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Long-Term Incentive Plans (Tables)
12 Months Ended
Dec. 31, 2020
Share-based Payment Arrangement [Abstract]  
Schedule of transactions involving stock option awards
Transactions involving stock option awards during 2020 under the Company's Incentive Plans are summarized in the table below.
Number of SharesWeighted-Average Exercise PriceWeighted-Average Remaining Contractual Term (in years)Intrinsic Value
Outstanding as of December 31, 201928,609,277 $337.24 
2020:Granted2,850,590 $492.60 
Forfeited(562,629)$379.02 
Expired(56,282)$473.77 
Exercised(9,139,287)$281.90 
Outstanding as of December 31, 202021,701,669 $379.51 6.34$2,347.4 
Vested and expected to vest as of December 31, 202020,764,534 $377.23 6.22$2,294.1 
Exercisable as of December 31, 202013,648,899 $357.65 4.96$1,799.1 
Schedule of weighted-average exercise prices and weighted-average grant-date fair values of options issued
The table below summarizes the weighted-average exercise prices and weighted-average grant-date fair values of options issued during the years ended December 31, 2020, 2019, and 2018.
Number of Options GrantedWeighted-Average Exercise PriceWeighted-Average Fair Value
2020:
Exercise price equal to Market Price2,850,590 $492.60 $126.50 
2019:
Exercise price equal to Market Price3,271,222 $366.65 $100.80 
2018:
Exercise price equal to Market Price4,665,320 $378.51 $114.39 
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 2020, 2019, and 2018.
202020192018
Expected volatility28 %28 %29 %
Expected lives from grant date5.0 years5.0 years4.9 years
Expected dividend yield%%%
Risk-free interest rate0.47 %1.74 %2.69 %
The following table summarizes the weighted average values of the assumptions used in computing the fair value of PSUs during 2020 and 2019.
20202019
Expected volatility35%33%
Expected dividend yield0%0%
Risk-free interest rate0.36%1.63%
Schedule of activity related to restricted stock awards
A summary of the Company's activity related to restricted stock awards and time-based restricted stock units (excluding performance-based restricted stock units, which are detailed further below) (collectively, "restricted stock") during 2020 is summarized below.
Number of Shares/UnitsWeighted-Average Grant
Date Fair Value
Balance as of December 31, 20191,102,390 $377.32 
2020:Granted646,844 $496.44 
Vested(15,630)$526.62 
Forfeited/Cancelled(46,061)$377.85 
Balance as of December 31, 20201,687,543 $421.58 
Schedule of activity related to performance-based awards A summary of the Company's activity related to PSUs during 2020 is summarized below.
Number of Shares/UnitsWeighted-Average Grant
Date Fair Value
Balance as of December 31, 201959,396 $198.10 
2020:Granted1,240,540 $209.59 
Vested— — 
Forfeited/Cancelled— — 
Balance as of December 31, 20201,299,936 $209.06