We provide equity awards to our employees under the GATX Corporation 2012 Incentive Award Plan, including grants of non-qualified stock options, restricted stock units, performance shares, and phantom stock awards. We previously granted stock appreciation rights under this plan as well; however, no stock appreciation rights were granted in 2022, 2021, or 2020. As of December 31, 2022, 5.4 million shares were authorized under the 2012 Plan and 2.3 million shares were available for future issuance. We recognize compensation expense for our equity awards in selling, general and administrative expenses over the applicable service period of each award. Share-based compensation expense was $12.7 million for 2022, $17.4 million for 2021, and $15.9 million for 2020, and the related tax benefits were $3.2 million for 2022, $4.4 million for 2021, and $4.0 million for 2020.

Stock options and stock appreciation rights entitle the holder to purchase shares of common stock for periods up to seven years from the grant date. Stock appreciation rights entitle the holder to receive the difference between the market price of our common stock at the time of exercise and the exercise price, either in shares of common stock, cash, or a combination thereof, at our discretion. Stock options entitle the holder to purchase shares of our common stock at a specified exercise price. The dividends that accrue on all stock options and stock appreciation rights are paid upon vesting and continue to be paid until the stock options or stock appreciation rights are exercised, canceled, or expire. The exercise price for stock options and stock appreciation rights is equal to the average of the high and low trading prices of our common stock on the date of grant. We recognize compensation expense on a straight-line basis over the vesting period of the award, which is generally three years.

The estimated fair value of a stock option or stock appreciation right is the sum of the value we derive using the Black-Scholes option pricing model and the present value of dividends we expect to pay over the expected term of the award. The Black-Scholes valuation incorporates various assumptions, including expected term, expected volatility, and risk free interest rates. We base the expected term on historical exercise patterns and post-vesting terminations, and we base the expected volatility on the historical volatility of our stock price over a period equal to the expected term. We use risk-free interest rates that are based on the implied yield on recently-issued U.S. Treasury zero-coupon bonds with a term comparable to the expected term. No stock appreciation rights were issued during 2022, 2021, and 2020.


	2022			2021			2020
Weighted-average estimated fair value	$	34.77		$	29.56		$	22.50
Quarterly dividend rate	$	0.52		$	0.50		$	0.48
Expected term of stock options, in years	4.3			4.3			4.2
Risk-free interest rate	1.6		%	0.3		%	1.3		%
Dividend yield	2.0		%	2.2		%	2.5		%
Expected stock price volatility	35.0		%	34.4		%	28.5		%
Present value of dividends	$	8.58		$	8.61		$	7.89


	Number of Stock Options and Stock Appreciation Rights (in thousands)	Weighted-Average Exercise Price
Outstanding at beginning of the year	1,189	$	73.94
Granted	284	103.15
Exercised	(300)	63.07
Forfeited/Cancelled	(172)	94.04
Expired	—	79.89
Outstanding at end of the year	1,001	82.04
Vested and exercisable at end of the year	660	75.00

The following table shows the aggregate intrinsic value of stock options and stock appreciation rights exercised in 2022, 2021, and 2020, and the weighted-average remaining contractual term and aggregate intrinsic value of stock options and stock appreciation rights outstanding and vested as of December 31, 2022:


Stock Options and Stock Appreciation Rights	Weighted-Average Remaining Contractual Term (Years)	Aggregate Intrinsic Value (in millions)

Exercised in 2020		$	7.6
Exercised in 2021		22.5
Exercised in 2022		13.4

Outstanding at December 31, 2022 (a)	3.9	24.3
Vested and exercisable at December 31, 2022	3.1	20.7

Total cash received from employees for exercises of stock options during the years ended December 31, 2022, 2021, and 2020 was $30.9 million, $21.9 million, and $6.6 million. As of December 31, 2022, we had $6.2 million of unrecognized compensation expense related to nonvested stock options, which we expect to recognize over a weighted-average period of 1.8 years.

Restricted stock units entitle the recipient to receive a specified number of restricted shares of common stock upon vesting. Restricted stock units do not carry voting rights and are not transferable prior to the expiration of a specified restriction period, which is generally three years, as determined by the Compensation Committee of the Board of Directors ("Compensation Committee"). We accrue dividends on all restricted stock units and pay those dividends when the awards vest. We recognize compensation expense for these awards over the applicable vesting period.

Performance shares are restricted shares that we grant to key employees for achieving certain strategic objectives. The shares convert to common stock at the end of a specified performance period if predetermined performance goals are achieved, as determined by the Compensation Committee. We estimate the number of shares we expect will vest as a result of actual performance against the performance criteria at the time of grant to determine total compensation expense to be recognized. We reevaluate the estimate annually and adjust total compensation expense for any changes to the estimate of the number of shares we expect to vest. The performance shares granted include an option to settle shares earned in cash upon vesting for certain eligible employees. As a result, these awards are accounted for as liability awards and recorded in other liabilities. The liability and related compensation expense is adjusted to reflect the fair value of the underlying shares at the end of each reporting period. We recognize compensation expense for these awards over the applicable vesting period, which is generally three years.

We value our restricted stock units and performance share awards using the average of the high and low values of our common stock on the grant date of the awards. As of December 31, 2022, there was $8.3 million of unrecognized compensation expense related to these awards, which we expect to be recognized over a weighted-average period of 1.8 years.


	Number of Share Units Outstanding (in thousands)	Weighted-Average Grant-Date Fair Value
Restricted Stock Units:
Nonvested at beginning of the year	107	$	79.37
Granted	42	103.37
Vested	(36)	72.50
Forfeited	(5)	92.63
Nonvested at end of the year	108	90.47
Performance Shares:
Nonvested at beginning of the year	88	$	83.79
Granted	62	101.03
Net decrease due to estimated performance	(4)	84.18
Vested	(40)	80.63
Forfeited	(33)	96.27
Nonvested at end of the year	73	94.79

We grant awards to non-employee directors as a component of their compensation for service on our board of directors. Prior to April 2022, these awards were in the form of phantom stock. In accordance with the terms of the phantom stock awards, each director is credited with a quantity of units that equate to, but are not, common shares. Phantom stock awards are dividend participating, and all dividends are reinvested in additional phantom shares at the average of the high and low trading prices of our stock on the dividend payment date. At the expiration of each director’s service on the board of directors, or in accordance with his or her deferral election, whole units of phantom stock will be settled with shares of common stock and fractional units will be paid in cash. In 2022, we granted 11,133 units of phantom stock and there were 240,463 units outstanding as of December 31, 2022.

Effective January 1, 2022, our plan was amended, and these awards are now in the form of restricted stock units. Restricted stock awards are dividend participating and, for awards elected to defer, dividends are reinvested in additional restricted stock shares at the average of the high and low trading prices of our stock on the dividend payment date. At the expiration of each director’s service on the board of directors, or in accordance with the deferral election, whole units of restricted stock will be settled with shares of common stock and fractional units will be paid in cash. In 2022, we granted 7,896 restricted stock units to directors and there were 9,044 units outstanding as of December 31, 2022.