Stock-based Compensation (Tables)
 12 Months Ended
Dec. 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award  
Share-based Payment Arrangement, Cost by Plan

The following table summarizes stock-based compensation costs for the years ended December 31, 2019, 2018 and 2017.
 
Year Ended December 31
Millions of dollars
2019
2018
2017
Stock-based compensation cost
$
257

$
274

$
290

Tax benefit
(48
)
(51
)
(64
)
Stock-based compensation cost, net of tax
$
209

$
223

$
226
Stock Options  
Share-based Compensation Arrangement by Share-based Payment Award  
Share-based Payment Arrangement, Option, Activity
The following table represents our stock options activity during 2019.
 
Number
of Shares
(in millions)
Weighted
Average
Exercise
Price
per Share
Weighted
Average
Remaining
Contractual Term (years)
Aggregate
Intrinsic
Value
(in millions)
Outstanding at January 1, 2019
21.2

$
45.44

 
 
Granted
5.4

25.46

 
 
Exercised
(0.2
)
21.30

 
 
Forfeited/expired
(1.1
)
40.71

 
 
Outstanding at December 31, 2019
25.3

$
41.58

5.9
$
1

Exercisable at December 31, 2019
17.6

$
45.56

4.6
$
—
Schedule of Share-based Payment Award, Stock Options, Valuation Assumptions The assumptions and resulting fair values of options granted were as follows:

 
Year Ended December 31
 
2019
2018
2017
Expected term (in years)
5.31
5.27
5.24
Expected volatility
31%
28%
32%
Expected dividend yield
2.25 - 3.88%
1.37 - 2.29%
1.28 - 1.72%
Risk-free interest rate
1.35 - 2.51%
2.27 - 2.84%
1.79 - 2.14%
Weighted average grant-date fair value per share
$5.91
$11.56
$13.11
Restricted Stock  
Share-based Compensation Arrangement by Share-based Payment Award  
Schedule of Share-based Payment Award, Stock Options, Valuation Assumptions
The following table represents our restricted stock awards and restricted stock units granted, vested and forfeited during 2019.
 
Number of Shares
(in millions)
Weighted Average
Grant-Date Fair
Value per Share
Nonvested shares at January 1, 2019
14.4

$
46.01

Granted
9.8

24.75

Vested
(4.7
)
46.91

Forfeited
(1.4
)
40.34

Nonvested shares at December 31, 2019
18.1

$
34.72
Employee Stock Purchase Plan  
Share-based Compensation Arrangement by Share-based Payment Award  
Schedule of Share-based Payment Award, Stock Options, Valuation Assumptions The assumptions and resulting fair values were as follows:
 
Year Ended December 31
 
2019
2018
2017
Expected volatility
34
%
25
%
29
%
Expected dividend yield
3.06
%
1.62
%
1.51
%
Risk-free interest rate
2.20
%
1.92
%
0.86
%
Weighted average grant-date fair value per share
$
5.22

$
8.86

$
9.95