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Equity Incentive Program
6 Months Ended
Jun. 30, 2019
Share-based Compensation [Abstract]  
Share-based Compensation
14. Equity Incentive Program

The Company typically grants equity awards annually at its regularly scheduled first quarter meeting of the Compensation Committee of the Board of Directors. Additionally, in the second quarter of 2018, the Company granted equity awards to its new President and Chief Executive Officer. During the six months ended June 30, 2019, the Company issued stock-settled appreciation rights ("SARs") covering 615,089 shares, performance share awards of 35,172 and restricted stock units ("RSUs") of 124,929.

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 SARs is based on the U.S. Treasury yield curve in effect at the time of grant.
The range of assumptions used in determining the fair value of the SARs awarded during the respective periods were as follows:
SARs
 20192018
Risk-free interest rate2.51 %2.58 %-2.87 %
Dividend yield2.13 %1.99 %-2.43 %
Expected life (years)5.65.6-5.7
Volatility22.35 %20.95 %-21.20 %
Grant price
$91.20 $79.75 -$82.09 
Fair value per share at date of grant
$17.55 $14.58 -$15.41 

The performance share awards granted in 2019 and 2018 are considered performance condition awards as attainment is based on Dover's performance relative to established internal metrics. The fair value of these awards was determined using Dover's closing stock price on the date of grant. The expected attainment of the internal metrics for these awards is analyzed each reporting period, and the related expense is adjusted based on expected attainment, if that attainment differs from previous estimates. The cumulative effect on current and prior periods of a change in attainment is recognized in selling, general and administrative expenses in the Condensed Consolidated Statements of Earnings in the period of change.  

The fair value and average attainment used in determining stock-based compensation cost for the performance shares issued in 2019 and 2018 were as follows for the six months ended June 30, 2019:
Performance Shares
 20192018
Fair value per share at date of grant
$91.20 $79.75 $82.09 
Average attainment rate reflected in expense240.05%  288.57%  

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.

Stock-based compensation is reported within selling, general and administrative expenses of continuing operations 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 June 30,  Six Months Ended June 30, 
 2019201820192018
Pre-tax stock-based compensation expense (continuing)$8,435 $3,658 $16,617 $10,403 
Tax benefit(498)(817)(1,546)(2,313)
Total stock-based compensation expense, net of tax$7,937 $2,841 $15,071 $8,090 

Stock-based compensation expense attributable to Apergy employees for the three and six months ended June 30, 2018 was $174 and $744, respectively. These costs are reported within earnings from discontinued operations in the Condensed Consolidated Statement of Earnings.