Vested (in USD per share)

[Table of Contents](#i90c0b6fc77a94e699123e3f505f83787_7)9. Stock Based Compensation (continued)The weighted-average fair value per option at the date of grant during the six months ended June 30, 2022 and 2021 using the Black-Scholes option-pricing model was $17.58 and $14.03, respectively. Assumptions were as follows: 

|  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  |  |  |  |  |  |  |  |  |  |  |  |
|  | Six Months EndedJune 30, |
|  | 2022 |  | 2021 |
| Expected life (years) | 5.7 |  | 5.8 |
| Risk-free interest rate | 1.9  | % |  | 1.2  | % |
| Dividend yield | 1.5  | % |  | 1.6  | % |
| Expected volatility | 26.8  | % |  | 27.4  | % |

The expected lives of options for purposes of these models are based on historical exercise behavior. The risk-free interest rates for purposes of these models are based on the U.S. Treasury yield curve in effect on the date of grant for the respective expected lives of the option. The expected dividend yields for purposes of these models are based on the dividends paid in the preceding four quarters divided by the grant date market value of the Common Stock. The expected volatility for purposes of these models are based on the historical volatility of the Common Stock.Restricted Stock and Share Units Participants may also be awarded shares of restricted stock or share units under the Incentive Plan. Share units vest three years after the date of grant. The Company granted 93,211 and 100,676 share units under the Incentive Plan in the six months ended June 30, 2022 and 2021, respectively. The share units were valued at $6.9 million and $6.1 million at the date of issuance in 2022 and 2021, respectively, based on the price of the Company’s Common Stock at the date of grant. The share units are recognized as compensation expense ratably over the three-year vesting period; however, included in share unit expense in the three and six months ended June 30, 2022 and 2021 was expense associated with accelerated vesting of restricted stock and share unit awards for certain employees who either are retirement eligible or will become retirement eligible during the vesting period. Stock based compensation expense attributable to share units of $0.8 million and $1.0 million was recognized in the three months ended June 30, 2022 and 2021, respectively. Stock based compensation expense attributable to share units of $4.5 million and $4.8 million was recognized in the six months ended June 30, 2022 and 2021, respectively. Certain non-U.S.-based employees receive the cash value of the share price at the vesting date in lieu of shares. Unvested cash-settled awards are remeasured at each reporting period.A summary of share unit activity under the Incentive Plan is as follows for the six months ended June 30, 2022:

|  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  |  |  |  |  |  |  |  |  |  |  |  |
|  | Number of Units |  | Weighted-AverageGrant Date Value |
| Issued and unvested at January 1, 2022 | 421,138  |  |  | $ | 47.28  |  |
| Granted | 93,211  |  |  | 73.70  |  |
| Vested | (126,631) |  |  | 49.49  |  |
| Forfeited | (6,777) |  |  | 53.93  |  |
| Issued and unvested at June 30, 2022 | 380,941  |  |  | 52.98  |  |

  
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