Stock-Based Compensation

The Roper Technologies, Inc. 2016 Incentive Plan (“2016 Plan”) is a stock-based compensation plan used to grant incentive stock options, nonqualified stock options, restricted stock, stock appreciation rights or equivalent instruments to Roper’s employees, officers and directors. At December 31, 2018, 6.019 shares were available to grant under the 2016 Plan.

Under the Roper Technologies, Inc., Employee Stock Purchase Plan (“ESPP”), all employees in the U.S. and Canada are eligible to designate up to 10% of eligible earnings to purchase Roper’s common stock at a 5% discount to the average closing price of its common stock at the beginning and end of a quarterly offering period. Common stock sold to the employees may be either treasury stock, stock purchased on the open market, or newly issued shares.

Stock based compensation expense for the years ended December 31, 2018, 2017 and 2016 was as follows:



	2018		2017		2016
Stock based compensation	$	133.8	$	83.1	$	78.8
Tax benefit recognized in net earnings	28.1		29.1		27.6

In 2018, this expense included $29.4 associated with accelerated vesting due to the passing of our former executive chairman.

Stock Options – Stock options are typically granted at prices not less than 100% of market value of the underlying stock at the date of grant. Stock options typically vest over a period of three to five years from the grant date and expire ten years after the grant date. The Company recorded $23.2, $18.3, and $20.1 of compensation expense relating to outstanding options during 2018, 2017 and 2016, respectively, as a component of general and administrative expenses, primarily at corporate.

The Company estimates the fair value of its option awards using the Black-Scholes option valuation model. The stock volatility for each grant is measured using the weighted-average of historical daily price changes of the Company’s common stock over the most recent period equal to the expected life of the grant. The expected term of options granted is derived from historical data to estimate option exercises and employee forfeitures, and represents the period of time that options granted are expected to be outstanding. The risk-free rate for periods within the contractual life of the option is based on the U.S. Treasury yield curve in effect at the time of grant. The weighted-average fair value of options granted in 2018, 2017 and 2016 were calculated using the following weighted-average assumptions:



	2018	2017	2016
Weighted-average fair value ($)	57.75	40.87	34.57
Risk-free interest rate (%)	2.65	2.03	1.44
Average expected option life (years)	5.32	5.26	5.20
Expected volatility (%)	18.05	18.74	21.35
Expected dividend yield (%)	0.59	0.67	0.70

The following table summarizes the Company’s activities with respect to its share-based compensation plans for the years ended December 31, 2018 and 2017:



	Number of shares		Weighted-average exercise price per share		Weighted-average contractual term	Aggregate intrinsic value
Outstanding at January 1, 2017	3.420		$	121.31
Granted	0.609		210.56
Exercised	(0.645	)	95.14
Canceled	(0.188	)	170.75
Outstanding at December 31, 2017	3.196		140.68		6.09	$	368.6
Granted	0.723		279.10
Exercised	(0.650	)	90.43
Canceled	(0.064	)	211.57
Outstanding at December 31, 2018	3.205		180.69		6.58	$	284.0
Exercisable at December 31, 2018	1.627		$	129.39	4.71	$	223.1

The following table summarizes information for stock options outstanding at December 31, 2018:



	Outstanding options				Exercisable options
Exercise price	Number	Average exercise price		Average remaining life (years)	Number	Average exercise price
$41.78 - $60.80	0.121	$	48.49	0.8	0.121	$	48.49
$60.80 - $91.21	0.149	72.06		2.2	0.149	72.06
$91.21 - $121.61	0.359	107.23		3.5	0.359	107.23
$121.61 - $152.01	0.436	136.54		5.1	0.436	136.54
$152.01 - $182.41	0.783	169.01		6.8	0.498	167.63
$182.41 - $212.81	0.534	201.40		8.1	0.055	186.22
$212.81 - $243.22	0.097	230.02		8.5	0.008	227.94
$243.22 - $273.62	0.027	258.82		9.0	0.001	260.01
$273.62 - $304.02	0.699	279.24		9.2	—	—
$41.78 - 304.02	3.205	$	180.69	6.6	1.627	$	129.39

At December 31, 2018, there was $45.4 of total unrecognized compensation expense related to nonvested options granted under the Company’s share-based compensation plans. That cost is expected to be recognized over a weighted-average period of 2.5 years. The total intrinsic value of options exercised in 2018, 2017 and 2016 was $124.6, $90.6 and $38.9, respectively. Cash received from option exercises under all plans in 2018 and 2017 was $58.8 and $61.3, respectively.

Restricted Stock Grants - During 2018 and 2017, the Company granted 0.410 and 0.410 shares, respectively, of restricted stock to certain employee and director participants under its share-based compensation plans. Restricted stock grants generally vest over a period of 1 to 4 years. The Company recorded $109.7, $63.0 and $57.8 of compensation expense related to outstanding shares of restricted stock held by employees and directors during 2018, 2017 and 2016, respectively. In 2018, this expense included $29.4 associated with accelerated vesting due to the passing of our former executive chairman. A summary of the Company’s nonvested shares activity for 2018 and 2017 is as follows:



	Number of shares		Weighted-average grant date fair value
Nonvested at December 31, 2016	0.953		$	164.62
Granted	0.410		205.88
Vested	(0.387	)	155.95
Forfeited	(0.117	)	173.53
Nonvested at December 31, 2017	0.859		$	187.01
Granted	0.410		278.29
Vested	(0.492	)	204.24
Forfeited	(0.038	)	191.51
Nonvested at December 31, 2018	0.739		$	225.93

At December 31, 2018, there was $86.6 of total unrecognized compensation expense related to nonvested awards granted to both employees and directors under the Company’s share-based compensation plans. That cost is expected to be recognized over a weighted-average period of 2.1 years. Unrecognized compensation expense related to nonvested shares of restricted stock grants is recorded as a reduction to additional paid-in capital in stockholder’s equity at December 31, 2018.

Employee Stock Purchase Plan - During 2018, 2017 and 2016, participants of the ESPP purchased 0.020, 0.020 and 0.019 shares, respectively, of Roper’s common stock for total consideration of $5.4, $4.2, and $3.3, respectively. All of these shares were purchased from Roper’s treasury shares.