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Stock-based Compensation and Other Stock Plans (Tables)
 12 Months Ended
Jan. 01, 2022
Share-based Payment Arrangement [Abstract]  
Summary of Weighted-Average Assumptions of Fair Value Granted Using Black-Scholes Valuation Model, Stock Options
The following weighted-average assumptions were used in calculating the fair value of stock options granted during 2021, 2020 and 2019, using the Black-Scholes valuation model: 
202120202019
Expected term of option (in years)
5.335.535.53
Expected volatility factor21.80%21.67%21.30%
Expected dividend yield2.59%2.78%1.79%
Risk-free interest rate0.67%1.50%2.54%
Summary of Stock Option Activity
A summary of stock option activity during 2021 is presented below: 
Shares (in thousands)
Exercise
 Price per 
Share*
Remaining Contractual   
Term*
(in years)
Aggregate
Intrinsic
Value
(in millions)
Outstanding at beginning of year3,120 $142.47 
Granted333 189.91 
Exercised(991)135.88 
Forfeited or expired(30)168.82 
Outstanding at end of year2,432 151.32 5.7$155.8 
Exercisable at end of year1,675 142.82 4.5121.5 
* Weighted-average
Summary of Changes in Non-Vested PSUs and RSUs
Changes to the company’s non-vested PSUs and RSUs in 2021 are as follows:
Shares
(in thousands)
Fair Value
Price per
Share*
Non-vested PSUs and RSUs at beginning of year76 $155.61 
Granted188 184.32 
Vested(46)155.92 
Cancellations and other(3)181.51 
Non-vested PSUs and RSUs at end of year215 180.29 
* Weighted-average
Summary of Weighted-Average Assumptions of Fair Value Granted Using Black-Scholes Valuation Model, SAR's
The following weighted-average assumptions were used in calculating the fair value of stock-settled SARs granted during 2021, 2020 and 2019, using the Black-Scholes valuation model:
202120202019
Expected term of stock-settled SARs (in years)
3.943.753.65
Expected volatility factor22.50%22.50%22.60%
Expected dividend yield2.59%2.78%1.81%
Risk-free interest rate0.19%1.42%2.48%
The following weighted-average assumptions were used in calculating the fair value of cash-settled SARs granted during 2021, 2020 and 2019, using the Black-Scholes valuation model:
202120202019
Expected term of cash-settled SARs (in years)
3.093.002.87
Expected volatility factor22.49%34.58%23.33%
Expected dividend yield2.64%2.87%2.02%
Risk-free interest rate0.97%0.17%1.60%
Summary of Changes in SARs
Changes to the company’s stock-settled SARs in 2021 are as follows:
Stock-settled
SARs (in thousands)
Exercise
 Price per 
Share*
Remaining Contractual   
Term*
(in years)
Aggregate
Intrinsic
Value
(in millions)
Outstanding at beginning of year502 $151.59 
Granted83 189.89 
Exercised(48)144.38 
Forfeited or expired(140)152.52 
Outstanding at end of year397 160.09 6.7$21.9 
Exercisable at end of year227 151.18 5.314.6 
* Weighted-average
Changes to the company’s non-vested cash-settled SARs in 2021 are as follows:
Cash-settled
SARs
(in thousands)
Fair Value
 Price per 
Share*
Non-vested cash-settled SARs at beginning of year2 $36.99 
Granted1 37.69 
Vested(1)54.83 
Non-vested cash-settled SARs at end of year2 47.13 
* Weighted-average