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Stock Based Compensation | 9 Months Ended
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Sep. 30, 2020
Share-based Payment Arrangement [Abstract] |
Stock Based Compensation | Stock Based Compensation The Roper Technologies, Inc. 2016 Incentive Plan (“2016 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,
| 2020 |  | 2019 |  | 2020 |  | 2019
Stock-based compensation | $ | 30.1 |  |  | $ | 26.1 |  |  | $ | 88.3 |  |  | $ | 80.4 |
Tax effect recognized in net earnings | 6.3 |  |  | 5.5 |  |  | 18.5 |  |  | 16.9 |
Stock Options - In the nine months ended September 30, 2020, 0.758 options were granted with a weighted average fair value of $63.01 per option. During the same period in 2019, 0.753 options were granted with a weighted average fair value of $68.05 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 2016 Plan. 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,
| 2020 |  | 2019
Risk-free interest rate (%) | 0.81 |  |  | 2.38 |
Expected option life (years) | 5.64 |  | 5.42
Expected volatility (%) | 20.36 |  |  | 19.22 |
Expected dividend yield (%) | 0.62 |  |  | 0.58 |
Cash received from option exercises for the nine months ended September 30, 2020 and 2019 was $88.9 and $55.8, respectively. Restricted Stock Grants - During the nine months ended September 30, 2020, the Company granted 0.234 shares with a weighted average grant date fair value of $353.68 per restricted share. During the same period in 2019, the Company granted 0.317 shares with a weighted average grant date fair value of $318.46 per restricted share. All grants were issued at grant date fair value. During the nine months ended September 30, 2020, 0.146 restricted shares vested with a weighted average grant date fair value of $259.42 per restricted share and a weighted average vest date fair value of $354.28 per restricted share. Employee Stock Purchase Plan - Roper’s stock purchase plan previously allowed employees in the U.S. and Canada to designate up to 10% of eligible earnings to purchase Roper’s common stock at a 5% discount to the average closing price of the stock at the beginning and end of a 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. We amended the Roper stock purchase plan effective July 1, 2020, which 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 stock purchase plan may be either treasury stock, stock purchased on the open market, or newly issued shares. During the nine months ended September 30, 2020 and 2019, participants in the employee stock purchase plan purchased 0.022 and 0.016 shares of Roper’s common stock for total consideration of $7.3 and $5.2, respectively. All shares were purchased from Roper’s treasury shares.

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- Definition The entire disclosure for share-based payment arrangement. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -URI http://asc.fasb.org/topic&trid=2228938 + Details
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