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Stock option and award plan: | 12 Months Ended
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Dec. 31, 2024
Stock option and award plan: |
Stock option and award plan: | 8. Stock option and award plan: Incentive award plan The Company grants restricted stock and options for common stock under its award plan, as amended (the “Award Plan”). Stock options granted under the Award Plan generally vest over a four-year period and have a term of ten years. Grants of shares of restricted stock granted under the Award Plan generally vest over periods ranging from three to four years. Compensation expense for all awards is recognized on a straight-line basis over the service period. Awards with graded vesting terms that are subject only to service conditions are recognized on a straight-line basis. Certain option and share grants provide for accelerated vesting if there is a change in control, as defined. For grants of restricted stock, when an employee terminates prior to full vesting the employee retains their vested shares, and the employees’ unvested shares are returned to the Award Plan. For grants of options for common stock, when an employee terminates prior to full vesting, the employee may elect to exercise their vested options for a period of ninety days, and any unvested options are returned to the Award Plan. Shares issued to satisfy awards are provided from the Company’s authorized shares. The vesting of certain shares granted to the Company’s executives is subject to certain performance conditions determined by the Company’s Board of Directors. The vesting of certain shares granted to the Company’s CEO is subject to the total shareholder return of the Company’s common stock compared to the total shareholder return of the Nasdaq Telecommunications Index, the Company’s growth rate in revenue, the Company’s growth rate in cash flow from operating activities,and the Company’s growth rate in earnings before interest and depreciation, as adjusted, with each portion of the CEO’s performance-based equity award subject to a cap and no shares earned if performance with respect to a target is less than zero. The accounting for equity-based compensation expense requires the Company to make estimates and judgments that affect its financial statements. These estimates for stock options include the following: Expected Dividend Yield—The Company uses an expected dividend yield based upon expected annual dividends and the Company’s stock price. Expected Volatility—The Company uses its historical volatility for a period commensurate with the expected term of the option. Risk-Free Interest Rate—The Company uses the zero-coupon US Treasury rate during the quarter having a term that most closely resembles the expected term of the option. Expected Term of the Option—The Company estimates the expected life of the option term by analyzing historical stock option exercises. Forfeiture Rates—The Company estimates its forfeiture rate based on historical data with further consideration given to the class of employees to whom the options or shares were granted. The weighted-average per share grant date fair value of options was $12.95 in 2024, $12.81 in 2023 and $10.73 in 2022. The following assumptions were used for determining the fair value of options granted in the three years ended December 31, 2024: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Years Ended |
​ | ​ | December 31, | ​
Black-Scholes Assumptions |  | 2024 |  | 2023 |  | 2022 |
Dividend yield |  | 6.0 | % | 5.8 | % | 5.9 | %
Expected volatility |  | 34.9 | % | 33.4 | % | 33.1 | %
Risk-free interest rate |  | 4.1 | % | 3.8 | % | 3.0 | %
Expected life of the option term (in years) |  | 4.1 | ​ | 4.1 | ​ | 4.1 | ​
​ Stock option activity under the Company’s Award Plan during the year ended December 31, 2024, was as follows: ​
​ | ​ | ​ | ​ | ​ | ​
​ |  | Number of |  | Weighted-Average
​ |  | Options |  | Exercise Price
Outstanding at December 31, 2023 |  | 198,775 | ​ | $ | 61.97
Granted |  | 120,784 | ​ | $ | 70.21
Cancelled and expired |  | (62,138) | ​ | $ | 66.05
Exercised—intrinsic value $0.5 million; cash received $1.2 million |  | (36,465) | ​ | $ | 60.45
Outstanding at December 31, 2024—$2.7 million intrinsic value and 7.7 years weighted-average remaining contractual term |  | 220,956 | ​ | $ | 65.58
Exercisable at December 31, 2024—$1.5 million intrinsic value and 6.1 years weighted-average remaining contractual term |  | 95,330 | ​ | $ | 62.15
Expected to vest—$2.3 million intrinsic value and 7.4 years weighted-average remaining contractual term |  | 183,864 | ​ | $ | 64.94
​ A summary of the Company’s non-vested restricted stock awards as of December 31, 2024 and the changes during the year ended December 31, 2024 are as follows: ​
​ | ​ | ​ | ​ | ​ | ​
​ | ​ | ​ | ​ | Weighted-Average
​ | ​ | ​ | ​ | Grant Date
Non-vested awards |  | Shares |  | Fair Value
Non-vested at December 31, 2023 |  | 1,261,623 | ​ | $ | 62.89
Granted |  | 672,098 | ​ | $ | 68.58
Vested |  | (315,559) | ​ | $ | 66.11
Forfeited |  | (128,885) | ​ | $ | 66.66
Non-vested at December 31, 2024 |  | 1,489,277 | ​ | $ | 64.45
​ The weighted average per share grant date fair value of restricted stock granted was $68.58 in 2024 (0.7 million shares), $60.05 in 2023 (0.6 million shares) and $66.08 in 2022 (0.4 million shares). The fair value was determined using the quoted market price of the Company’s common stock on the date of grant. Valuations were obtained to determine the fair value for the shares granted to the Company’s CEO that are subject to the total shareholder return of the Company’s common stock compared to the total shareholder return of the Nasdaq Telecommunications Index. ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | Years Ended
​ |  | December 31,
Additional Award Plan Information – Related to Stock Options & Restricted Stock (thousands) |  | 2024 |  | 2023 |  | 2022
Equity-based compensation expense | ​ | $ | 25,738 | ​ | $ | 26,924 | ​ | $ | 24,439
Income tax benefit related to stock options and restricted stock | ​ |  | 2,469 | ​ |  | 3,307 | ​ |  | 2,489
Capitalized compensation expense related to stock options and restricted stock | ​ |  | 3,100 | ​ |  | 3,541 | ​ |  | 2,277
Intrinsic value of stock options exercised | ​ |  | 573 | ​ |  | 456 | ​ |  | 305
Fair value of shares of restricted stock vested | ​ |  | 22,489 | ​ |  | 30,113 | ​ |  | 25,792
​ As of December 31, 2024, there was $48.0 million of total unrecognized compensation cost related to non-vested equity-based compensation awards. That cost is expected to be recognized over a weighted average period of 1.9 years.

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