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Share-based payments (Tables)
12 Months Ended
Oct. 31, 2020
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Summary of Assumptions Used to Determine Fair Value of Options Granted
The following weighted-average assumptions were used as inputs into the Black-Scholes option pricing model to determine the fair value of options on the date of grant:
 
For the year ended October 31
 
2020
 
 
2019
 
 
2018
 
Weighted-average assumptions
 
 
 
 
 
 
 
 
 
 
 
 
Risk-free interest rate
 
 
2.00
 % 
 
 
2.63
 % 
 
 
2.08
 % 
Expected dividend yield
 
 
6.80
 % 
 
 
5.87
 % 
 
 
5.15
 % 
Expected share price volatility
 
 
15.30
 % 
 
 
18.36
 % 
 
 
14.74
 % 
Expected life
 
 
6 years
 
 
 
6 years
 
 
 
6 years
 
Share price/exercise price
 
$
    109.87
 
 
$
    111.50
 
 
$
    120.02
 
Summary of Stock Option Activity and Related Information
The following tables summarize the activities of the stock options and provide additional details related to stock options outstanding and vested.
 
As at or for the year ended October 31
  
 
 
 
 
2020
 
  
 
 
 
  
2019
 
  
 
 
 
  
2018
 
 
 
  
Number
of stock
options
 
 
Weighted-
average
exercise
price 
(1)
 
  
Number
of stock
options
 
  
Weighted-
average
exercise
price
 
  
Number
of stock
options
 
  
Weighted-
average
exercise
price
 
Outstanding at beginning of year
  
 
5,176,962
 
 
$
    96.93
 
  
 
4,713,163
 
  
$
      91.05
 
  
 
4,876,673
 
  
$
      84.28
 
Granted
  
 
818,290
 
 
 
109.87
 
  
 
894,324
 
  
 
111.50
 
  
 
756,516
 
  
 
120.02
 
Exercised
(2)
  
 
(314,469
 
 
68.10
 
  
 
(393,055
  
 
58.60
 
  
 
(876,309
  
 
67.84
 
Forfeited
  
 
(672
 
 
70.66
 
  
 
(35,714
  
 
110.42
 
  
 
(42,443
  
 
103.98
 
Cancelled/expired
  
 
 
 
 
 
  
 
(1,756
  
 
45.63
 
  
 
(1,274
  
 
45.08
 
Outstanding at end of year
  
 
5,680,111
 
 
$
100.39
 
  
 
5,176,962
 
  
$
96.93
 
  
 
4,713,163
 
  
$
91.05
 
Exercisable at end of year
  
 
2,783,694
 
 
$
88.63
 
  
 
2,290,139
 
  
$
80.27
 
  
 
1,898,125
 
  
$
71.89
 
Available for grant
  
 
9,316,226
 
 
 
 
 
  
 
10,133,844
 
  
 
 
 
  
 
10,990,698
 
  
 
 
 
Reserved for future issue
  
 
14,996,337
 
 
 
 
 
  
 
15,310,806
 
  
 
 
 
  
 
15,703,861
 
  
 
 
 
 
(1)
For foreign currency-denominated options granted and exercised during the year, the weighted-average exercise prices are translated using exchange rates as at the grant date and settlement date, respectively. The weighted-average exercise price of outstanding balances as at October 31, 2020 reflects the conversion of foreign currency-denominated options at the
year-end
exchange rate.
(2)
The weighted-average share price at the date of exercise was $97.72 (2019: $106.94; 2018: $120.55).
Summary of Stock Options Outstanding and Vested
 
As at October 31, 2020
 
Stock options outstanding
 
  
 
 
 
Stock options vested
 
Range of exercise prices
 
Number
outstanding
 
  
Weighted-
average
contractual life
remaining
 
  
Weighted-
average
exercise
price
 
  
 
 
 
 
Number
outstanding
 
  
Weighted-
average
exercise
price
 
$11.00 – $55.00
 
 
239,891
 
  
 
1.84
 
  
$
31.19
 
  
  
  
  
 
 
239,891
 
  
$
31.19
 
$55.01 – $65.00
 
 
146,085
 
  
 
4.75
 
  
 
60.93
 
  
  
  
  
 
 
146,085
 
  
 
60.93
 
$65.01 – $75.00
 
 
158,106
 
  
 
1.13
 
  
 
71.43
 
  
  
  
  
 
 
158,106
 
  
 
71.43
 
$75.01 – $85.00
 
 
304,285
 
  
 
1.87
 
  
 
79.88
 
  
  
  
  
 
 
304,285
 
  
 
79.88
 
$85.01 – $95.00
 
 
362,400
 
  
 
3.28
 
  
 
90.97
 
  
  
  
  
 
 
362,400
 
  
 
90.97
 
$95.01 – $105.00
 
 
1,126,241
 
  
 
4.65
 
  
 
99.71
 
  
  
  
  
 
 
1,126,241
 
  
 
99.71
 
$105.01 – $115.00
 
 
2,602,275
 
  
 
7.70
 
  
 
110.74
 
  
  
  
  
 
 
446,686
 
  
 
110.77
 
$115.01 – $125.00
 
 
740,828
 
  
 
7.06
 
  
 
120.02
 
  
 
 
 
 
 
 
  
 
 
 
 
 
5,680,111
 
  
 
5.91
 
  
$
    101.11
 
  
 
 
 
 
 
2,783,694
 
  
$
    88.63