7. Share-Based Compensation

The Company has share-based compensation plans, which are more fully described in Note 9, Share-Based Compensation, to the Consolidated Financial Statements in the 2015 10-K. During the six months ended June 30, 2016, the Company granted stock appreciation rights, or SARs, subject to service conditions and service and performance conditions, and stock units subject to service conditions.

For the three months ended June 30, 2016 and 2015, share-based compensation expense amounted to $10.7 million and $12.7 million, respectively. For the six months ended June 30, 2016 and 2015, share-based compensation expense amounted to $20.5 million and $23.9 million, respectively. As of June 30, 2016, the total unrecognized compensation cost related to all non-vested stock awards was $70.4 million and the related weighted-average period over which it is expected to be recognized is approximately 1.7 years.

The following tables summarize the activity under all share-based compensation plans for the six months ended June 30, 2016:

The weighted-average grant date fair value of SARs granted during the three months ended June 30, 2016 and 2015 was $29.77 and $19.46, respectively. The weighted-average grant date fair value of SARs granted during the six months ended June 30, 2016 and 2015 was $29.47 and $12.81, respectively. The total intrinsic value of stock options and SARs exercised during the three months ended June 30, 2016 and 2015 was $8.2 million and $2.0 million, respectively. The total intrinsic value of stock options and SARs exercised during the six months ended June 30, 2016 and 2015 was $14.1 million and $19.6 million, respectively.

The total vesting date fair value of stock units which vested during the three months ended June 30, 2016 and 2015 was $1.8 million and $1.0 million, respectively. The total vesting date fair value of stock units which vested during the six months ended June 30, 2016 and 2015 was $1.8 million and $1.0 million, respectively.

The Company recognizes excess tax benefits associated with share-based compensation to shareholders’ equity (deficit) only when realized. When assessing whether excess tax benefits relating to share-based compensation have been realized, the Company follows the with-and-without approach. Under this approach, excess tax benefits related to share-based compensation are not deemed to be realized until after the utilization of all other tax benefits available to the Company, which are also subject to applicable limitations. As of both June 30, 2016 and December 31, 2015, the Company had $25.4 million of unrealized excess tax benefits.