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Share-based Compensation (Tables)
12 Months Ended
Dec. 31, 2019
Share-based Payment Arrangement [Abstract]  
Summary of stock-based compensation The following table summarizes our share-based compensation expense:
 
Year ended December 31,
 
2019
 
2018
 
2017
 
in millions
Included in:
 
 
 
 
 
Other operating expense
$
0.9

 
$
0.6

 
$
0.5

SG&A expense
56.6

 
39.2

 
13.7

Total
$
57.5

 
$
39.8

 
$
14.2


Schedule of assumptions used
The following table summarizes certain information related to the share-based incentive awards granted and exercised:
 
Year ended December 31,
Assumptions used to estimate fair value of SARs granted:
2019
 
2018
 
 
 
 
Risk-free interest rate
1.69 - 2.41%
 
2.24 - 3.05%
Expected life
4.6 - 7.0 years
 
4.6 - 7.0 years
Expected volatility
33.1 - 36.4%
 
29.8 - 38.2%
Expected dividend yield
none
 
none
Weighted average grant-date fair value per share of awards granted:
 
 
 
SARs
$
6.86

 
$
7.05

RSUs
$
19.75

 
$
18.41

PSUs
$
16.95

 
$
19.49

Total intrinsic value of SARs exercised (in millions)
$

 
$

Income tax benefit related to share-based compensation (in millions)
$
3.8

 
$
6.2


Schedule of SARs
The following tables summarize the share-based incentive award activity during 2019 with respect to Liberty Latin America awards held by our employees and our board of directors.
 
Number of
shares
 
Weighted
average
base price
 
Weighted
average
remaining
contractual
term
 
Aggregate intrinsic value
SARs Class A shares
 
 
 
 
in years
 
in millions
Outstanding at January 1, 2019
2,536,333

 
$
22.77

 
 
 
 
Granted
1,125,735

 
$
19.60

 
 
 
 
Forfeited
(225,202
)
 
$
22.03

 
 
 
 
Exercised
(9,203
)
 
$
18.80

 
 
 
 
Outstanding at December 31, 2019
3,427,663

 
$
21.80

 
5.2
 
$
0.9

Exercisable at December 31, 2019
1,290,049

 
$
24.45

 
4.4
 
$
0.2


 
Number of
shares
 
Weighted
average
base price
 
Weighted
average
remaining
contractual
term
 
Aggregate intrinsic value
SARs Class C shares
 
 
 
 
in years
 
in millions
Outstanding at January 1, 2019
5,136,950

 
$
22.82

 
 
 
 
Granted
2,226,828

 
$
19.75

 
 
 
 
Forfeited
(441,804
)
 
$
22.52

 
 
 
 
Exercised
(17,562
)
 
$
18.24

 
 
 
 
Outstanding at December 31, 2019
6,904,412

 
$
21.87

 
5.1
 
$
2.7

Exercisable at December 31, 2019
2,626,453

 
$
24.67

 
4.3
 
$
0.8


The following tables summarize the share-based incentive awards related to Liberty Global Shares held by employees of Liberty Latin America as of December 31, 2019:
 
Number of
shares
 
Weighted
average
base price
 
Weighted
average
remaining
contractual
term
Share-based incentive award type
 
 
 
 
in years
SARs:
 
 
 
 
 
Liberty Global Class A ordinary shares:
 
 
 
 
 
Outstanding
1,131,589

 
$
33.65

 
2.1
Exercisable
1,051,164

 
$
33.61

 
2.0
Liberty Global Class C ordinary shares:
 
 
 
 
 
Outstanding
2,596,472

 
$
31.64

 
1.9
Exercisable
2,435,590

 
$
31.53

 
1.8
Schedule of RSUs
 
Number of
shares
 
Weighted
average
grant-date fair value per share
 
Weighted
average
remaining
contractual
term
RSUs Class A shares
 
 
 
 
in years
Outstanding at January 1, 2019
199,994

 
$
21.94

 
 
Granted
233,388

 
$
19.70

 
 
Forfeited
(32,025
)
 
$
21.06

 
 
Released from restrictions
(155,531
)
 
$
21.35

 
 
Outstanding at December 31, 2019
245,826

 
$
20.23

 
2.5
 
Number of
shares
 
Weighted
average
grant-date fair value per share
 
Weighted
average
remaining
contractual
term
RSUs Class C shares
 
 
 
 
in years
Outstanding at January 1, 2019
399,747

 
$
21.86

 
 
Granted
466,776

 
$
19.77

 
 
Forfeited
(64,028
)
 
$
21.04

 
 
Released from restrictions
(311,170
)
 
$
21.33

 
 
Outstanding at December 31, 2019
491,325

 
$
20.25

 
2.5

 
Number of
shares
 
Weighted
average
grant-date fair value per share
 
Weighted
average
remaining
contractual
term
Share-based incentive award type
 
 
 
 
in years
RSUs outstanding:
 
 
 
 
 
Liberty Global Class A ordinary shares
4,550

 
$
32.37

 
1.4
Liberty Global Class C ordinary shares
9,085

 
$
32.05

 
1.4

Schedule of PSUs
 
Number of
shares
 
Weighted
average
grant-date fair value per share
 
Weighted
average
remaining
contractual
term
Share-based incentive award type
 
 
 
 
in years
RSUs outstanding:
 
 
 
 
 
Liberty Global Class A ordinary shares
4,550

 
$
32.37

 
1.4
Liberty Global Class C ordinary shares
9,085

 
$
32.05

 
1.4

 
Number of
shares
 
Weighted
average
grant-date fair value per share
 
Weighted
average
remaining
contractual
term
PSUs Class A shares
 
 
 
 
in years
Outstanding at January 1, 2019
505,722

 
$
20.63

 
 
Granted
366,795

 
$
16.90

 
 
Forfeited
(173,987
)
 
$
21.72

 
 
Released from restrictions
(19,682
)
 
$
31.63

 
 
Outstanding at December 31, 2019
678,848

 
$
18.08

 
1.3
 
Number of
shares
 
Weighted
average
grant-date fair value per share
 
Weighted
average
remaining
contractual
term
PSUs Class C shares
 
 
 
 
in years
Outstanding at January 1, 2019
1,011,451

 
$
20.84

 
 
Granted
721,238

 
$
16.99

 
 
Forfeited
(336,805
)
 
$
22.28

 
 
Released from restrictions
(38,188
)
 
$
31.89

 
 
Outstanding at December 31, 2019
1,357,696

 
$
18.19

 
1.3