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SHARE-BASED COMPENSATION (Tables)
12 Months Ended
Oct. 29, 2023
SHARE-BASED COMPENSATION  
Vesting Period and Dividend Equivalents Received Prior to Vesting The stock awards vesting periods and the dividend equivalents earned during the vesting period follow:

Vesting

Dividend

Period

Equivalents

Stock options

1-3 years

Not included

Service-based RSUs

1-3 years

Included

Performance/service-based RSUs

3 years

Not included

Share-based Compensation Expense, Recognized Tax Benefits, and Total Grant-date Fair Value

The total share-based compensation expense, recognized income tax benefits, and total grant-date fair values of stock options and restricted stock units vested consisted of the following:

2023

2022

2021

Share-based compensation expense

$

130

$

85

$

82

Income tax benefits

21

17

16

Stock options and restricted stock units vested

84

74

93

Assumptions Used for the Binomial Lattice Model to Determine Fair Value of Options The assumptions used for the binomial lattice model to determine the fair value of options follow:

  

        2023        

  

        2022        

  

        2021        

 

Risk-free interest rate*

 

2.68%

 

1.27%

 

.47%

Expected dividends

1.1%

1.2%

1.2%

Volatility*

33.0%

32.0%

31.0%

Expected term (in years)*

 

5.1

 

5.1

 

5.5

*    Weighted-averages

Stock Option Activity

The activity for outstanding stock options at October 29, 2023, and changes during 2023 follow:

  

Remaining

Aggregate

 

Exercise

Contractual

Intrinsic

 

Shares

Price*

Term

Value

 

(millions)

 

(per share)

 

(years)

 

(millions)

 

Outstanding at beginning of year

 

2.0

$

153.11

Granted

 

.2

 

438.44

Exercised

 

(.5)

 

118.54

Outstanding at end of year

 

1.7

 

190.08

 

4.62

 

$

302.3

Exercisable at end of year

 

1.3

 

144.71

 

3.66

 

292.3

*    Weighted-averages

Amounts Related to Stock Options

The amounts related to stock options were as follows in millions of dollars unless otherwise noted:

2023

2022

2021

Weighted-average grant date fair value (per share)

$

136.46

$

89.20

$

62.73

Intrinsic value of options exercised

153

169

318

Cash received from exercises

60

63

148

Tax benefit from exercises

34

39

71

Weighted-average Grant Date Fair Values

The weighted-average grant date fair values were as follows:

2023

2022

2021

Service-based

$

428.35

$

347.59

$

258.86

Performance/service-based

424.93

331.47

245.73

Restricted Stock Units Activity

Our restricted stock units at October 29, 2023 and changes during 2023 in dollars and thousands of shares follow:

Grant-Date

 

Shares

Fair Value*

 

Service-based

Nonvested at beginning of year

 

404

$

251.42

Granted

 

126

 

428.35

Vested

 

(211)

 

211.03

Forfeited

(9)

333.29

Nonvested at end of year

 

310

 

348.82

Performance/service based

Nonvested at beginning of year

 

143

 

227.70

Granted

 

41

 

424.93

Vested

 

(130)

 

160.81

Performance change

 

65

 

160.81

Nonvested at end of year

 

119

 

331.78

* Weighted-averages