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Stock Based Compensation | 6 Months Ended
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Jun. 30, 2021
Share-based Payment Arrangement [Abstract] |
Stock Based Compensation | Stock Based Compensation 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. The following table provides information regarding the Company’s stock-based compensation expense:
| Three Months Ended June 30, |  | Six Months Ended June 30,
| 2021 |  | 2020 |  | 2021 |  | 2020
Stock-based compensation | $ | 36.4 |  |  | $ | 30.5 |  |  | $ | 69.3 |  |  | $ | 58.2 |
Tax effect recognized in net earnings | 7.6 |  |  | 6.4 |  |  | 14.6 |  |  | 12.2 |
Stock Options - In the six months ended June 30, 2021, 0.504 options were granted with a weighted average fair value of $94.81 per option. During the same period in 2020, 0.735 options were granted with a weighted average fair value of $62.30 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 2021 Plan and 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:
| Six months ended June 30,
| 2021 |  | 2020
Risk-free interest rate (%) | 0.94 |  |  | 0.83 |
Expected option life (years) | 5.61 |  | 5.64
Expected volatility (%) | 25.16 |  |  | 20.23 |
Expected dividend yield (%) | 0.56 |  |  | 0.62 |
Cash received from option exercises for the six months ended June 30, 2021 and 2020 was $61.1 and $63.0, respectively. Restricted Stock Grants - During the six months ended June 30, 2021, the Company granted 0.216 shares with a weighted average grant date fair value of $406.38 per restricted share. During the same period in 2020, the Company granted 0.191 shares with a weighted average grant date fair value of $344.16 per restricted share. All grants were issued at grant date fair value. During the six months ended June 30, 2021, 0.133 restricted shares vested with a weighted average grant date fair value of $314.99 per restricted share and a weighted average vest date fair value of $399.74 per restricted share. Employee Stock Purchase Plan - Roper’s employee stock purchase plan (“ESPP”) 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 ESPP 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 ESPP may be either treasury stock, stock purchased on the open market, or newly issued shares. During the six months ended June 30, 2021 and 2020, participants in the ESPP purchased 0.022 and 0.014 shares of Roper’s common stock for total consideration of $8.2 and $4.5, respectively. All shares were purchased from Roper’s treasury shares.

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