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Stock-based compensation (Tables)
12 Months Ended
Dec. 31, 2023
Share-Based Payment Arrangement [Abstract]  
Summary of Stock Option Plan
The following table summarizes the activity related to the stock options during 2023:

Options outstandingNon-vested options
Number of
stock options
Weighted-average
exercise price
Number of
stock options
Weighted-average
grant date
fair value
Outstanding, January 1, 20237,353,133 $61.69 2,597,008 $18.09 
Granted856,332 $105.13 856,332 $29.79 
Exercised(1,634,730)$42.13 N/AN/A
VestedN/AN/A(1,047,434)$16.66 
Forfeited(102,803)$92.84 (102,803)$23.08 
Outstanding, December 31, 20236,471,932 $71.03 2,303,103 $22.87 
Vested or expected to vest at December 31, 2023(1)
6,428,547 $70.83 N/AN/A
Exercisable, December 31, 20234,168,829 $58.20 N/AN/A
(1) As at December 31, 2023, the weighted-average remaining term of vested or expected to vest options was 3.3 years with an aggregate intrinsic value of $219 million.
Stock Options Outstanding and Exercisable
The following table provides the number of stock options outstanding and exercisable as at December 31, 2023 by range of exercise price and their related intrinsic aggregate value, and for stock 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, 2023 at the Company’s closing stock price of $104.84.

Options outstandingOptions exercisable
Range of exercise pricesNumber of
stock options
Weighted-average
years to
expiration
Weighted-average
exercise
price
Aggregate
intrinsic
value
(millions)
Number of
stock options
Weighted-average
exercise
price
Aggregate
intrinsic
value
(millions)
$30.94 - $50.19
1,693,436 1.2$40.04 $110 1,693,436 $40.04 $110 
$50.20 - $70.36
1,395,999 2.3$58.53 $65 1,284,814 $57.53 $61 
$70.37 - $94.27
1,610,826 4.0$82.99 $35 822,618 $80.20 $20 
$94.28 - $109.01
1,771,671 5.3$99.62 $367,961 $94.94 $
Total(1)
6,471,932 3.3$71.03 $219 4,168,829 $58.20 $195 
(1) As at December 31, 2023, the total number of in-the-money stock options outstanding was 5,787,281 with a weighted-average exercise price of $66.96. The weighted-average years to expiration of exercisable stock options is 2.3 years.
Weighted-Average Fair Value Assumptions The following table provides assumptions used to determine the fair values of stock option awards, and the weighted-average grant date fair values for units granted in 2023, 2022 and 2021:
202320222021
Expected option life (years)(1)
4.754.754.75
Risk-free interest rate(2)
3.35 %1.62 %0.53 %
Expected stock price volatility(3)
28.44 %26.85 %27.14 %
Expected annual dividends per share(4)
$0.76 $0.76 $0.76 
Expected forfeiture rate(5)
3.18 %3.01 %2.62 %
Weighted-average grant date fair value of options granted during the year$29.79 $21.33 $19.06 
(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 stock options exercised in the plan during the years ended December 31:

(in millions of Canadian dollars)202320222021
Total intrinsic value$101 $53 $43 
Cash received by the Company upon exercise of options69 32 25 
Summary of Performance Share Unit Plan
The following table summarizes the activity related to PSUs and PDSUs during for each of the years ended December 31:

20232022
Outstanding, January 11,336,358 1,577,781 
Granted917,744 429,166 
Issued in lieu of dividends10,845 11,207 
Settled(460,667)(637,073)
PDSUs converted into DSUs(45,058)— 
Forfeited(80,669)(44,723)
Outstanding, December 311,678,553 1,336,358 
Summary of Deferred Share Unit Plan
The following table summarizes the activity related to DSUs for each of the years ended December 31:

20232022
Outstanding, January 1744,530 841,333 
Granted85,750 60,262 
PDSUs converted into DSUs81,533 — 
Issued in lieu of dividends5,685 6,510 
Settled(15,935)(162,319)
Forfeited(1,745)(1,256)
Outstanding, December 31899,818 744,530 
Summary of Share-Based Liabilities Paid
The following table summarizes the total share unit liabilities paid for each of the years ended December 31:

(in millions of Canadian dollars)202320222021
Plan
PSUs$86 $116 $119 
DSUs2 16 
Other1 
Total$89 $137 $126