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Stock-Based Compensation (Tables)
9 Months Ended
Jun. 30, 2021
Share-based Payment Arrangement [Abstract]  
Stock Based Compensation Included in Consolidated Statements of Operations The amounts included in the consolidated statements of operations related to stock-based compensation are as follows (dollars in thousands): 
 Three Months Ended June 30,Nine Months Ended June 30,
2021202020212020
Cost of hosting and professional services$6,327 $5,748 $19,732 $16,525 
Cost of product and licensing103 124 280 382 
Cost of maintenance and support423 360 1,268 1,200 
Research and development9,230 8,530 26,402 25,274 
Sales and marketing8,974 8,002 26,475 22,825 
General and administrative9,597 9,723 30,279 28,817 
Total$34,654 $32,487 $104,436 $95,023 
Summary of Stock Options Activity
The table below summarizes activities related to stock options for the nine months ended June 30, 2021:
Number of
Shares
Weighted
Average
Exercise
Price
Weighted
Average
Remaining
Contractual
Term
Aggregate
Intrinsic
Value (a)
Outstanding at September 30, 20209,355 $17.18 
Outstanding at June 30, 20219,355 $17.18 0.8 years$0.3  million
Exercisable at June 30, 20219,355 $17.18 0.8 years$0.3  million
Exercisable at June 30, 20209,355 $17.18 1.8 years$0.1  million
__________
(a)The aggregate intrinsic value in this table represents any excess of the closing market price of our common stock as of June 30, 2021 ($54.44) over the exercise price of the underlying options.
Summary of Activity Relating to Restricted Units and Restricted Stock Awards The table below summarizes activities relating to restricted units for the nine months ended June 30, 2021:
Number of Shares Underlying Restricted Units — Performance-Based AwardsNumber of Shares Underlying Restricted Units — Time-Based Awards
Outstanding at September 30, 20202,620,120 7,157,649 
Granted1,048,943 2,094,247 
Earned/released(1,067,802)(3,489,771)
Forfeited(137,340)(275,159)
Outstanding at June 30, 20212,463,921 5,486,966 
Weighted average remaining recognition period of outstanding Restricted Units1.2 years1.5 years
Unrecognized stock-based compensation expense of outstanding Restricted Units$23.1 million$65.3 million
Aggregate intrinsic value of outstanding Restricted Units (a)
$134.1 million$298.7 million
__________
(a)The aggregate intrinsic value in this table represents any excess of the closing market price of our common stock as of June 30, 2021 ($54.44) over the purchase price of the underlying restricted units.
Summary of Weighted-Average Grant-Date Fair Value and Intrinsic Value of Restricted Units and Restricted Stock Awards Vested
A summary of the weighted-average grant-date fair value of restricted units granted, and the aggregate intrinsic value of restricted units vested during the periods noted is as follows: 
 Nine Months Ended June 30,
20212020
Weighted-average grant-date fair value per share$38.05 $17.71 
Total intrinsic value of shares vested (in millions)$193.5 $115.6 
Schedule of Key Assumptions of the Valuation Below is a summary of key assumptions of the valuation:
Nine Months Ended June 30,
20212020
Dividend yield
0.0%
0.0%
Expected volatility
34.95%
27.73% - 28.24%
Risk-free interest rate
0.21%
1.40% - 1.62%
Expected term (in years)
3.00
2.72 - 3.00