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Stock-based Compensation Expense (Tables)
 3 Months Ended
Apr. 30, 2020
Share-based Payment Arrangement [Abstract]  
Schedule of summary of restricted stock activity
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


 _______________
(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 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

 _______________
(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 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
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:
 
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%