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Stock-based Compensation Expense (Tables) | 6 Months Ended
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Jul. 31, 2020
Share-based Payment Arrangement [Abstract] |
Schedule of summary of restricted stock activity | A summary of restricted stock activity for the six months ended July 31, 2020, is as follows:
| Unvested restricted stock units |  | Weighted average grant date fair value per share
| (in thousands) |  |
Unvested restricted stock units at January 31, 2020 | 4,732.3 |  |  | $ | 147.24 |
Granted | 867.8 |  |  | 176.50 |
Vested | (818.5 | ) |  | 147.68 |
Canceled/Forfeited | (123.1 | ) |  | 148.02 |
Performance Adjustment (1) | 15.4 |  |  | 166.97 |
Unvested restricted stock units at July 31, 2020 | 4,673.9 |  |  | $ | 152.44 |
_______________
(1) | Based on Autodesk's financial results and relative total stockholder return for the fiscal 2020 performance period. The performance stock units were attained at rates ranging from 96.6% to 101.1% of the target award.
Schedule of summary of the ESPP activity | A summary of the ESPP activity for the six months ended July 31, 2020 and 2019, is as follows:
| Six Months Ended July 31,
| 2020 |  | 2019
Issued shares (in millions) | 0.5 |  |  | 0.5 |
Average price of issued shares | $ | 122.54 |  |  | $ | 99.46 |
Weighted average grant date fair value of awards granted under the ESPP (1) | $ | 45.70 |  |  | $ | 52.41 |
_______________ (1) Calculated as of the award grant date using the Black-Scholes Merton (“BSM") option pricing model.
Schedule of stock-based compensation expense | The following table summarizes stock-based compensation expense for the three and six months ended July 31, 2020 and 2019, respectively, as follows:
| Three Months Ended July 31, |  | Six Months Ended July 31,
(in millions) | 2020 |  | 2019 |  | 2020 |  | 2019
Cost of subscription and maintenance revenue | $ | 4.2 |  |  | $ | 3.4 |  |  | $ | 7.9 |  |  | $ | 7.0 |
Cost of other revenue | 1.5 |  |  | 1.4 |  |  | 3.0 |  |  | 2.7 |
Marketing and sales | 43.4 |  |  | 36.0 |  |  | 84.1 |  |  | 68.5 |
Research and development | 35.3 |  |  | 30.8 |  |  | 68.2 |  |  | 57.5 |
General and administrative | 11.5 |  |  | 16.6 |  |  | 30.9 |  |  | 27.7 |
Stock-based compensation expense related to stock awards and ESPP purchases | 95.9 |  |  | 88.2 |  |  | 194.1 |  |  | 163.4 |
Tax benefit | (0.2 | ) |  | (0.1 | ) |  | (0.3 | ) |  | (0.3 | )
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax | $ | 95.7 |  |  | $ | 88.1 |  |  | $ | 193.8 |  |  | $ | 163.1 |
Schedule of assumptions to estimate the fair value of stock-based awards | Autodesk uses the following assumptions to estimate the fair value of stock-based awards:
| Six Months Ended July 31, 2020 |  | Six Months Ended July 31, 2019
| Performance Stock Units (1) |  | ESPP (1) |  | Performance Stock Units (1) |  | ESPP (1)
Range of expected volatilities | 50.7% |  | 39.4 - 45.8% |  | 36.3% |  | 36.6 - 39.7%
Range of expected lives (in years) | N/A |  | 0.5 - 2.0 |  | N/A |  | 0.5 - 2.0
Expected dividends | —% |  | —% |  | —% |  | —%
Range of risk-free interest rates | 0.3% |  | 0.3 - 0.5% |  | 2.5% |  | 2.4 - 2.5%
—————— (1) There were no performance stock units or ESPP awards granted during the three months ended July 31, 2020 and 2019, where the fair value was estimated by a Monte Carlo simulation model or a BSM option pricing model, respectively.

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- Definition Tabular disclosure of allocation of amount expensed and capitalized for award under share-based payment arrangement to statement of income or comprehensive income and statement of financial position. Includes, but is not limited to, corresponding line item in financial statement. + 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 (h)(1) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SAB Topic 14.F) -URI http://asc.fasb.org/extlink&oid=115993241&loc=d3e301413-122809 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 1 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5047-113901 + Details
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- Definition Tabular disclosure of employee stock purchase plan activity. + 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 (g) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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- Definition Disclosure of the number and weighted-average grant date fair value for restricted stock and restricted stock units that were outstanding at the beginning and end of the year, and the number of restricted stock and restricted stock units that were granted, vested, or forfeited during the year. + References No definition available. + Details
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