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Share-Based Compensation (Tables)
 9 Months Ended
Sep. 30, 2019
Share-based Payment Arrangement [Abstract]  
Summary of Share-Based Compensation Expense
The following table shows the total share-based compensation expense resulting from equity awards and the 15.0% discount for the ESPP for the three and nine months ended September 30, 2019 and 2018 in the Condensed Consolidated Statements of Income:
 
Three Months Ended September 30,
 
Nine Months Ended September 30,
 
2019
 
2018
 
2019
 
2018
 
(in millions)
Share-based compensation expense before income taxes
$
21

 
$
18

 
$
57

 
$
51

Income tax benefit
(6
)
 
(5
)
 
(16
)
 
(14
)
Share-based compensation expense after income taxes
$
15

 
$
13

 
$
41

 
$
37
Summary of Restricted Stock Activity
The following table summarizes our restricted stock activity for the nine months ended September 30, 2019:
 
Restricted Stock
 
Number of Awards
 
Weighted-Average Grant Date Fair Value
 
 
 
 
Unvested balances at January 1, 2019
1,583,375

 
$
68.62

Granted
587,987

 
$
84.73

Vested
(492,535
)
 
$
59.46

Forfeited
(127,501
)
 
$
73.36

Unvested balances at September 30, 2019
1,551,326

 
$
77.23
Schedule of Weighted-Average Assumptions Used to Determine the Weighted-Average Fair Values
The following weighted-average assumptions were used to determine the weighted-average fair values of the PSU awards granted under the three-year PSU program for the nine months ended September 30, 2019:
 
Nine Months Ended September 30,
 
2019
 
2018
Weighted-average risk free interest rate(1)
2.26
%
 
2.36
%
Expected volatility(2)
16.5
%
 
18.7
%
Weighted-average grant date share price
$89.00
 
$
86.24

Weighted-average fair value at grant date
$97.65
 
$
116.86

____________
(1) 
The risk-free interest rate for periods within the expected life of the award is based on the U.S. Treasury yield curve in effect at the time of grant.
(2) 
We use historic volatility for PSU awards issued under the three-year PSU program, as implied volatility data could not be obtained for all the companies in the peer groups used for relative performance measurement within the program.
Summary of PSU Activity
The following table summarizes our PSU activity for the nine months ended September 30, 2019:
 
PSUs
 
One-Year Program
 
Three-Year Program
 
Number of Awards
 
Weighted-Average Grant Date Fair Value
 
Number of Awards
 
Weighted-Average Grant Date Fair Value
Unvested balances at January 1, 2019
314,231

 
$
74.01

 
837,750

 
$
96.57

Granted(1)
179,599

 
$
83.56

 
397,553

 
$
96.55

Vested
(12,733
)
 
$
67.51

 
(431,751
)
 
$
93.25

Forfeited
(22,943
)
 
$
75.03

 
(6,101
)
 
$
103.29

Unvested balances at September 30, 2019
458,154

 
$
77.88

 
797,451

 
$
98.31


____________
(1) 
Includes target awards granted and certain additional awards granted based on overachievement of performance parameters.
Summary of Stock Options, Valuation Assumptions We estimated the fair value of this stock option award using the Black-Scholes valuation model using the following assumptions:
Expected life (in years)
6

Weighted-average risk free interest rate
2.1
%
Expected volatility
25.6
%
Dividend yield
1.92
%
Summary of Stock Option Activity
A summary of stock option activity for the nine months ended September 30, 2019 is as follows:
 
Number of Stock Options
 
Weighted-Average Exercise Price
 
Weighted-Average Remaining Contractual Term (in years)
 
Aggregate Intrinsic Value (in millions)
 
 
 
 
 
 
 
 
Outstanding at January 1, 2019
448,966

 
$
49.25

 
5.51
 
$
14

Exercised
(62,624
)
 
20.92

 
 
 
 
Forfeited
(25
)
 
20.10

 
 
 
 
Outstanding at September 30, 2019
386,317

 
$
53.68

 
5.43
 
$
18

Exercisable at September 30, 2019
296,711

 
$
49.76

 
4.87
 
$
15