| Schedule of Fair Value Information for Stock Options and Stock Appreciation Rights |
The following table summarizes fair value information for stock options and stock appreciation rights:
| | | | | | | | | | | | | | | | | | | | | | | 2024 (1) | | 2023 (1) | | 2022 (1) | | Stock options and stock appreciation rights weighted-average fair value per award | | $ | 14.84 | | | $ | 11.64 | | | $ | 10.68 | | | Assumptions: | | | | | | | | Volatility | | 30.6% to 31.7% | | 30.9% | | 30.8% to 31.3% | | | | | | | | | Expected term (in years) | | 5.6 to 7.8 | | 5.8 | | 6.1 | | Expected dividend yield | | 1.8% | | 1.8% | | 1.5% | | Range of risk-free rates | | 4.0% to 4.3% | | 3.6% | | 1.7% to 3.0% |
(1) Carrier has limited historical trading data and used peer group data to estimate expected volatility for the 2024, 2023 and 2022 awards.
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| Schedule of Share-based Payment Arrangement, Activity |
Changes in stock options and stock appreciation rights outstanding were as follows:
| | | | | | | | | | | | | | | | | | | | | | | | | Shares Subject to Option
(in thousands) | | Weighted-Average Exercise Price | | Aggregate Intrinsic Value
(in millions) | | Weighted- Average Remaining Life
(in years) | | As of December 31, 2021 | 32,441 | | | $ | 22.02 | | | | | | | Granted | 2,715 | | | $ | 47.72 | | | | | | | Exercised | (3,495) | | | $ | 17.76 | | | | | | | Cancelled | (883) | | | $ | 30.33 | | | | | | | As of December 31, 2022 | 30,778 | | | $ | 24.53 | | | | | | | Granted | 3,494 | | | $ | 46.13 | | | | | | | Exercised | (8,432) | | | $ | 20.48 | | | | | | | Cancelled | (769) | | | $ | 42.94 | | | | | | | As of December 31, 2023 | 25,071 | | | $ | 28.34 | | | | | | | Granted | 4,187 | | | $ | 56.46 | | | | | | | Exercised | (8,041) | | | $ | 23.21 | | | | | | | Cancelled | (430) | | | $ | 50.77 | | | | | | | Outstanding as of December 31, 2024 | 20,787 | | | $ | 35.52 | | | $ | 681 | | | 5.8 | | | | | | | | | | Exercisable as of December 31, 2024 | 12,746 | | | $ | 25.48 | | | $ | 545 | | | 4.1 |
Changes in restricted stock units were as follows:
| | | | | | | | | | | | | RSUs (in thousands) | | Weighted-Average Grant Date Fair Value | | Outstanding and unvested as of December 31, 2021 | 3,570 | | | $ | 23.33 | | | Granted | 555 | | | $ | 41.88 | | | Vested | (1,915) | | | $ | 20.85 | | | Cancelled | (143) | | | $ | 32.92 | | | Outstanding and unvested as of December 31, 2022 | 2,067 | | | $ | 29.87 | | | Granted | 577 | | | $ | 45.71 | | | Vested | (1,140) | | | $ | 26.09 | | | Cancelled | (161) | | | $ | 35.09 | | | Outstanding and unvested as of December 31, 2023 | 1,343 | | | $ | 39.22 | | | Granted | 264 | | | $ | 59.88 | | | Vested | (448) | | | $ | 38.17 | | | Cancelled | (68) | | | $ | 49.14 | | | Outstanding and unvested as of December 31, 2024 | 1,091 | | | $ | 43.94 | |
Changes in PSUs were as follows:
| | | | | | | | | | | | | PSUs (in thousands) | | Weighted-Average Grant Date Fair Value | Outstanding and unvested as of December 31, 2021 | 1,421 | | | $ | 30.75 | | | Granted | 653 | | | $ | 46.93 | | | Vested | (5) | | | $ | 41.81 | | | Forfeited | (139) | | | $ | 35.45 | | Outstanding and unvested as of December 31, 2022 | 1,930 | | | $ | 35.86 | | | Granted | 902 | | | $ | 47.93 | | | Vested | (607) | | | $ | 18.23 | | | Forfeited | (183) | | | $ | 46.52 | | Outstanding and unvested as of December 31, 2023 | 2,042 | | | $ | 45.47 | | | Granted | 1,741 | | | $ | 50.75 | | | Vested | (1,339) | | | $ | 41.49 | | | Forfeited | (121) | | | $ | 52.56 | | Outstanding and unvested as of December 31, 2024 | 2,323 | | | $ | 51.35 | |
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