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Stock-based Compensation and Other Stock Plans (Tables)
 12 Months Ended
Jan. 02, 2021
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 2020, 2019 and 2018, using the Black-Scholes valuation model: 
202020192018
Expected term of option (in years)
5.535.535.35
Expected volatility factor21.67%21.30%20.08%
Expected dividend yield2.78%1.79%1.68%
Risk-free interest rate1.50%2.54%2.71%
Summary of Stock Option Activity
A summary of stock option activity during 2020 is presented below: 
Shares (in thousands)
Exercise
 Price per 
Share*
Remaining Contractual   
Term*
(in years)
Aggregate
Intrinsic
Value
(in millions)
Outstanding at beginning of year3,114 $135.60 
Granted459 155.34 
Exercised(434)106.04 
Forfeited or expired(19)159.78 
Outstanding at end of year3,120 142.47 5.9$89.5 
Exercisable at end of year2,217 136.76 4.976.2 

* Weighted-average
Summary of Changes in Non-Vested Performance Awards
Changes to the company’s non-vested performance awards in 2020 are as follows:
Shares
(in thousands)
Fair Value
Price per
Share*
Non-vested performance awards at beginning of year98 $158.94 
Granted82 155.34 
Vested(30)161.18 
Cancellations and other(74)157.49 
Non-vested performance awards at end of year76 155.61 

* 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 2020, 2019 and 2018, using the Black-Scholes valuation model:
202020192018
Expected term of stock-settled SARs (in years)
3.753.653.58
Expected volatility factor22.50%22.60%20.08%
Expected dividend yield2.78%1.81%1.63%
Risk-free interest rate1.42%2.48%2.40%
The following weighted-average assumptions were used in calculating the fair value of cash-settled SARs granted during 2020, 2019 and 2018, using the Black-Scholes valuation model:
202020192018
Expected term of cash-settled SARs (in years)
3.002.872.76
Expected volatility factor34.58%23.33%21.96%
Expected dividend yield2.87%2.02%1.75%
Risk-free interest rate0.17%1.60%2.50%
Summary of Changes in SARs
Changes to the company’s stock-settled SARs in 2020 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 year450 $149.18 
Granted92 155.34 
Exercised(7)112.50 
Forfeited or expired(33)138.12 
Outstanding at end of year502 151.59 6.6$9.8 
Exercisable at end of year325 148.93 5.67.2 

* Weighted-average
hanges to the company’s non-vested cash-settled SARs in 2020 are as follows:
Cash-settled
SARs
(in thousands)
Fair Value
 Price per 
Share*
Non-vested cash-settled SARs at beginning of year2 $25.96 
Granted1 37.99 
Vested(1)34.02 
Non-vested cash-settled SARs at end of year2 36.99 

* Weighted-average