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Stock-Based Compensation Programs
12 Months Ended
Dec. 31, 2022
Stock-Based Compensation Programs  
Stock-Based Compensation Programs

19. Stock-Based Compensation Programs

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The company has shareholder-approved stock plans under which options and stock-settled appreciation rights (SSARs) have been granted to employees at the market value of the company’s stock on the date of grant. In general, options and SSARs are exercisable in four equal installments commencing one year from the date of grant and terminating 10 years from the date of grant. A summary of outstanding stock option and SSAR activity for the year ended December 31, 2022, follows:

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Number of

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Weighted Average

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Shares

    

Exercise Price

Beginning of year

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9,766,096

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$

46.66

Granted

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1,160,180

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​

86.31

Exercised

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(1,186,020)

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​

32.58

Canceled/forfeited

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(388,372)

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77.72

End of period

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9,351,884

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52.07

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​

​

​

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Vested and exercisable, end of year

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6,656,599

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$

41.21

Reserved for future grants

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12,933,109

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The weighted average remaining contractual term for all options and SSARs outstanding at December 31, 2022, was 5.2 years and the aggregate intrinsic value (difference in exercise price and closing price at that date) was $86 million. The weighted average remaining contractual term for options and SSARs vested and exercisable at December 31, 2022, was 4.1 years and the aggregate intrinsic value was $86 million. The company received $26 million, $33 million and $38 million from options and SSARs exercised during 2022, 2021 and 2020, respectively, and the intrinsic value associated with these exercises was $62 million, $84 million and $230 million for the same periods, respectively. The excess tax benefit associated with the company’s stock compensation programs was $15 million for 2022, and was reported as a discrete item in the consolidated tax provision. The total fair value of options and SSARs vested during 2022, 2021 and 2020 was $19 million, $18 million and $17 million, respectively.

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Based on the Black-Scholes option pricing model, options and SSARs granted in 2022, 2021 and 2020 have estimated weighted average fair values at the date of grant of $21.68 per share, $19.86 per share and $15.36 per share, respectively. The fair values were estimated using the following weighted average assumptions:

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2022 Grants

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2021 Grants

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2020 Grants

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Expected dividend yield

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0.92

%  

0.70

%  

0.83

%  

Expected stock price volatility

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25.56

%  

25.08

%  

20.84

%  

Risk-free interest rate

​

1.77

%  

0.61

%  

1.47

%  

Expected life of options (in years)

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6.10

years  

6.25

years  

6.40

years  

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In addition to stock options and SSARs, the company issues to certain employees restricted shares and restricted stock units, which vest over various periods. Such restricted shares and restricted stock units generally vest in equal installments over five years.

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Following is a summary of restricted stock activity for the year ended December 31, 2022:

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Weighted

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Number of

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Average

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Shares/Units

    

Grant Price

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Beginning of year

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1,246,404

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$

56.64

Granted

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420,731

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75.82

Vested

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(412,367)

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​

53.62

Canceled/forfeited

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(50,266)

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​

79.55

End of year

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1,204,502

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$

63.06

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For the years ended December 31, 2022, 2021 and 2020, the company recognized pretax expense of $39 million ($34 million after tax), $40 million ($35 million after tax) and $43 million ($37 million after tax), respectively, for all of its share-based compensation arrangements. At December 31, 2022, there was $62 million of total unrecognized compensation cost related to nonvested share-based compensation arrangements. This cost is expected to be recognized in earnings over a weighted average period of 2.3 years.

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