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Long-Term Incentive Plans (Tables)
12 Months Ended
Dec. 31, 2017
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]  
Transactions Involving Stock Option Awards
Transactions involving stock option awards during 2017 under the Company's Incentive Plans are summarized in the table below.
 
 
Number of Shares
 
Weighted-Average Exercise Price
 
Weighted-Average Remaining Contractual Term (in years)
 
Intrinsic Value
Outstanding as of December 31, 2016
 
25,136,027

 
$
269.69

 

 


2017:
Granted
 
4,235,015

 
$
383.56

 
 
 
 
 
Forfeited
 
(704,136
)
 
$
434.25

 
 
 
 
 
Expired
 
(100,727
)
 
$
505.96

 
 
 
 
 
Exercised
 
(2,360,806
)
 
$
122.92

 
 
 
 
Outstanding as of December 31, 2017
 
26,205,373

 
$
295.98

 
6.52
 
$
2,904,974

 
 
 
 
 
 
 
 
 
Vested and expected to vest as of December 31, 2017
 
24,667,723

 
$
293.65

 
6.46
 
$
2,904,723

 
 
 
 
 
 
 
 
 
Exercisable as of December 31, 2017
 
16,263,766

 
$
223.00

 
5.08
 
$
2,894,474

Weighted-Average Exercise Prices and Weighted-Average Grant-Date Fair Values of Options Issued
The fair value of each option granted under the Company's Incentive Plans during these periods was estimated on the date of grant using the Black-Scholes option-pricing model.
 
 
Number of Options Granted
 
Weighted-Average Exercise Price
 
Weighted-Average Fair Value
2017:
 
 
 
 
 
 
Exercise price equal to Market Price
 
4,235,015

 
$
383.56

 
$
118.70

2016:
 
 
 
 
 
 
Exercise price equal to Market Price
 
4,201,978

 
$
386.44

 
$
126.68

2015:
 
 
 
 
 
 
Exercise price equal to Market Price
 
4,495,487

 
$
537.29

 
$
181.65

Weighted-Average Values of Assumptions Used in Computing Fair Value of Option Grants
The following table summarizes the weighted average values of the assumptions used in computing the fair value of option grants during 2017, 2016, and 2015.
 
 
2017
 
2016
 
2015
Expected volatility
 
31
%
 
34
%
 
35
%
Expected lives from grant date
 
5.1 years

 
5.1 years

 
5.1 years

Expected dividend yield
 
0
%
 
0
%
 
0
%
Risk-free interest rate
 
2.16
%
 
1.84
%
 
1.68
%
Activity Related to Restricted Stock Awards
A summary of the Company's activity related to restricted stock awards during 2017 is summarized below:
 
 
Number of Shares
 
Weighted-Average Grant Date Fair Value
Outstanding as of December 31, 2016
 
546,820

 
$
141.85

2017:
Granted
 
63,030

 
$
379.60

 
Vested
 
(501,590
)
 
$
115.07

 
Forfeited
 
(2,000
)
 
$
381.92

Outstanding as of December 31, 2017
 
106,260

 
$
404.72