The Company typically makes its annual grants of equity awards pursuant to actions taken by the Compensation Committee of the Board of Directors at its regularly scheduled first quarter meeting. For the years presented herein, employee awards were made pursuant to the terms of the Company's 2021 Omnibus Incentive Plan (the "2021 Plan") and 2012 Equity and Cash Incentive Plan (the "2012 Plan").

On May 7, 2021, the shareholders approved the 2021 Plan, to replace the 2012 Plan, which otherwise would have terminated according to its terms on May 3, 2022. Upon approval of the 2021 Plan, no additional awards could be granted under the 2012 Plan, and the remaining 4,888,197 shares available for additional award grant purposes became available for issuance under the 2021 Plan. The 2021 Plan provides for stock options and SARs, RSUs, PSAs, cash performance awards, directors' shares and deferred stock units. Under the 2021 Plan, a total of 8,300,000 newly authorized shares of common stock are reserved for issuance, resulting in a total of 13,188,197 authorized shares available for issuance. These shares are subject to adjustments resulting from stock dividends, stock splits, recapitalizations, reorganizations and other similar changes.

Officers and other key employees, as well as non-employee directors, are eligible to participate in the 2021 Plan, and were also eligible under the 2012 Plan which had a ten-year term between May 3, 2012 to May 3, 2022.

Stock-based compensation costs are reported within selling, general and administrative expenses in the consolidated statements of earnings. The following table summarizes the Company's compensation expense relating to all stock-based incentive plans:


	Years Ended December 31,
	2023		2022		2021
Pre-tax stock-based compensation expense	$	31,465	$	30,821	$	31,111
Tax benefit	(3,266)		(2,993)		(2,859)
Total stock-based compensation expense, net of tax	$	28,199	$	27,828	$	28,252

The exercise price per share for SARs is equal to the closing price of the Company's stock on the New York Stock Exchange on the date of grant. New common shares are issued when SARs are exercised. The period during which SARs are exercisable is fixed by the Company's Compensation Committee at the time of grant. Generally, the SARs vest after three years of service and expire at the end of ten years.

In 2023, 2022 and 2021, the Company issued SARs covering 359,715, 335,285 and 413,173 shares, respectively. The fair value of each SAR grant was estimated on the date of grant using a Black-Scholes option-pricing model with the following assumptions:


	2023		2022		2021
Risk-free interest rate	3.91	%	1.86	%	0.59	%
Dividend yield	1.32	%	1.25	%	1.62	%
Expected life (years)	5.4		5.4		5.5
Volatility	30.65	%	29.46	%	30.49	%
Grant price	$153.25		$160.21		$122.73
Fair value per share at date of grant	$47.27		$42.07		$29.08

Expected volatilities are based on Dover's stock price history, including implied volatilities from traded options on Dover stock. The Company uses historical data to estimate SAR exercises and employee termination patterns within the valuation model. The expected life of SARs granted is derived from the output of the option valuation model and represents the average period of time that SARs granted are expected to be outstanding. The interest rate for periods within the contractual life of the awards is based on the U.S. Treasury yield curve in effect at the time of grant.


	SARs
	Number of Shares	Weighted Average Exercise Price		Weighted Average Remaining Contractual Term (Years)	Aggregate Intrinsic Value
Outstanding at January 1, 2023	2,444,542	$	98.70
Granted	359,715	153.25


Forfeited / expired	(65,178)	142.25
Exercised	(329,469)	69.93
Outstanding at December 31, 2023	2,409,610	109.65		5.8	$	108,242

Exercisable at December 31, 2023	1,446,739	$	86.31	4.3	$	97,651

Unrecognized compensation expense related to SARs not yet exercisable was $10,967 at December 31, 2023. This cost is expected to be recognized over a weighted average period of 1.5 years.

Other information regarding the exercise of SARs is listed below:


	2023		2022		2021
Fair value of SARs that became exercisable	$	7,492	$	8,939	$	10,199
Aggregate intrinsic value of SARs exercised	$	26,041	$	11,992	$	62,895

PSAs granted are expensed over the three-year requisite performance and service period. Awards become vested if (1) the Company achieves certain market conditions and (2) the employee remains continuously employed by the Company during the performance period. Partial vesting may occur after separation from service in the case of certain terminations not for cause and for retirements.

The PSAs granted are market condition awards as attainment is based on Dover's performance relative to its peer group (companies listed under the S&P 500 Industrials sector) for the relevant performance period. The performance period and vesting period for these awards is approximately three years. These awards were valued on the date of grant using the Monte Carlo simulation model (a binomial lattice-based valuation model), and are generally recognized ratably over the vesting period. The fair value is not subject to change based on future market conditions. The assumptions used in determining the fair value of the PSAs granted were as follows:


	2023		2022		2021
Risk-free interest rate	4.28	%	1.68	%	0.19	%
Dividend yield	1.32	%	1.25	%	1.62	%
Expected life (years)	2.9		2.9		2.9
Volatility	27.30	%	31.10	%	31.90	%

Grant price	$153.25		$160.21		$122.73
Fair value per share at date of grant	$249.48		$196.40		$148.29


	Number of Shares	Weighted Average Grant-Date Fair Value
Unvested at January 1, 2023	85,807	$	170.03
Granted	43,656	249.48


Forfeited	(7,360)	197.65
Vested	(44,342)	148.29
Unvested at December 31, 2023	77,761	$	224.42

The Company also has restricted stock authorized for grant. Common stock of the Company may be granted at no cost to certain officers and key employees. In general, restrictions limit the sale or transfer of these shares during a three-year period, and restrictions lapse proportionately over the three-year period. The Company granted 91,439, 79,556 and 87,177 of RSUs in 2023, 2022 and 2021, respectively. The fair value of these awards was determined using Dover's closing stock price on the date of grant, which was $153.25, $160.21, and $122.73 in 2023, 2022 and 2021, respectively.

A summary of activity for RSUs for the year ended December 31, 2023 is as follows:


	Number of Shares	Weighted Average Grant-Date Fair Value
Unvested at January 1, 2023	147,676	$	135.98
Granted	91,439	153.25


Forfeited	(12,513)	148.95
Vested	(73,628)	133.83
Unvested at December 31, 2023	152,974	$	145.45