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Stock-Based Compensation (Tables)
3 Months Ended
Oct. 31, 2019
Share-based Payment Arrangement [Abstract]  
Schedule of the income statement components of stock-based compensation expense recognized in the Condensed Consolidated Statements of Income
The following table shows the components of stock-based compensation expense recognized in the condensed consolidated statements of income:
 
Three Months Ended October 31,
 
2019
 
2018
Cost of sales
$
260

 
$
237

Operating expenses:
 

 
 

Selling
536

 
571

General and administrative
1,527

 
1,710

Research and development
81

 
58

Total operating expenses
2,144

 
2,339

Stock-based compensation expense
$
2,404

 
$
2,576


Schedule of weighted-average assumptions used to estimate fair value of stock options
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,
 
2019
 
2018
Volatility of common stock
30.73
%
 
27.54
%
Average volatility of peer companies
36.28
%
 
36.55
%
Average correlation coefficient of peer companies
24.63
%
 
27.18
%
Risk-free interest rate
1.49
%
 
2.93
%

Summary of nonvested stock award activity
A summary of nonvested stock award activity for the three months ended October 31, 2019 follows:
 
 
Number of
Time-based Awards
 
Number of Performance-based Awards
 
Number of Market-based Awards
 
Number of
Total
Awards
 
Weighted Average
Fair Value
July 31, 2019
 
234,864

 
40,210

 
32,079

 
307,153

 
$
88.99

Granted
 
204,206

 

 
47,967

 
252,173

 
$
73.67

Vested(1)
 
(86,937
)
 
(8,475
)
 
(3,462
)
 
(98,874
)
 
$
90.74

Forfeited
 
(8,016
)
 
(215
)
 

 
(8,231
)
 
$
80.25

October 31, 2019
 
344,117

 
31,520

 
76,584

 
452,221

 
$
80.14

_______________________________________________
(1)
The aggregate fair value of all nonvested stock awards which vested was approximately $8,971.
Summary of stock option activity
A summary of stock option activity for the three months ended October 31, 2019 follows:
 
Number of shares
 
Weighted Average Exercise Price
 
Weighted Average Contractual Life Remaining (Years)
 
Aggregate Intrinsic Value
Outstanding at July 31, 2019
40,000

 
$
43.70

 
 
 
 
Exercised
(25,000
)
 
$
36.70

 
 
 
 
Outstanding at October 31, 2019
15,000

 
$
55.36

 
0.95
 
$
263

Exercisable at October 31, 2019
15,000

 
$
55.36

 
0.95
 
$
263