The Roper Technologies, Inc. 2021 Incentive 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 following table provides information regarding the Company’s stock-based compensation expense:


	Three Months Ended September 30,				Nine Months Ended September 30,
	2022		2021		2022		2021
Stock-based compensation	$	29.6	$	32.0	$	90.8	$	93.5
Tax effect recognized in net earnings from continuing operations	6.2		6.7		19.1		19.6

Stock Options - In the nine months ended September 30, 2022, 0.379 options were granted with a weighted average fair value of $115.91 per option. During the same period in 2021, 0.513 options were granted with a weighted average fair value of $95.04 per option. All options were issued with an exercise price equal to the closing price of Roper’s common stock on the date of grant, as required by the Company’s stock-based compensation plans.

Roper records compensation expense for employee stock options based on the estimated fair value of the options on the date of grant using the Black-Scholes option-pricing model. Historical data is used to estimate the expected price volatility, the expected dividend yield, the expected option life and the expected forfeiture rate. The risk-free rate is based on the U.S. Treasury yield curve in effect at the time of grant for the estimated life of the option.

The following weighted average assumptions were used to estimate the fair value of options granted during current and prior year periods using the Black-Scholes option-pricing model:


	Nine months ended September 30,
	2022	2021
Risk-free interest rate (%)	2.09	0.94
Expected option life (years)	5.63	5.61
Expected volatility (%)	24.54	25.15
Expected dividend yield (%)	0.55	0.56

Cash received from option exercises for the nine months ended September 30, 2022 and 2021 was $80.8 and $81.8, respectively.

Restricted Stock Grants - During the nine months ended September 30, 2022, the Company granted 0.239 shares with a weighted average grant date fair value of $450.49 per restricted share. During the same period in 2021, the Company granted 0.225 shares with a weighted average grant date fair value of $408.07 per restricted share. All grants were issued at grant date fair value.

During the nine months ended September 30, 2022, 0.163 restricted shares vested with a weighted average grant date fair value of $345.79 per restricted share and a weighted average vest date fair value of $449.67 per restricted share.

Employee Stock Purchase Plan - Roper’s employee stock purchase plan (“ESPP”) allows employees in the U.S. and Canada 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 ESPP may be either treasury stock, stock purchased on the open market, or newly issued shares.

During the nine months ended September 30, 2022 and 2021, participants in the ESPP purchased 0.031 and 0.031 shares of Roper’s common stock for total consideration of $11.6 and $11.8, respectively. All shares were purchased from Roper’s treasury shares.