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Stock-Based Compensation | 6 Months Ended
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Jun. 30, 2019
Stock-Based Compensation |
Stock-Based Compensation | 9. Stock-Based Compensation ​ The Company issued 89,053 and 115,422 shares of restricted stock and deferred shares during the first six months of 2019 and 2018, respectively. The company grants these awards to key employees and stock awards to non-employee members of the Company’s Board of Directors under the 2004 Stock Incentive Plan. Stock awards to employees typically vest over a three-year period and awards to non-employee members of the Company’s Board of Directors vest immediately. ​ The Company also grants performance stock units to key employees under the 2004 Stock Incentive Plan. Performance stock units cliff vest at the end of a three-year performance period with the number of shares of the Company’s Class A common stock awarded to each performance stock unit recipient determined based on the Company’s performance relative to certain performance goals set at the time the performance stock units were granted. The performance stock units are amortized to expense over the vesting period, and based on the Company’s performance relative to the performance goals, which may be adjusted with changes to the related expense recorded in the period of adjustment. If the performance goals are not met, no awards are earned and previously recognized compensation expense is reversed. The Company granted 82,898 and 94,215 performance stock units during the first six months of 2019 and 2018, respectively. ​ Under the Management Stock Purchase Plan (“MSPP”) the Company granted 37,486 restricted stock units (“RSUs”) and 36,208 RSUs during the first six months of 2019 and 2018, respectively. The MSPP allows for the granting of RSUs to key employees. On an annual basis, key employees may elect to receive a portion of their annual incentive compensation in RSUs instead of cash. Participating employees may use up to 50% of their annual incentive bonus to purchase RSUs for a purchase price equal to 80% of the fair market value of the Company’s Class A common stock as of the date of grant. ​ The fair value of each share issued under the Management Stock Purchase Plan is estimated on the date of grant, using the Black-Scholes-Merton Model, based on the following weighted average assumptions: ​
​ | ​ | ​ | ​ | ​ | ​
​ |  | 2019 |  | 2018 |
Expected life (years) | ​ | 3.0 | ​ | 3.0 | ​
Expected stock price volatility |  | 23.3 | % | 24.1 | %
Expected dividend yield |  | 1.1 | % | 1.0 | %
Risk-free interest rate |  | 2.5 | % | 2.4 | %
​ The risk-free interest rate is based upon the U.S. Treasury yield curve at the time of grant for the respective expected life of the RSUs. The expected life (estimated period of time outstanding) of RSUs and volatility were calculated using historical data. The expected dividend yield of stock is the Company’s best estimate of the expected future dividend yield. ​ The above assumptions were used to determine the weighted average grant-date fair value of RSUs granted of $22.16 and $21.80 in 2019 and 2018, respectively. ​ A more detailed description of each of these plans can be found in Note 14 of the Notes to Consolidated Financial Statements in the Company’s Annual Report on Form 10-K for the year ended December 31, 2018.

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