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Stock-based compensation (Tables)
12 Months Ended
Dec. 31, 2022
Share-Based Payment Arrangement [Abstract]  
Summary of Stock Option Plan
The following table summarizes information related to the stock option plan as at December 31, 2022:

Options outstandingNon-vested options
Number of
options
Weighted-average
exercise price
Number of
options
Weighted-average
grant date
fair value
Outstanding, January 1, 20227,392,188 $53.36 3,748,983 $14.25 
Granted839,108 $94.18 839,108 $21.33 
Exercised(840,795)$38.46 N/AN/A
VestedN/AN/A(1,953,715)$12.10 
Forfeited(37,368)$84.78 (37,368)$17.94 
Outstanding, December 31, 20227,353,133 $61.69 2,597,008 $18.09 
Vested or expected to vest at December 31, 2022(1)
7,304,289 $61.51 N/AN/A
Exercisable, December 31, 20224,756,125 $49.02 N/AN/A
(1) As at December 31, 2022, the weighted-average remaining term of vested or expected to vest options was 3.3 years with an aggregate intrinsic value of $288 million.
Stock Options Outstanding and Exercisable
The following table provides the number of stock options outstanding and exercisable as at December 31, 2022 by range of exercise price and their related intrinsic aggregate value, and for options outstanding, the weighted-average years to expiration. The table also provides the aggregate intrinsic value for in-the-money stock options, which represents the amount that would have been received by option holders had they exercised their options on December 31, 2022 at the Company’s closing stock price of $100.95.

Options outstandingOptions exercisable
Range of exercise pricesNumber of
options
Weighted-average
years to
expiration
Weighted-average
exercise
price
Aggregate
intrinsic
value
(millions)
Number of
options
Weighted-average
exercise
price
Aggregate
intrinsic
value
(millions)
$23.84 - $41.51
2,105,506 1.6$36.62 $135 2,105,506 $36.62 $135 
$41.52 - $55.48
1,655,284 2.3$49.09 $86 1,526,734 $48.64 $80 
$55.49 - $90.81
1,795,994 4.0$70.03 $56 883,395 $66.85 $30 
$90.82 - $111.52
1,796,349 5.6$94.35 $12 240,490 $94.49 $
Total(1)
7,353,133 3.3$61.69 $289 4,756,125 $49.02 $247 
(1) As at December 31, 2022, the total number of in-the-money stock options outstanding was 7,339,374 with a weighted-average exercise price of $61.60. The weighted-average years to expiration of exercisable stock options is 2.4 years.
Weighted-Average Fair Value Assumptions The weighted-average fair value assumptions were approximately:
202220212020
Expected option life (years)(1)
4.754.754.75
Risk-free interest rate(2)
1.62 %0.53 %1.28 %
Expected stock price volatility(3)
26.85 %27.14 %23.14 %
Expected annual dividends per share(4)
$0.760 $0.760 $0.664 
Expected forfeiture rate(5)
3.01 %2.62 %4.41 %
Weighted-average grant date fair value of options granted during the year$21.33 $19.06 $13.80 
(1) Represents the period of time that awards are expected to be outstanding. Historical data on exercise behaviour or, when available, specific expectations regarding future exercise behaviour were used to estimate the expected life of the option.
(2) Based on the implied yield available on zero-coupon government issues with an equivalent term commensurate with the expected term of the option.
(3) Based on the historical volatility of the Company’s stock price over a period commensurate with the expected term of the option.
(4) Determined by the current annual dividend at the time of grant. The Company does not employ different dividend yields throughout the contractual term of the option.
(5) The Company estimates forfeitures based on past experience. The rate is monitored on a periodic basis.
Schedule of Options Exercised
The following table provides information related to all options exercised in the stock option plan during the years ended December 31:

(in millions of Canadian dollars)202220212020
Total intrinsic value$53 $43 $52 
Cash received by the Company upon exercise of options32 25 52 
Summary of Performance Share Unit Plan
The following table summarizes information related to PSUs and PDSUs as at December 31:

20222021
Outstanding, January 11,577,781 1,909,345 
Granted429,166 444,124 
Units in lieu of dividends11,207 14,668 
Settled(637,073)(743,512)
Forfeited(44,723)(46,844)
Outstanding, December 311,336,358 1,577,781 
Summary of Deferred Share Unit Plan
The following table summarizes information related to DSUs as at December 31:

20222021
Outstanding, January 1841,333 774,053 
Granted60,262 70,112 
Units in lieu of dividends6,510 6,753 
Settled(162,319)(6,677)
Forfeited(1,256)(2,908)
Outstanding, December 31744,530 841,333 
Summary of Share-Based Liabilities Paid
The following table summarizes the total share-based liabilities paid for each of the years ended December 31:

(in millions of Canadian dollars)202220212020
Plan
PSUs$116 $119 $76 
DSUs16 
Other5 
Total$137 $126 $86