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Stock-Based Compensation
3 Months Ended
Oct. 31, 2020
Share-based Payment Arrangement [Abstract]  
Stock-Based Compensation Stock-Based Compensation
2016 Equity Incentive Plan
 
At October 31, 2020, 763,315 nonvested restricted stock awards were outstanding under the 2016 plan. No options were outstanding under the 2016 plan. At October 31, 2020, 51,760 shares were collectively available for issuance pursuant to restricted stock and other stock awards, stock options and stock appreciation rights.
 
The following table shows the components of stock-based compensation expense recognized in the condensed consolidated statements of income:
 Three Months Ended October 31,
 20202019
Cost of sales$299 $260 
Operating expenses:  
Selling826 536 
General and administrative2,208 1,527 
Research and development89 81 
Total operating expenses3,123 2,144 
Stock-based compensation expense$3,422 $2,404 

At October 31, 2020, total unrecognized stock-based compensation expense related to total nonvested stock options and restricted stock awards was $36,996 with a remaining weighted average period of 21 months over which such expense is expected to be recognized.

We determined the fair value of our market-based restricted stock awards using a Monte Carlo simulation on the date of grant using the following assumptions:
Three Months Ended October 31,
20202019
Volatility of common stock57.27 %30.73 %
Average volatility of peer companies45.37 %36.28 %
Average correlation coefficient of peer companies34.81 %24.63 %
Risk-free interest rate0.20 %1.49 %
A summary of nonvested stock award activity for the three months ended October 31, 2020 is as follows:
 Number of
Time-based Awards
Number of Performance-based AwardsNumber of Market-based AwardsNumber of
Total
Awards
Weighted Average
Fair Value
At July 31, 2020318,702 29,174 63,839 411,715 $76.29 
Granted388,605 (4,455)86,915 471,065 $46.80 
Vested(1)
(103,819)(3,037)(6,383)(113,239)$82.34 
Forfeited(5,255)— (971)(6,226)$74.10 
At October 31, 2020598,233 21,682 143,400 763,315 $57.53 
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(1)The aggregate fair value of all nonvested stock awards which vested was approximately $9,328.

A summary of stock option activity for the three months ended October 31, 2020 is as follows:
 Number of sharesWeighted Average Exercise Price
Outstanding at July 31, 202015,000 $55.36 
Expired(15,000)$55.36 
Outstanding at October 31, 2020— $— 

Excess tax benefits arise when the ultimate tax effect of the deduction for tax purposes is greater than the income tax benefit on stock-based compensation. For the three months ended October 31, 2020, income tax deductions of $1,698 were generated, of which $2,778 was recorded as a reduction in income tax expense over the equity awards’ vesting period and the remaining excess tax expense of $1,080 was recorded as an increase in income tax expense. For the three months ended October 31, 2019, income tax deductions of $2,022 were generated, of which $2,581 were recorded as a reduction in income tax expense over the equity awards’ vesting period and the remaining excess tax expense of $559 was recorded as an increase to income tax expense.