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STOCK OPTION AND RESTRICTED STOCK AWARDS (Tables)
12 Months Ended
Oct. 31, 2021
STOCK OPTION AND RESTRICTED STOCK AWARDS  
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:

  

        2021        

  

       2020       

  

        2019        

 

Risk-free interest rate*

 

.47%

 

1.67%

 

2.85%

Expected dividends

1.2%

1.8%

2.0%

Volatility*

31.0%

26.0%

30.0%

Expected term (in years)*

 

5.5

 

5.7

 

8.2

*    Weighted-averages

Stock Option Activity

Stock option activity at October 31, 2021, and changes during 2021 in millions of dollars and shares follow:

Remaining

 

Contractual

Aggregate

 

Exercise

Term

Intrinsic

 

Shares

  

Price*

  

(Years)

  

Value

 

Outstanding at beginning of year

 

3.7

$

107.30

Granted

 

.3

 

254.83

Exercised

 

(1.5)

 

99.38

Outstanding at end of year

 

2.5

 

127.82

 

5.07

 

$

527.3

Exercisable at end of year

 

1.9

 

103.25

 

4.00

 

445.0

*    Weighted-averages

Restricted Stock Units Activity

The company’s restricted stock units at October 31, 2021 and changes during 2021 in millions of shares follow:

Grant-Date

 

Shares

Fair Value*

 

Service-only based

Nonvested at beginning of year

 

.9

$

155.47

Granted

 

.2

 

258.86

Vested

 

(.5)

 

190.87

Forfeited

(.1)

163.16

Nonvested at end of year

 

.5

 

190.87

Performance/service based

Nonvested at beginning of year

 

.2

$

147.55

Granted

 

.1

 

245.73

Vested

 

(.2)

 

145.16

Performance change

 

.1

 

144.98

Nonvested at end of year

 

.2

 

171.82

* Weighted-averages