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Equity Incentive Program | 3 Months Ended
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Mar. 31, 2025
Share-Based Payment Arrangement [Abstract] |
Equity Incentive Program | 13. Equity Incentive Program The Company typically makes its annual grants of equity awards pursuant to actions taken by the Compensation Committee of the Board of Directors at its regularly scheduled first quarter meeting. During the three months ended March 31, 2025, the Company issued stock-settled appreciation rights ("SARs") covering 282,917 shares, performance share awards ("PSAs") of 34,458 and restricted stock units ("RSUs") of 57,614. During the three months ended March 31, 2024, the Company issued SARs covering 348,324 shares, PSAs of 42,536 and RSUs of 79,821. The Company uses the Black-Scholes option pricing model to determine the fair value of each SAR on the date of grant. Expected volatilities are based on Dover's stock price history, including implied volatilities from traded options on Dover stock. The Company uses historical data to estimate SAR exercise and employee termination patterns within the valuation model. The expected life of SARs granted is derived from the output of the option valuation model and represents the average period of time that SARs granted are expected to be outstanding. The interest rate for periods within the contractual life of the awards is based on the U.S. Treasury yield curve in effect at the time of grant. The assumptions used in determining the fair value of the SARs awarded during the respective periods were as follows:
| SARs
| 2025 |  | 2024
Risk-free interest rate | 4.35 | % |  | 4.13 | %
Dividend yield | 1.02 | % |  | 1.28 | %
Expected life (years) | 5.5 |  | 5.5
Volatility | 30.50 | % |  | 31.32 | %
Grant price | $202.33 |  | $160.11
Fair value per share at date of grant | $66.39 |  | $51.17
The PSAs granted in 2025 and 2024 vest based on the attainment of two equally weighted measures: (i) Dover’s performance relative to established internal metrics (performance condition) and (ii) Dover's performance relative to its peer group (companies listed under the S&P 500 Industrials sector; market condition). The grant date fair value of the performance condition portion is determined using Dover’s closing stock price at the date of grant and the amount of expense recognized over the vesting period is subject to adjustment based on the expected attainment of the performance condition. The fair value per share at the date of grant for the 2025 performance condition portion is $202.33. The grant date fair value of the 2025 and 2024 market condition portion is determined using the Monte Carlo simulation model. The amount of expense recognized over the vesting period is not subject to change based on future market conditions. The assumptions used in the Monte Carlo model to determine the fair value of the PSAs granted in the respective periods were as follows:
| PSAs
| 2025 |  | 2024
Risk-free interest rate | 4.21 | % |  | 4.37 | %
Dividend yield | 1.02 | % |  | 1.15 | %
Expected life (years) | 2.9 |  | 2.8
Volatility | 23.10 | % |  | 23.30 | %
Grant price | $202.33 |  | $177.19
Fair value per share at date of grant | $318.38 |  | $287.62
The performance and vesting periods for all 2025 and 2024 PSAs is three years. The Company also has granted RSUs, and the fair value of these awards was determined using Dover's closing stock price on the date of grant, which was $202.33 and $160.11 for RSUs granted in 2025 and 2024, respectively. Stock-based compensation is reported within selling, general and administrative expenses in the condensed consolidated statements of earnings. The following table summarizes the Company’s compensation expense relating to all stock-based incentive plans:
| Three Months Ended March 31, |  |
| 2025 |  | 2024 |  |  |  |
Pre-tax stock-based compensation expense | $ | 23,874 |  |  | $ | 14,690 |  |  |  |  |
Tax benefit | (2,504) |  |  | (1,600) |  |  |  |  |
Total stock-based compensation expense, net of tax | $ | 21,370 |  |  | $ | 13,090 |  |  |  |  |
For the three months ended March 31, 2025, there was no pre-tax stock-based compensation expense attributable to discontinued operations and for the three months ended March 31, 2024, there was $469 of expense. These expenses were included within stock-based compensation expense in the condensed consolidated statements of stockholders' equity. See Note 4 — Discontinued and Disposed Operations for further details.

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