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Equity Incentive Program
 9 Months Ended
Sep. 30, 2016
Share-based Compensation [Abstract]  
Share-based Compensation
11. 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. During the first and second quarters of 2016, the Company issued stock-settled appreciation rights ("SARs") covering 1,346,354 shares, performance share awards of 79,561 and restricted stock units of 244,707.

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 assumptions used in determining the fair value of the SARs awarded during the respective periods are as follows:
 
SARs
 
2016
 
2015
Risk-free interest rate
1.05
%
 
1.51
%
Dividend yield
3.09
%
 
2.24
%
Expected life (years)
4.6

 
5.1

Volatility
26.17
%
 
27.19
%
 
 
 
 
Grant price
$
57.25

 
$
73.28

Fair value per share at date of grant
$
9.25

 
$
14.55



The performance share awards granted in 2016 and 2015 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 and administrative expenses in the unaudited 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 2016 and 2015 is as follows for the nine months ended September 30, 2016:
 
Performance shares
 
2016
 
2015
Fair value per share at date of grant
$
57.25

 
$
73.28

Average attainment rate reflected in expense
20.38
%
 
31.78
%

Stock-based compensation is reported within selling and administrative expenses in the accompanying unaudited Condensed Consolidated Statements of Earnings. The following table summarizes the Company’s compensation expense relating to all stock-based incentive plans:
 
Three Months Ended September 30,
 
Nine Months Ended September 30,
 
2016
 
2015
 
2016
 
2015
Pre-tax stock-based compensation expense
$
3,431

 
$
6,674

 
$
17,791

 
$
25,525

Tax benefit
(1,192
)
 
(2,368
)
 
(6,272
)
 
(9,049
)
Total stock-based compensation expense, net of tax
$
2,239

 
$
4,306

 
$
11,519

 
$
16,476