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Stock-based Compensation Expense (Tables)
 9 Months Ended
Oct. 31, 2019
Share-based Payment Arrangement [Abstract]  
Schedule of stock options roll forward
A summary of stock option activity for the nine months ended October 31, 2019 is as follows:
 
Number of shares (in millions)
 
Weighted average exercise price per share
 
Weighted average remaining contractual term (in years)
 
Aggregate intrinsic value (1) (in millions)
Options outstanding at January 31, 2019
0.8

 
$
23.95

 
 
 
 
Exercised
(0.2
)
 
23.16

 
 
 
 
Canceled/Forfeited
(0.1
)
 
21.25

 
 
 
 
Options outstanding at October 31, 2019
0.5

 
$
24.66

 
6.7
 
$
63.3

Options vested and exercisable at October 31, 2019
0.2

 
$
31.13

 
4.0
 
$
22.0

Shares available for grant at October 31, 2019
15.0

 
 
 
 
 
 
_______________
(1)
Represents the total pre-tax intrinsic value, based on Autodesk’s closing stock price of $147.36 per share as of October 31, 2019.
Intrinsic value of options exercised
The following table summarizes information about the pre-tax intrinsic value of options exercised during the nine months ended October 31, 2019 and 2018:
(in millions)
Nine Months Ended October 31,
 
2019
 
2018
Pre-tax intrinsic value of options exercised (1)
$
32.0

 
$
6.9

——————
(1)
The intrinsic value of options exercised is calculated as the difference between the exercise price of the option and the market value of the stock on the date of exercise.
Schedule of summary of restricted stock activity
A summary of restricted stock activity for the nine months ended October 31, 2019, is as follows:
 
 
Unvested
restricted
stock units
 
Weighted
average grant
date fair value
per share
 
(in thousands)
 
 
Unvested restricted stock units at January 31, 2019
4,287.4

 
$
120.07

Granted
2,812.3

 
153.63

Vested
(1,814.0
)
 
109.19

Canceled/Forfeited
(326.1
)
 
130.34

        Performance Adjustment (1)
23.8

 
156.69

Unvested restricted stock units at October 31, 2019
4,983.4

 
$
143.06


 _______________
(1)
Based on Autodesk's financial results and relative total stockholder return for the fiscal 2019 performance period. The performance stock units were attained at rates ranging from 105.2% to 122.5% of the target award.

Schedule of summary of the ESPP activity
A summary of the ESPP activity for the three and nine months ended October 31, 2019 and 2018 is as follows:

 
Three Months Ended October 31,
 
Nine Months Ended October 31,
 
2019
 
2018
 
2019
 
2018
Issued shares (in millions)
0.4

 
0.5

 
0.9

 
1.0

Average price of issued shares
$
105.42

 
$
92.50

 
$
102.20

 
$
90.25

Weighted average grant date fair value of awards granted under the ESPP (1)
$
44.77

 
$
47.21

 
$
47.78

 
$
42.75

 _______________
(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 nine months ended October 31, 2019 and 2018, respectively, as follows:
 
 
Three Months Ended October 31,
 
Nine Months Ended October 31,
 
2019
 
2018
 
2019
 
2018
Cost of subscription and maintenance revenue
$
3.1

 
$
3.6

 
$
10.1

 
$
9.4

Cost of other revenue
1.6

 
1.3

 
4.3

 
3.0

Marketing and sales
38.7

 
27.8

 
107.2

 
77.7

Research and development
30.8

 
20.6

 
88.3

 
57.1

General and administrative
19.8

 
10.9

 
47.5

 
28.3

Stock-based compensation expense related to stock awards and ESPP purchases
94.0

 
64.2

 
257.4

 
175.5

Tax benefit
(0.5
)
 
(1.6
)
 
(0.8
)
 
(2.2
)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax
$
93.5

 
$
62.6

 
$
256.6

 
$
173.3
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 October 31, 2019
 
Three Months Ended October 31, 2018
 
Performance Stock Units (1)
 
ESPP
 
Performance Stock Units (1)

ESPP
Range of expected volatilities
N/A
 
32.7 - 35.9%
 
N/A

32.7 - 34.6%
Range of expected lives (in years)
N/A
 
0.5 - 2.0
 
N/A

0.5 - 2.0
Expected dividends
N/A
 
—%
 
N/A

—%
Range of risk-free interest rates
N/A
 
1.7 - 1.9%
 
N/A

2.3 - 2.8%
 
Nine Months Ended October 31, 2019
 
Nine Months Ended October 31, 2018
 
Performance Stock Units
 
ESPP
 
Performance Stock Units
 
ESPP
Range of expected volatilities
36.3%
 
32.7 - 39.7%
 
35.7%
 
32.7 - 37.5%
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
2.5%
 
1.7 - 2.5%
 
2.0%
 
1.9 - 2.8%

_______________ 
(1) There were no performance stock units granted for the three months ended October 31, 2019 and 2018 where the fair value was estimated by a Monte Carlo simulation model.