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. 2016 Incentive Plan, as amended (“2016 Plan”), and no additional grants will be made from the 2016 Plan. At December 31, 2023, 7.499 shares were available to grant under the 2021 Plan.

Under the Roper Technologies, Inc. Employee Stock Purchase Plan, as amended and restated (“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, 2023, 2022, and 2021 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 approximately 3 years from the grant date and expire 10 years after the grant date. The Company recorded $38.0, $38.1, and $40.4 of compensation expense relating to outstanding options during 2023, 2022, and 2021, respectively, as a component of corporate general and administrative expenses.

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 is based on the U.S. Treasury yield curve in effect at the time of grant for the expected life of the option.

The weighted-average fair value of options granted in 2023, 2022, and 2021 were calculated using the following weighted average assumptions:


	2023	2022	2021
Weighted-average fair value ($)	130.23	116.55	95.17
Risk-free interest rate (%)	3.76	2.19	0.94
Expected option life (years)	5.61	5.63	5.61
Expected volatility (%)	26.05	24.59	25.14
Expected dividend yield (%)	0.63	0.55	0.56

The following table summarizes stock option activities, with respect to the Company’s share-based compensation plans, for the years ended December 31, 2023 and 2022:


	Number of options	Weighted-average exercise price		Weighted-average remaining contractual term (years)	Aggregate intrinsic value
Outstanding at December 31, 2021	3.223	$	287.15
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
Granted	0.383	432.77
Exercised	(0.593)	246.77
Canceled	(0.087)	425.80
Outstanding at December 31, 2023	2.688	340.89		6.00	$	549.1
Exercisable at December 31, 2023	1.763	$	291.74	4.75	$	446.7

At December 31, 2023, there was $53.5 of total unrecognized compensation expense related to nonvested options granted under the Company’s stock-based compensation plans. That cost is expected to be recognized over a weighted average period of 1.86 years. The total intrinsic value of options exercised in 2023, 2022, and 2021 was $133.7, $92.7, and $138.2, respectively. Cash received from option exercises under all plans in 2023, 2022, and 2021 was $146.5, $110.0, and $104.7 respectively.

Restricted Stock Grants – During 2023 and 2022, the Company granted 0.280 and 0.271 shares, respectively, of restricted stock to certain employee and director participants under its stock-based compensation plans. Restricted stock grants generally vest over a period of 1 to 4 years. The Company recorded $83.3, $77.6, and $82.7 of compensation expense related to outstanding shares of restricted stock held by employees and directors during 2023, 2022, and 2021, respectively. A summary of the Company’s nonvested shares activity for 2023 and 2022 is as follows:


	Number of shares	Weighted-average grant date fair value
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
Granted	0.280	439.72
Vested	(0.202)	406.36
Forfeited	(0.083)	434.87
Nonvested at December 31, 2023	0.440	$	431.96

At December 31, 2023, there was $95.9 of total unrecognized compensation expense related to nonvested awards granted to both employees and directors under the Company’s stock-based compensation plans. That cost is expected to be recognized over a weighted average period of 1.73 years.

Employee Stock Purchase Plan – During 2023, 2022, and 2021, participants of the ESPP purchased 0.038, 0.039, and 0.040 shares, respectively, of Roper’s common stock for total consideration of $15.5, $14.3, and $15.1, respectively. All of these shares were purchased from Roper’s treasury shares.