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Share-Based Compensation
6 Months Ended
Jun. 30, 2015
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]  
Share-Based Compensation
Share-Based Compensation

During the six months ended of 2015, we granted 341,800 stock appreciation rights (“SARs”), 65,850 restricted stock units, 61,740 performance shares, and 5,617 phantom stock units. For the three and six months ended June 30, 2015, total share-based compensation expense was $3.2 million and $6.1 million and the related tax benefits were $1.2 million and $2.3 million. For the three and six months ended June 30, 2014, total share-based compensation expense was $3.1 million and $6.2 million and the related tax benefits were $1.2 million and $2.3 million.
The estimated fair value of our 2015 SARs awards and related underlying assumptions are shown in the table below.
 
2015
Estimated fair value
$
18.16

Quarterly dividend rate
$
0.38

Expected term of stock appreciation rights, in years
4.7

Risk-free interest rate
1.2
%
Dividend yield
2.6
%
Expected stock price volatility
29.2
%
Present value of dividends
$
6.90