The Roper Technologies, Inc. 2021 Incentive Plan (“2021 Plan”) is a stock-based compensation plan used to grant incentive stock options, nonqualified stock options, restricted stock, stock appreciation rights or equivalent instruments to Roper’s employees, officers, directors and consultants. The 2021 Plan was approved by shareholders at the Annual Meeting of Shareholders on June 14, 2021. The 2021 Plan replaces the Roper Technologies, Inc. Amended and Restated 2016 Incentive Plan (“2016 Plan”), and no additional grants will be made from the 2016 Plan. At December 31, 2022, 8.387 shares were available to grant under the 2021 Plan.

Under the Roper Technologies, Inc., Employee Stock Purchase Plan (“ESPP”), employees in the U.S. and Canada are allowed to designate up to 10% of eligible earnings to purchase Roper’s common stock at a 10% discount on the lower of the closing price of the stock on the first and last day of each quarterly offering period. Common stock sold to employees pursuant to the stock purchase plan may be either treasury stock, stock purchased on the open market, or newly issued shares.

Stock-based compensation expense is not allocated to our reportable segments, which are described further in Note 14. Stock based compensation expense for the years ended December 31, 2022, 2021 and 2020 included as a component of “Selling, general and administrative expenses” was as follows:

Stock Options – Stock options are granted at prices not less than 100% of market value of the underlying stock at the date of grant. Stock options typically vest over a weighted average period of 3 years from the grant date and expire 10 years after the grant date. The Company recorded $38.1, $40.4, and $34.9 of compensation expense relating to outstanding options during 2022, 2021 and 2020, respectively, as a component of general and administrative expenses at Corporate.

The Company estimates the fair value of its option awards using the Black-Scholes option valuation model. The stock volatility for each grant is measured using the weighted-average of historical daily price changes of the Company’s common stock over the most recent period equal to the expected life of the grant. The expected term of options granted is derived from historical data to estimate option exercises and employee forfeitures, and represents the period of time that options granted are expected to be outstanding. The risk-free rate for periods aligns with the expected life of the option is based on the U.S. Treasury yield curve in effect at the time of grant. The weighted-average fair value of options granted in 2022, 2021 and 2020 were calculated using the following weighted-average assumptions:


	2022	2021	2020
Weighted-average fair value ($)	116.55	95.17	63.22
Risk-free interest rate (%)	2.19	0.94	0.81
Average expected option life (years)	5.63	5.61	5.64
Expected volatility (%)	24.59	25.14	20.39
Expected dividend yield (%)	0.55	0.56	0.62


	Number of shares	Weighted-average exercise price per share		Weighted-average contractual term	Aggregate intrinsic value
Outstanding at December 31, 2020	3.366	$	255.32
Granted	0.516	405.20
Exercised	(0.537)	195.07
Canceled	(0.122)	312.97
Outstanding at December 31, 2021	3.223	287.15		6.61	$	659.9
Granted	0.399	452.08
Exercised	(0.460)	239.11
Canceled	(0.177)	359.06
Outstanding at December 31, 2022	2.985	312.34		6.18	$	366.3
Exercisable at December 31, 2022	1.842	$	256.87	4.90	$	322.8


	Outstanding options				Exercisable options
Exercise price	Number	Average exercise price		Average remaining life (years)	Number	Average exercise price
$115.22 - $170.66	0.366	$	153.15	2.1	0.366	$	153.15
$170.67 - $267.22	0.326	199.08		4.0	0.324	198.79
$267.23 - $279.28	0.247	273.07		5.5	0.247	273.07
$279.29 - $316.24	0.296	281.55		5.3	0.289	280.89
$316.25 -$324.71	0.435	323.09		7.2	0.209	323.09
$324.72 - $347.81	0.333	327.22		6.2	0.332	327.19
$347.82 - $398.19	0.160	372.19		7.0	0.069	368.53
$398.20 - $413.85	0.425	403.57		8.2	—	—
$413.86 - $491.86	0.397	453.54		9.2	0.006	450.17
$115.22 - $491.86	2.985	$	312.34	6.2	1.842	$	256.87

At December 31, 2022, there was $51.7 of total unrecognized compensation expense related to nonvested options granted under the Company’s share-based compensation plans. That cost is expected to be recognized over a weighted-average period of 1.84 years. The total intrinsic value of options exercised in 2022, 2021 and 2020 was $92.7, $138.2 and $155.4, respectively. Cash received from option exercises under all plans in 2022, 2021, and 2020 was $110.0, $104.7, and $105.5 respectively.

Restricted Stock Grants – During 2022 and 2021, the Company granted 0.271 and 0.228 shares, respectively, of restricted stock to certain employee and director participants under its share-based compensation plans. Restricted stock grants generally vest over a period of 1 to 4 years. The Company recorded $77.6, $82.7 and $72.6 of compensation expense related to outstanding shares of restricted stock held by employees and directors during 2022, 2021 and 2020, respectively. A summary of the Company’s nonvested shares activity for 2022 and 2021 is as follows:


	Number of shares	Weighted-average grant date fair value
Nonvested at December 31, 2020	0.601	$	320.36
Granted	0.228	409.36
Vested	(0.294)	308.79
Forfeited	(0.037)	350.53
Nonvested at December 31, 2021	0.498	$	365.79
Granted	0.271	446.42
Vested	(0.272)	360.14
Forfeited	(0.052)	386.06
Nonvested at December 31, 2022	0.445	$	416.00

At December 31, 2022, there was $89.4 of total unrecognized compensation expense related to nonvested awards granted to both employees and directors under the Company’s share-based compensation plans. That cost is expected to be recognized over a weighted-average period of 1.7 years.