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Stock-based compensation (Tables)
 12 Months Ended
Dec. 31, 2017
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]  
Schedule providing assumptions used in determining the fair value of stock-based awards
The following table provides the assumptions used in determining the fair value of the Option/SAR awards for the years ended December 31, 2017, 2016 and 2015, respectively.

 
Grant Year
 
2017
 
2016
 
2015
Weighted-average dividend yield
3.4
%
 
3.2
%
 
2.3
%
Weighted-average volatility
29.2
%
 
31.1
%
 
28.4
%
Range of volatilities
22.1-33.0%

 
22.5-33.4%

 
19.9-35.9%

Range of risk-free interest rates
0.81-2.35%

 
0.62-1.73%

 
0.22-2.08%

Weighted-average expected lives
8 years

 
8 years

 
8 years

 
 
 
 
 
 
Schedule of stock-based compensation activity
Please refer to Tables I and II below for additional information on our stock-based compensation awards.  

TABLE I — Financial Information Related to Stock-based Compensation
 
 
 
 
 
 
 
Stock options / SARs
 
RSUs
 
PRSUs
 
Shares
 
Weighted-
 Average
 Exercise
 Price
 
Shares
 
Weighted-
Average
Grant Date Fair Value
 
Shares
 
Weighted-
Average
Grant Date Fair Value
 
 

 
 

 
 

 
 

 
 

 
 

Outstanding at January 1, 2017
32,064,790

 
$
82.13

 
3,071,014

 
$
78.50

 
710,286

 
$
66.92

Granted to officers and key employees 1
2,701,644

 
$
95.66

 
924,421

 
$
90.11

 
437,385

 
$
86.78

Exercised
(12,997,205
)
 
$
76.89

 
—

 
$
—

 
—

 
$
—

Vested
—

 
$
—

 
(1,982,565
)
 
$
82.37

 
(129,000
)
 
$
77.47

Forfeited / expired
(269,334
)
 
$
94.23

 
(48,353
)
 
$
79.43

 
(11,680
)
 
$
78.14

Outstanding at December 31, 2017
21,499,895

 
$
86.86

 
1,964,517

 
$
80.04

 
1,006,991

 
$
74.06

Exercisable at December 31, 2017
15,309,691

 
$
87.29

 
 
 
 
 
 
 
 

Stock options/SARs outstanding and exercisable as of December 31, 2017:
 
 
 
 
 
 
 
Outstanding
 
Exercisable
Exercise Prices
 
Shares Outstanding at 12/31/17
 
Weighted-
 Average
 Remaining
 Contractual Life (Years)
 
Weighted-
 Average
 Exercise Price
 
Aggregate
 Intrinsic Value 2
 
Shares Outstanding at 12/31/17
 
Weighted-
 Average
 Remaining
Contractual Life (Years)
 
Weighted-
 Average
 Exercise Price
 
Aggregate
 Intrinsic Value 2
$22.17 - 57.85
 
1,562,670

 
1.96
 
$
50.47

 
$
167

 
1,562,670

 
1.96
 
$
50.47

 
$
167

$73.20 - 74.77
 
3,577,767

 
8.02
 
$
74.74

 
296

 
1,645,141

 
7.83
 
$
74.70

 
136

$83.00
 
5,266,798

 
7.17
 
$
83.00

 
393

 
3,630,345

 
7.17
 
$
83.00

 
271

$89.75 - 96.31
 
7,912,539

 
6.88
 
$
94.17

 
502

 
5,291,414

 
5.74
 
$
93.44

 
339

$102.13 - 110.09
 
3,180,121

 
3.74
 
$
106.55

 
162

 
3,180,121

 
3.74
 
$
106.55

 
162

 
 
21,499,895

 
 
 
$
86.86

 
$
1,520

 
15,309,691

 
 
 
$
87.29

 
$
1,075


1 
No SARs were granted during the year ended December 31, 2017.
2 
The difference between a stock award’s exercise price and the underlying stock’s closing market price at December 31, 2017, for awards with market price greater than the exercise price. Amounts are in millions of dollars.
 
 
 
 
 
Schedule of financial information related to stock-based compensation
TABLE II— Additional Stock-based Award Information
 
 
 
 
 
 
 
(Dollars in millions except per share data)
 
2017
 
2016
 
2015
Stock options/SARs activity:
 
 

 
 

 
 

Weighted-average fair value per share of stock awards granted
 
$
25.01

 
$
20.64

 
$
23.61

Intrinsic value of stock awards exercised
 
$
504

 
$
185

 
$
93

Fair value of stock awards vested 1
 
$
191

 
$
163

 
$
155

Cash received from stock awards exercised
 
$
629

 
$
30

 
$
59

 
 
 
 
 
 
 
RSUs activity:
 
 

 
 

 
 

Weighted-average fair value per share of stock awards granted
 
$
90.11

 
$
68.04

 
$
77.55

Fair value of stock awards vested 2
 
$
189

 
$
162

 
$
109

 
 
 
 
 
 
 
PRSUs activity:
 
 

 
 

 
 

Weighted-average fair value per share of stock awards granted
 
$
86.78

 
$
64.71

 
$
77.47

Fair value of stock awards vested 2
 
$
20

 
$
—

 
$
—

 
1 
Based on the grant date fair value.
2 
Based on the underlying stock's closing market price on the vesting date.