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Share Based Compensation (Tables)
 12 Months Ended
Dec. 31, 2018
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]  
Weighted Average Fair Value and Assumptions
The following table shows the weighted average fair value for our stock options and the assumptions we used to estimate fair value:
 
2018
 
2017
 
2016
Weighted average estimated fair value
$
21.87

 
$
19.40

 
$
13.86

Quarterly dividend rate
$
0.44

 
$
0.42

 
$
0.40

Expected term of stock options, in years
4.5

 
4.7

 
4.7

Risk-free interest rate
2.4
%
 
1.9
%
 
1.4
%
Dividend yield
2.5
%
 
2.8
%
 
4.1
%
Expected stock price volatility
27.9
%
 
27.7
%
 
29.4
%
Present value of dividends
$
7.51

 
$
7.50

 
$
7.27
Data With Respect to Stock Options SARs Activity

The following table shows information about outstanding stock options and stock appreciation rights for the year ended December 31, 2018:


 
Number of Stock Options and Stock Appreciation Rights
(in thousands)
 
Weighted Average Exercise Price
Outstanding at beginning of the year
 
1,723
 
$
50.07

Granted
 
320
 
69.73

Exercised
 
(611)
 
47.19

Forfeited/Cancelled
 
(33)
 
53.94

Outstanding at end of the year
 
1,399
 
55.73

Vested and exercisable at end of the year
 
733
 
51.17
Schedule of Share-Based Compensation, Aggregate Intrinsic Value and Weighted Average Remaining Contractual Term
The following table shows the aggregate intrinsic value of stock options and stock appreciation rights exercised in 2018, 2017, and 2016, and the weighted average remaining contractual term and aggregate intrinsic value of stock options and stock appreciation rights outstanding and vested as of December 31, 2018:
Stock Options and Stock Appreciation Rights
 
Weighted Average Remaining Contractual Term
(Years)
 
Aggregate Intrinsic Value
(in millions)
 
 
 
 
 
Exercised in 2016
 
 
 
$
6.2

Exercised in 2017
 
 
 
4.4

Exercised in 2018
 
 
 
17.2

 
 
 
 
 
Outstanding at December 31, 2018 (a)
 
4.2
 
21.5

Vested and exercisable at December 31, 2018
 
3.1
 
14.6

_______
(a) As of December 31, 2018, 435,552 stock appreciation rights and 963,557 stock options were outstanding.
Schedule of Share-Based Compensation, Restricted Stock Units and Performance Shares Award Activity
The following table shows information about restricted stock units and performance shares for the year ended December 31, 2018:


Number of Share Units Outstanding (in thousands)
 
Weighted Average Grant-Date Fair Value
Restricted Stock Units:
 
 
 
Nonvested at beginning of the year
187

 
$
50.62

Granted
73

 
73.60

Vested
(52
)
 
55.56

Forfeited
(4
)
 
53.82

Nonvested at end of the year
204

 
57.57

Performance Shares:
 
 
 
Nonvested at beginning of the year
161

 
$
46.25

Granted
58

 
65.00

Net increase due to estimated performance
49

 
53.27

Vested
(117
)
 
38.83

Forfeited
(8
)
 
51.28

Nonvested at end of the year
143

 
62.08