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Stock-Based Compensation | 6 Months Ended
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Jun. 30, 2024
Stock-Based Compensation |
Stock-Based Compensation | 7. Stock-Based Compensation ​ The Company granted 44,459 and 42,491 units of deferred stock awards during the first six months of 2024 and 2023, respectively. The Company grants shares of deferred stock awards to key employees and stock awards to non-employee members of the Company’s Board of Directors under the Third Amended and Restated 2004 Stock Incentive Plan (“2004 Stock Incentive Plan”). Deferred stock awards to employees typically vest over a three-year period, and stock 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 performance period set by the Compensation Committee of the Board of Directors at the time of grant, which is currently three years. Upon vesting, the number of shares of the Company’s Class A common stock awarded to each performance stock unit recipient will be determined based on the Company’s performance relative to certain performance goals set at the time the performance stock units were granted. The recipient of a performance stock unit award may earn from zero shares to twice the number of target shares awarded to such recipient. The performance stock units are amortized to expense over the vesting period and, based on the Company’s performance relative to the performance goals, may be adjusted. Changes to the estimated shares expected to vest will result in adjustments to the related share-based compensation expense that will be recorded in the period of change. If the performance goals are not met, no awards are earned and previously recognized compensation expense is reversed. The Company granted 39,085 and 36,076 performance stock units during the first six months of 2024 and 2023, respectively. The performance goals for the performance stock units are based on the compound annual growth rate of the Company’s revenue over the three-year performance period and the Company’s return on invested capital (“ROIC”) for the third year of the performance period. ​ Under the Management Stock Purchase Plan (“MSPP”), the Company granted 20,076 and 26,645 restricted stock units (“RSUs”) during the first six months of 2024 and 2023, 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. RSUs vest either annually over a three-year period from the grant date or upon the third anniversary of the grant date. Receipt of the shares underlying RSUs is deferred for a minimum of three years, or such greater number of years from the date of the grant as is chosen by the employee. ​ The fair value of the discount of each purchased RSU is estimated on the date of grant, using the Black-Scholes-Merton Model, based on the following weighted average assumptions: ​
​ | ​ | ​ | ​ | ​ | ​
​ |  | 2024 |  | 2023 |
Expected life (years) | ​ | 3.0 | ​ | 3.0 | ​
Expected stock price volatility |  | 28.9 | % | 33.7 | %
Expected dividend yield |  | 0.80 | % | 0.80 | %
Risk-free interest rate |  | 4.5 | % | 4.1 | %
​ 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 the discount on RSUs granted in 2024 and 2023 of $68.94 and $57.50, 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, 2023.

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