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Long-Term Incentive Plans (Tables)
 12 Months Ended
Dec. 31, 2016
Dec. 31, 2014
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]    
Transactions Involving Stock Option Awards
Transactions involving stock option awards during 2016 under the Company's Incentive Plans are summarized in the table below.
Stock Options:
 
Number of Shares
 
Weighted-Average Exercise Price
 
Weighted-Average Remaining Contractual Term (in years)
 
Intrinsic Value
Outstanding as of December 31, 2015
 
23,165,769

 
$
236.75

 

 


2016:
Granted
 
4,201,978

 
$
386.44

 
 
 
 
 
Forfeited
 
(468,798
)
 
$
398.57

 
 
 
 
 
Expired
 
(20,645
)
 
$
420.04

 
 
 
 
 
Exercised
 
(1,742,277
)
 
$
76.79

 
 
 
 
Outstanding as of December 31, 2016
 
25,136,027

 
$
269.69

 
6.66
 
$
3,399,815

 
 
 
 
 
 
 
 
 
Vested and expected to vest as of December 31, 2016
 
24,598,430

 
$
266.16

 
6.60
 
$
3,397,437

 
 
 
 
 
 
 
 
 
Exercisable as of December 31, 2016
 
15,140,287

 
$
166.96

 
5.19
 
$
3,299,296

  
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
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

2014:
 
 
 
 
 
 
Exercise price equal to Market Price
 
3,913,368

 
$
385.33

 
$
140.38

  
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 2016, 2015, and 2014.
 
 
2016
 
2015
 
2014
Expected volatility
 
34
%
 
35
%
 
39
%
Expected lives from grant date
 
5.1 years

 
5.1 years

 
5.2 years

Expected dividend yield
 
0
%
 
0
%
 
0
%
Risk-free interest rate
 
1.84
%
 
1.68
%
 
1.62
%
  
Activity Related to Restricted Stock Awards
A summary of the Company's activity related to Restricted Stock awards during 2016 is summarized below:
Restricted Stock:
 
Number of Shares
 
Weighted-Average Grant Date Fair Value
Outstanding as of December 31, 2015
 
541,700

 
$
133.96

2016:
Granted
 
16,750

 
$
385.84

 
Vested
 
(11,590
)
 
$
125.38

 
Forfeited
 
(40
)
 
$
237.68

Outstanding as of December 31, 2016
 
546,820

 
$
141.85

  
Schedule of Error Corrections and Prior Period Adjustments  
.