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Share-based compensation (Tables)
 6 Months Ended
Jan. 31, 2018
Disclosure Of Compensation Related Costs Sharebased Payments [Abstract]  
Share-Based Compensation Expense

The following table presents share-based compensation expense included in our Consolidated Statements of Operations:

 

 

 

Three Months Ended

 

 

Six Months Ended

 

 

 

January 31,

 

 

January 31,

 

(in millions)

 

2018

 

 

2017

 

 

2018

 

 

2017

 

Cost of product sales

 

$

0.1

 

 

$

0.1

 

 

$

0.2

 

 

$

0.2

 

Cost of engineering sales

 

 

0.1

 

 

 

0.1

 

 

 

0.1

 

 

 

0.1

 

Research and product development

 

 

0.4

 

 

 

0.5

 

 

 

0.9

 

 

 

0.9

 

Selling and marketing

 

 

0.2

 

 

 

0.5

 

 

 

0.4

 

 

 

0.9

 

General and administrative

 

 

1.1

 

 

 

1.4

 

 

 

2.3

 

 

 

2.2

 

Total share-based compensation expense before tax

 

 

1.9

 

 

 

2.6

 

 

 

3.9

 

 

 

4.2

 

Income tax effect

 

 

(0.4

)

 

 

(0.8

)

 

 

(0.5

)

 

 

(1.3

)

Share-based compensation expense included in net income

 

$

1.5

 

 

$

1.8

 

 

$

3.4

 

 

$

2.9

 

 
Fair Value of TSR Performance-Based Awards Grant Assumptions

The fair value of our TSR performance-based awards at the date of grant was estimated using the Monte-Carlo simulation model with the following assumptions:

 

 

Three Months Ended

 

 

Six Months Ended

 

 

 

January 31,

 

 

January 31,

 

 

 

2018

 

 

2017

 

 

2018

 

 

2017

 

Stock price (1)

 

$

-

 

 

$

-

 

 

$

77.15

 

 

$

90.23

 

Expected volatility (2)

 

 

0.00

%

 

 

0.00

%

 

 

26.88

%

 

 

27.0

%

Risk-free interest rate (3)

 

 

0.00

%

 

 

0.00

%

 

 

1.48

%

 

 

0.85

%

Expected annual dividend yield (4)

 

 

0.00

%

 

 

0.00

%

 

 

0.00

%

 

 

0.00

%

Weighted average grant date fair value of time-based

   restricted stock awards

 

$

82.71

 

 

$

92.30

 

 

$

77.19

 

 

$

89.48

 

Weighted average grant date fair value of performance

   based restricted stock awards

 

$

0.00

 

 

$

-

 

 

$

79.87

 

 

$

87.05

 

 

(1)

The stock price is the closing price of our common stock on the date of grant.

(2)

The expected volatility for each grant is determined based on the historical volatility for the peer group companies and our common stock over a period equal to the remaining term of the performance period from the date of grant for all awards.

(3)

The risk-free interest rate is determined based on the yield of zero-coupon U.S. Treasury securities for a period that is commensurate with the performance period.

(4)

Dividends are considered reinvested when calculating TSR. The dividend yield is therefore considered to be 0%.