| Fair value assumptions and methodology |
The fair value of our share-based awards, as shown below, was estimated using the Black-Scholes model with the following weighted-average assumptions: | | | | | | | | | | | | | | | | | | | Year Ended September 30, | | 2020 | | 2019 | | 2018 | | Weighted-average grant date fair value | $ | 39.68 | | | $ | 27.34 | | | $ | 26.59 | | | Expected term (in years) | 6.96 | | 6.86 | | 6.68 | | Expected volatility | 32 | % | | 26 | % | | 26 | % | | Risk-free rate of return | 1.6 | % | | 2.8 | % | | 2.4 | % | | Dividend yield | 1.3 | % | | 1.6 | % | | 1.0 | % |
A summary of stock option activity is as follows: | | | | | | | | | | | | | | | | | | | | | | | | | Stock
Options | | Weighted
Average
Exercise
Price | | Weighted
Average
Remaining
Contractual
Term
(in years) | | Aggregate
Intrinsic
Value
(in thousands) | | Outstanding at September 30, 2019 | 879 | | | $ | 63.44 | | | | | | | Granted | 121 | | | 129.60 | | | | | | | Exercised | (182) | | | 51.50 | | | | | | | Forfeited or canceled | (11) | | | 75.59 | | | | | | | Outstanding at September 30, 2020 | 807 | | | $ | 75.87 | | | 6.2 | | $ | 54,078 | | | | | | | | | | | Exercisable at September 30, 2020 | 499 | | | $ | 58.27 | | | 5.1 | | $ | 42,184 | | | | | | | | | | | Expected to vest at September 30, 2020 | 308 | | | $ | 104.39 | | | 8.1 | | $ | 11,836 | |
| | | | | | | | | | | | | | | | | | | Year Ended September 30, | | 2020 | | 2019 | | 2018 | | Intrinsic value of options exercised | $ | 19,077 | | | $ | 20,711 | | | $ | 30,345 | | | Cash received from exercise of options | 9,350 | | | 13,193 | | | 19,247 | | | Tax benefit from exercise of options | 3,629 | | | 4,449 | | | 7,503 | | | Fair value of options vested | 3,765 | | | 4,506 | | | 5,008 | |
| | | | | | | | | | | | | | | | | | | Year Ended September 30, | | 2020 | | 2019 | | 2018 | | Weighted-average grant date fair value | $ | 39.17 | | | $ | 25.16 | | | $ | 20.94 | | | Shares issued | 46 | | | 49 | | | 50 | | | Expected term (in years) | 0.5 | | 0.5 | | 0.5 | | Expected volatility | 52 | % | | 34 | % | | 26 | % | | Risk-free rate of return | 1.7 | % | | 2.3 | % | | 1.5 | % | | Dividend yield | 1.3 | % | | 1.6 | % | | 1.1 | % |
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| Summary of restricted stock awards and restricted stock unit awards |
A summary of the activity of the restricted stock awards, RSU awards, and PSU awards is presented below: | | | | | | | | | | | | | Restricted Stock
Awards and Units | | Weighted Average
Grant Date Fair
Value | | Nonvested at September 30, 2019 | 275 | | | $ | 87.36 | | Granted 1 | 88 | | | 125.14 | | | Vested | (100) | | | 74.65 | | | Forfeited | (6) | | | 83.65 | | | Nonvested at September 30, 2020 | 257 | | | $ | 104.83 | |
1 Includes PSUs awarded
| | | | | | | | | | | | | | | | | | | Year Ended September 30, | | 2020 | | 2019 | | 2018 | | Weighted average grant date fair value | $ | 104.83 | | | $ | 87.36 | | | $ | 70.42 | |
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| Share based compensation expense |
Total share-based compensation expense and the classification of that expense in the Consolidated Statements of Income for the years ended September 30, 2020, 2019 and 2018, is as follows:
| | | | | | | | | | | | | | | | | | | Year Ended September 30, | | 2020 | | 2019 | | 2018 | | Cost of sales | $ | 2,863 | | | $ | 2,727 | | | $ | 2,450 | | | Research, development and technical | 2,090 | | | 2,150 | | | 1,940 | | | Selling, general and administrative | 11,443 | | | 13,350 | | | 14,128 | | | Tax benefit | (3,162) | | | (3,767) | | | (4,306) | | | Total share-based compensation expense, net of tax | $ | 13,234 | | | $ | 14,460 | | | $ | 14,212 | |
Total gross share-based compensation expense is attributable to the following awards: | | | | | | | | | | | | | | | | | | | Year Ended September 30, | | 2020 | | 2019 | | 2018 | | Stock Options | $ | 4,406 | | | $ | 4,267 | | | $ | 6,392 | | | Restricted stock, restricted stock units, and replacement awards | 8,259 | | | 11,400 | | | 9,186 | | | Performance share units | 1,957 | | | 1,279 | | | 2,056 | | | ESPP | 1,774 | | | 1,281 | | | 885 | |
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