11. Share-based compensation

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

	Three Months Ended						Nine Months Ended
	April 30,						April 30,
(in millions)	2018			2017			2018			2017
Cost of product sales	$	0.1		$	0.1		$	0.3		$	0.3
Cost of engineering sales		-			-			0.1			0.1
Research and product development		0.5			0.4			1.4			1.2
Selling and marketing		0.2			0.2			0.5			1.1
General and administrative		1.4			1.5			3.8			3.7
Total share-based compensation expense before tax		2.2			2.2			6.1			6.4
Income tax effect		(0.6	)		(0.7	)		(1.1	)		(2.0	)
Share-based compensation expense included in net income	$	1.6		$	1.5		$	5.0		$	4.4

Stock options

We estimate the fair value of stock options using the Black-Scholes valuation model. Key input assumptions used to estimate the fair value of stock options include the exercise price of the award, the expected option term, the expected volatility of our stock over the option’s expected term, the risk-free interest rate over the option’s expected term, and our expected annual dividend yield. Estimates of fair value are not intended to predict actual future events or the value ultimately realized by persons who receive equity awards.

No stock options were granted during the three and nine months ended April 30, 2018 and April 30, 2017, respectively.

The total intrinsic value of options exercised during the three and nine months ended April 30, 2018 was $0.0 million and $0.1 million, respectively.

Restricted stock and restricted stock units

We estimate the fair value of time based restricted stock units, or RSU’s, that vest based on service conditions using the quoted closing price of our common stock on the date of grant. Share-based compensation expense is amortized over each award’s vesting period on a straight-line basis for all awards with service and performance conditions that vest at the end of the performance cycle, while the accelerated method applies to other awards with both service and performance conditions.

For our non-GAAP earnings per share, or EPS, awards, the compensation cost is amortized over the performance period on a straight-line basis, net of forfeitures as they occur, because such awards vest only at the end of the performance period. The compensation cost is based on the number of shares that are deemed probable of vesting at the end of the three-year performance cycle. This probability assessment is done each quarter and changes in estimates can result in significant expense fluctuations due to the cumulative catch-up adjustment. We estimate the fair value of the non-GAAP EPS awards using the quoted closing price of our common stock on the date of grant.

For our total shareholder return, or TSR, awards, the compensation cost is amortized over the performance period on a straight-line basis net of forfeitures as they occur, because the awards vest only at the end of the measurement period and the probability of actual shares expected to be earned is considered in the grant date valuation. As a result, the expense is not adjusted to reflect the actual shares earned. We estimate the fair value of the TSR awards using the Monte-Carlo simulation model.

We granted 0 and 22,080 TSR awards and 0 and 21,896 non-GAAP EPS awards during the three and nine months ended April 30, 2018, respectively. We granted 601 and 28,749 TSR awards and 594 and 62,626 non-GAAP EPS awards during the three and nine months ended April 30, 2017, respectively. 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						Nine Months Ended
	April 30,						April 30,
	2018			2017			2018			2017
Stock price (1)	$	-		$	73.60		$	77.15		$	89.88
Expected volatility (2)		0.00	%		27.00	%		26.88	%		27.0	%
Risk-free interest rate (3)		0.00	%		0.85	%		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	$	85.65		$	78.22		$	78.16		$	88.16
Weighted average grant date fair value of performance based restricted stock awards		-		$	73.60		$	79.87		$	86.88

(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%.

The total fair value of RSUs that vested during the three and nine months ended April 30, 2018 was $0.8 million and $4.0 million, respectively.

The total fair value of RSUs that vested during the three and nine months ended April 30, 2017 was $0.9 million and $4.1 million, respectively.

As of April 30, 2018, the unrecognized compensation cost, related to unvested stock options and restricted stock was $10.1 million. This cost will be recognized over an estimated weighted average amortization period of 1.4 years and assumes target performance for the non-GAAP EPS awards.