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Long-Term Incentive Plans (Tables)
 12 Months Ended
Dec. 31, 2015
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]  
Transactions Involving Stock Option Awards
Transactions involving stock option awards during 2015 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 (in thousands)
Outstanding as of December 31, 2014
 
21,506,260

 
$
158.54

 

 


2015:
Granted
 
4,495,487

 
$
537.29

 
 
 
 
 
Forfeited
 
(318,952
)
 
$
292.14

 
 
 
 
 
Expired
 
(363
)
 
$
92.20

 
 
 
 
 
Exercised
 
(2,516,663
)
 
$
98.26

 
 
 
 
Outstanding as of December 31, 2015
 
23,165,769

 
$
236.75

 
6.82
 
$
7,209,994,851

 
 
 
 
 
 
 
 
 
Vested and expected to vest as of December 31, 2015
 
22,635,728

 
$
231.75

 
6.76
 
$
7,156,754,651

 
 
 
 
 
 
 
 
 
Exercisable as of December 31, 2015
 
13,212,236

 
$
103.67

 
5.23
 
$
5,852,659,560
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
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

2013:
 
 
 
 
 
 
Exercise price equal to Market Price
 
3,937,989

 
$
263.77

 
$
104.90
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 2015, 2014 and 2013.
 
 
2015
 
2014
 
2013
Expected volatility
 
35
%
 
39
%
 
42
%
Expected lives from grant date
 
5.1 years

 
5.2 years

 
5.3 years

Expected dividend yield
 
0
%
 
0
%
 
0
%
Risk-free interest rate
 
1.68
%
 
1.62
%
 
1.73
%
Activity Related to Restricted Stock Awards
A summary of the Company's activity related to Restricted Stock awards for the year ended December 31, 2015 is summarized below:
Restricted Stock:
 
Number of Shares
 
Weighted-Average Grant Date Fair Value
Outstanding as of December 31, 2014
 
546,060

 
$
115.26

2015:
Granted
 
27,520

 
$
540.40

 
Vested
 
(31,880
)
 
$
164.65

Outstanding as of December 31, 2015
 
541,700

 
$
133.96