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Stock-based Compensation Expense | 3 Months Ended
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Apr. 30, 2020
Share-based Payment Arrangement [Abstract] |
Stock-based Compensation Expense | Stock-based Compensation Expense Restricted Stock Units: A summary of restricted stock activity for the three months ended April 30, 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 | 775.4 |  |  | 168.55 |
Vested | (727.6 | ) |  | 148.38 |
Canceled/Forfeited | (63.4 | ) |  | 148.64 |
Performance Adjustment (1) | 15.4 |  |  | 166.97 |
Unvested restricted stock units at April 30, 2020 | 4,732.1 |  |  | $ | 150.43 |
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(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.
The fair value of the shares vested during the three months ended April 30, 2020 and 2019, was $111.4 million and $50.3 million, respectively. During the three months ended April 30, 2020, Autodesk granted 0.5 million restricted stock units. Autodesk recorded stock-based compensation expense related to restricted stock units of $76.9 million and $54.4 million during the three months ended April 30, 2020 and 2019, respectively. During the three months ended April 30, 2020, Autodesk settled the remaining liability-classified awards in the amount of $28.7 million. The ultimate number of shares earned was based on the Autodesk closing stock price on the vesting date. As these awards were settled in a fixed dollar amount of shares, the awards were accounted for as a liability-classified award and were expensed using the straight-line method over the vesting period. During the three months ended April 30, 2020, Autodesk granted 0.3 million performance stock units for which the ultimate number of shares earned is determined based on the achievement of performance criteria at the end of the stated service and performance period. The performance criteria for the performance stock units are based on revenue goals adopted by the Compensation and Human Resource Committee, as well as total stockholder return compared against companies in the S&P North American Technology Software Index with a market capitalization over $2.0 billion (“Relative TSR”). The fair value of the performance stock units is expensed using the accelerated attribution method over the three-year vesting period and have the following vesting schedule:
• | Up to one third of the performance stock units may vest following year one, depending upon the achievement of the performance criteria for fiscal 2021 as well as 1-year Relative TSR (covering year one).
• | Up to one third of the performance stock units may vest following year two, depending upon the achievement of the performance criteria for year two as well as 2-year Relative TSR (covering years one and two).
• | Up to one third of the performance stock units may vest following year three, depending upon the achievement of the performance criteria for year three as well as 3-year Relative TSR (covering years one, two and three).
Performance stock units are not considered outstanding stock at the time of grant, as the holders of these units are not entitled to any of the rights of a stockholder, including voting rights. Autodesk recorded stock-based compensation expense related to performance stock units of $7.4 million and $6.5 million for the three months ended April 30, 2020 and 2019, respectively. 1998 Employee Qualified Stock Purchase Plan (“ESPP”) Under Autodesk’s ESPP, which was approved by stockholders in 1998, eligible employees may purchase shares of Autodesk’s common stock at their discretion using up to 15% of their eligible compensation, subject to certain limitations, at 85% of the lower of Autodesk's closing price (fair market value) on the offering date or the exercise date. The offering period for ESPP awards consists of four, six-month exercise periods within a 24-month offering period. A summary of the ESPP activity for the three months ended April 30, 2020 and 2019 is as follows:
| Three Months Ended April 30,
| 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 |
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(1) | Calculated as of the award grant date using the Black-Scholes Merton (“BSM") option pricing model.
Stock-based Compensation Expense The following table summarizes stock-based compensation expense for the three months ended April 30, 2020 and 2019, respectively, as follows:
| Three Months Ended April 30,
(in millions) | 2020 |  | 2019
Cost of subscription and maintenance revenue | $ | 3.7 |  |  | $ | 3.6 |
Cost of other revenue | 1.5 |  |  | 1.3 |
Marketing and sales | 40.7 |  |  | 32.5 |
Research and development | 32.9 |  |  | 26.7 |
General and administrative | 19.4 |  |  | 11.1 |
Stock-based compensation expense related to stock awards and ESPP purchases | 98.2 |  |  | 75.2 |
Tax benefit | (0.1 | ) |  | (0.2 | )
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax | $ | 98.1 |  |  | $ | 75.0 |
Stock-based Compensation Expense Assumptions Autodesk determines the grant date fair value of its share-based payment awards using a BSM option pricing model or the quoted stock price on the date of grant, unless the awards are subject to market conditions, in which case Autodesk uses a binomial-lattice model (e.g., Monte Carlo simulation model). The Monte Carlo simulation model uses multiple input variables to estimate the probability that market conditions will be achieved. Autodesk uses the following assumptions to estimate the fair value of stock-based awards:
| Three Months Ended April 30, 2020 |  | Three Months Ended April 30, 2019
| Performance Stock Units |  | ESPP |  | Performance Stock Units |  | ESPP
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%
Autodesk estimates expected volatility for stock-based awards based on the average of the following two measures: (1) a measure of historical volatility in the trading market for the Company’s common stock, and (2) the implied volatility of traded forward call options to purchase shares of the Company’s common stock. The expected volatility for performance stock units subject to market conditions includes the expected volatility of Autodesk's peer companies within the S&P North American Technology Software Index with a market capitalization over $2.0 billion, depending on the award type. The range of expected lives of ESPP awards are based upon the four, six-month exercise periods within a 24-month offering period. Autodesk does not currently pay, and does not anticipate paying in the foreseeable future, any cash dividends. Consequently, an expected dividend yield of zero is used in the BSM option pricing model and the Monte Carlo simulation model. The risk-free interest rate used in the BSM option pricing model and the Monte Carlo simulation model for stock-based awards is the historical yield on U.S. Treasury securities with equivalent remaining lives. Autodesk recognizes expense only for the stock-based awards that ultimately vest. Autodesk accounts for forfeitures of our stock-based awards as those forfeitures occur.

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