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Share-Based Compensation (Tables) | 12 Months Ended
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Dec. 31, 2019
Share-based Payment Arrangement [Abstract] |
Summary of Weighted Average Assumptions Used for Options Granted | The following weighted average assumptions were used for options granted:
| Years Ended December 31,
| 2019 |  | 2018 |  | 2017
Expected life (in years) | 6.0 |  |  | 6.0 |  |  | 6.0 |
Expected volatility | 26.6 | % |  | 26.7 | % |  | 28.1 | %
Risk-free interest rate | 1.8 | % |  | 2.7 | % |  | 2.0 | %
Expected forfeiture rate | — | % |  | — | % |  | — | %
Summarizes Restricted Stock Unit and Performance Share Activity | The following table summarizes restricted stock unit and performance stock unit activity during fiscal year 2019 (shares in thousands):
|  | Number of Shares |  | Weighted Average Grant Date Fair Value per Share
Unvested at January 1, 2018 |  | — |  |  | $ | — |
Granted |  | 336 |  |  | 221.29 |
Vested |  | — |  |  | — |
Forfeited |  | (2 | ) |  | 229.75 |
Unvested at December 31, 2018 |  | 334 |  |  | 221.25 |
Granted |  | 256 |  |  | 241.19 |
Vested |  | (76 | ) |  | 221.15 |
Forfeited |  | (14 | ) |  | 229.75 |
Unvested at December 31, 2019 |  | 500 |  |  | $ | 231.57 |
Stock Option Activity | Other information pertaining to option activity was as follows during the twelve months ended December 31:
| 2019 |  | 2018 |  | 2017
Weighted average grant-date fair value of stock options granted | $ | 74.54 |  |  | $ | 66.52 |  |  | $ | 55.56 |
Total intrinsic value of stock options exercised | $ | 155,899 |  |  | $ | 176,716 |  |  | $ | 137,699 |
Options granted, exercised, forfeited and expired are summarized as follows:
| Number of Shares |  | Weighted Average Exercise Price |  | Weighted Average Remaining Contractual Life (Years) |  | Aggregate Intrinsic Value
Outstanding at December 31, 2016 | 5,156 |  |  | $ | 83.64 |  |  |  |  |  |
Granted | 824 |  |  | 176.26 |  |  |  |  |  |
Exercised | (1,113 | ) |  | 44.80 |  |  |  |  |  |
Forfeited | (50 | ) |  | 134.83 |  |  |  |  |  |
Outstanding at December 31, 2017 | 4,817 |  |  | 107.91 |  |  |  |  |  |
Granted | 432 |  |  | 208.21 |  |  |  |  |  |
Exercised | (1,126 | ) |  | 66.53 |  |  |  |  |  |
Forfeited | (31 | ) |  | 158.80 |  |  |  |  |  |
Outstanding at December 31, 2018 | 4,092 |  |  | 129.51 |  |  |  |  |
Granted | 162 |  |  | 251.58 |  |  |  |  |
Exercised | (999 | ) |  | 96.92 |  |  |  |  |  |
Forfeited | (29 | ) |  | 174.54 |  |  |  |  |  |
Outstanding at December 31, 2019 | 3,226 |  |  | $ | 145.27 |  |  | 6 |  | $ | 499,124 |
Exercisable at December 31, 2019 | 2,067 |  |  | $ | 121.07 |  |  | 6 |  | $ | 369,938 |
Summary of Share-Based Compensation Expense Related to Share-Based Awards | The following table summarizes share-based compensation expense related to share-based awards which is recorded in the consolidated statements of comprehensive income:
| Years Ended December 31,
| 2019 |  | 2018 |  | 2017
Cost of software services, maintenance and subscriptions | $ | 15,002 |  |  | $ | 13,588 |  |  | $ | 9,415 |
Selling, general and administrative expenses | 44,965 |  |  | 39,152 |  |  | 27,933 |
Total share-based compensation expenses | 59,967 |  |  | 52,740 |  |  | 37,348 |
Excess tax benefit | (29,819 | ) |  | (32,487 | ) |  | (40,624 | )
Net decrease (increase) in net income | $ | 30,148 |  |  | $ | 20,253 |  |  | $ | (3,276 | )

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- Definition Tabular disclosure for stock option plans. Includes, but is not limited to, outstanding awards at beginning and end of year, grants, exercises, forfeitures, and weighted-average grant date fair value. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (d) -URI http://asc.fasb.org/extlink&oid=116856206&loc=d3e5070-113901 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (e) -URI http://asc.fasb.org/extlink&oid=116856206&loc=d3e5070-113901 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (c)(1) -URI http://asc.fasb.org/extlink&oid=116856206&loc=d3e5070-113901 + Details
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- Definition Tabular disclosure of the significant assumptions used during the year to estimate the fair value of stock options, including, but not limited to: (a) expected term of share options and similar instruments, (b) expected volatility of the entity's shares, (c) expected dividends, (d) risk-free rate(s), and (e) discount for post-vesting restrictions. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2) -URI http://asc.fasb.org/extlink&oid=116856206&loc=d3e5070-113901 + Details
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