Stock options are granted at an exercise price equal to or greater than the market price of our common stock on the grant date. Options vest ratably over three years and expire ten years from the grant date. At December 31, 2022, there was less than $1 million of unrecognized compensation cost related to stock options that is expected to be recognized over a weighted-average period of 1.3 years. The intrinsic value of options outstanding and exercisable at December 31, 2022 was not significant.


	2022			2021
	Shares	Per share weighted average exercise prices		Shares	Per share weighted average exercise prices
Options outstanding - beginning of the year	11,120,069	$	10.65	12,814,365	$	11.81
Granted	—	—		737,842	8.48
Exercised	—	—		(777,429)	6.11
Canceled	(93,021)	8.09		(604,101)	11.71
Expired	(1,000,000)	18.29		(1,050,608)	25.85
Options outstanding - end of the year	10,027,048	$	9.91	11,120,069	$	10.65
Options exercisable - end of the year	8,912,286	$	10.42	8,853,859	$	11.94

The following table provides additional information about stock options outstanding and exercisable at December 31, 2022:


	Options Outstanding				Options Exercisable
Range of per share exercise prices	Shares	Per share weighted-average exercise price		Weighted-average remaining contractual life	Shares	Per share weighted-average exercise price		Weighted-average remaining contractual life
$3.98 - $7.24	4,605,995	$	5.14	6.5 years	3,905,829	$	5.31	6.4 years
$8.21 - $13.16	3,674,457	$	12.05	5.1 years	3,259,861	$	12.49	4.8 years
$16.82 - $23.94	1,746,596	$	17.94	2.5 years	1,746,596	$	17.94	2.5 years

	10,027,048	$	9.91	5.3 years	8,912,286	$	10.42	5.0 years

The fair value of stock options is determined using a Black-Scholes valuation model and requires assumptions be made regarding the expected stock price volatility, risk-free interest rate, life of the award and dividend yield. The expected stock price volatility is based on historical price changes of our stock. The risk-free interest rate is based on U.S. Treasuries with a term equal to the expected life of the award. The expected life of the award and expected dividend yield are based on historical experience.

The following table lists the weighted average of assumptions used to calculate the fair value of stock options granted:


	Years Ended December 31,
	2021		2020
Expected dividend yield	2.4	%	5.0	%
Expected stock price volatility	70.0	%	43.0	%
Risk-free interest rate	1.1	%	1.5	%
Expected life	7 years		7 years
Weighted-average fair value per option granted	$4.53		$1.01
Fair value of options granted	$3,342		$2,830