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Long-Term Incentive Plans (Tables)
12 Months Ended
Dec. 31, 2018
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]  
Schedule of transactions involving stock option awards
Transactions involving stock option awards during 2018 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, 2017
 
26,205,373

 
$
295.98

 

 


2018:
Granted
 
4,665,320

 
$
378.51

 
 
 
 
 
Forfeited
 
(668,550
)
 
$
422.56

 
 
 
 
 
Expired
 
(205,030
)
 
$
467.40

 
 
 
 
 
Exercised
 
(1,717,417
)
 
$
66.87

 
 
 
 
Outstanding as of December 31, 2018
 
28,279,696

 
$
319.28

 
6.43
 
$
2,290.5

 
 
 
 
 
 
 
 
 
Vested and expected to vest as of December 31, 2018
 
27,192,461

 
$
316.51

 
6.32
 
$
2,289.1

 
 
 
 
 
 
 
 
 
Exercisable as of December 31, 2018
 
17,893,976

 
$
275.10

 
4.98
 
$
2,276.2

Schedule of 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
2018:
 
 
 
 
 
 
Exercise price equal to Market Price
 
4,665,320

 
$
378.51

 
$
114.39

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

Schedule of 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 2018, 2017, and 2016.
 
 
2018
 
2017
 
2016
Expected volatility
 
29
%
 
31
%
 
34
%
Expected lives from grant date
 
4.9 years

 
5.1 years

 
5.1 years

Expected dividend yield
 
0
%
 
0
%
 
0
%
Risk-free interest rate
 
2.69
%
 
2.16
%
 
1.84
%
Schedule of activity related to restricted stock awards
A summary of the Company's activity related to restricted stock awards and restricted stock units (collectively, "restricted stock") during 2018 is summarized below:
 
 
Number of Shares/Units
 
Weighted-Average Grant Date Fair Value
Balance as of December 31, 2017
 
106,260

 
$
404.72

2018:
Granted
 
380,980

 
$
381.21

 
Vested
 
(6,090
)
 
$
276.46

 
Forfeited/Cancelled
 
(8,520
)
 
$
478.19

Balance as of December 31, 2018
 
472,630

 
$
386.10