The Company maintains an Incentive Compensation Program (the “Program”) for executives, certain other employees of the Company and its operating segments and subsidiaries and the Company’s non-employee directors. Members of the Board of Directors (the "Board") that receive stock-based compensation are treated as employees for accounting purposes. The Program was approved by shareholders on May 6, 2015. The Program allows for up to 4.2 million awards to eligible employees of stock options, restricted stock, stock appreciation rights, performance shares and units or other awards based on Company common stock. As of December 31, 2019, 1.5 million shares were available for grant under this plan.

During the year ended December 31, 2019, the Company awarded 460 thousand stock options as part of the Program, 58 thousand restricted stock awards, 52 thousand performance share awards, and 12 thousand restricted stock units with an aggregate grant-date fair value of approximately $25.4 million to be recognized over the requisite service period for each award.


(in millions)	2019		2018		2017
Stock option awards	$	10.8	$	11.0	$	7.7
Restricted stock awards	7.4		7.7		6.0
Performance share awards	6.0		7.4		5.6
Restricted stock units	1.3		1.4		1.4
Stock appreciation rights	8.6		—		—
Total stock-based compensation cost	$	34.1	$	27.5	$	20.7
Income tax benefit	$	12.9	$	10.6	$	12.5

In 2018, the Board authorized a grant of stock options to U.S. employees and stock appreciation rights to employees outside of the U.S. This grant contributed $11.5 million and $2.7 million to stock-based compensation costs for the years ended December 31, 2019 and December 31, 2018, respectively. Compensation cost of $3.2 million and $0.5 million is capitalized as inventory as of December 31, 2019 and December 31, 2018, respectively. Inventory is recognized in costs of goods sold when that related inventory is sold.

Stock options awarded under the Program generally vest on a straight-line basis over a three-year period on the anniversary date of the grant. All stock options have a maximum contractual term of 10 years. Shares issued to cover stock options issued under the Program may be issued from shares held in treasury, from new issuances of shares or a combination of the two. Unrecognized compensation cost related to stock options of $9.8 million as of December 31, 2019, is to be recognized over a weighted-average period of 1.4 years.

The Company utilizes the Black-Scholes-Merton (“BSM”) option pricing model to determine the fair value of its stock options. The BSM relies on certain assumptions to estimate an option’s fair value. The weighted average assumptions used in the determination of fair value for stock options follows:


(in millions, except per share amounts)	2019			2018 One-time Grant			2018			2017
Expected dividend yield	1.6		%	1.4		%	1.4		%	1.3		%
Expected term (in years)	4.9			3.9			5.5			5.6
Expected volatility	21.3		%	20.7		%	23.1		%	25.6		%
Risk-free interest rate	2.5		%	2.6		%	2.6		%	1.9		%
Weighted-average grant date fair value (per share)	$	21.07		$	21.91		$	23.71		$	24.57
Fair value of options granted	$	9.7		$	13.6		$	9.1		$	8.8

The expected term of a stock option is based on the assumption that all outstanding stock options will be exercised at the midpoint of the valuation date (if vested) or the vesting dates (if unvested) and the stock options’ expiration date. The expected volatility is based on historical volatility, as well as implied volatility of the Company’s call options. The risk-free interest rate is based on rates of U.S. Treasury issues with a remaining life equal to the expected term of the stock option. The expected dividend yield is based on the latest quarterly dividend payment per share, annualized, divided by the average three-month stock price as of the date of grant.


	Number of Shares (in thousands)	Weighted-Average Exercise Price (per share)		Weighted-Average Contractual Term (in years)	Aggregate Intrinsic Value (in millions)
Outstanding as of December 31, 2018	1,964	$	95.76
Options granted	460	110.82
Options exercised	(448)	82.26
Options forfeited / expired	(151)	107.81
Outstanding as of December 31, 2019	1,825	101.95		7.6	$	109.3
Vested and exercisable as of December 31, 2019	646	89.69		5.9	$	46.6

Restricted stock awarded under the Program is generally released to the recipient after a period of approximately three years. Unrecognized compensation cost related to restricted stock of $6.7 million as of December 31, 2019, is to be recognized over a weighted-average period of 1.6 years.


	Number of Shares (in thousands)	Weighted-Average Grant Date Fair Value (per share)		Weighted-Average Contractual Term (in years)	Aggregate Intrinsic Value (in millions)
Outstanding as of December 31, 2018	169	$	103.47
Shares granted	58	112.70
Shares vested	(50)	92.53
Shares forfeited	(4)	109.22
Outstanding as of December 31, 2019	173	109.62		1.0	$	28.0


(in millions)	2019		2018		2017
Intrinsic value of restricted stock exercised	$	5.6	$	11.7	$	11.4
Fair value of restricted stock vested	$	4.6	$	9.8	$	8.1

Performance shares vest based on the employee rendering three years of service to the Company and the attainment of a market condition over the performance period, which is based on the Company’s relative total shareholder return versus the S&P Midcap 400 Index® over a pre-determined time period as determined by the Compensation Committee of the Board. Unrecognized compensation cost related to performance share awards of $6.9 million as of December 31, 2019, is to be recognized over a weighted-average period of 1.7 years.

For purposes of determining diluted earnings per share, the performance share awards are considered contingently issuable shares and are included in diluted earnings per share based upon the number of shares that would have been awarded had the conditions at the end of the reporting period continued until the end of the performance period. See Note 5 for further information regarding earnings per share computations.

The Company utilizes the Monte-Carlo simulation approach based on a three-year measurement period to determine the fair value of performance shares. Such approach entails the use of assumptions regarding the future performance of the Company’s stock and those of the S&P Midcap 400 Index_®. Those assumptions include expected volatility, risk-free interest rates, correlation coefficients and dividend reinvestment. Dividends accrue on the performance shares during the performance period and are to be paid in cash based upon the number of awards ultimately earned.


	Number of Shares (in thousands)	Weighted-Average Grant Date Fair Value (per share)		Weighted-Average Contractual Term (in years)	Aggregate Intrinsic Value (in millions)
Outstanding as of December 31, 2018	153	$	132.68
Awards granted	52	149.27
Awards vested	(49)	119.37
Awards withheld	(9)	118.80
Awards forfeited	(4)	143.31
Outstanding as of December 31, 2019	143	143.94		1.0	$	23.2


(in millions)	2019		2018		2017
Intrinsic value of performance share awards exercised	$	5.0	$	5.3	$	11.6
Fair value of performance share awards vested	$	5.9	$	5.2	$	10.0

Restricted stock units are awarded to eligible directors and fully vested and are expensed upon grant date. The restricted stock units are paid in shares of Company common stock after the director ceases to serve as a member of the Board, or if earlier, upon a change in control of the Company. The Company granted 12 thousand, 13 thousand and 13 thousand units in 2019, 2018 and 2017, respectively. Units had a weighted-average grant date fair value per share of $110.79, $108.72 and $107.87 in 2019, 2018 and 2017, respectively. Restricted stock units' fair value is based on the closing market price of the stock on the respective dates of the grants.

Stock appreciation rights issued under the 2018 one-time grant discussed above, cliff vest on May 2, 2021, at which date they will immediately vest and be settled in cash. Unrecognized compensation cost related to stock appreciation rights of $11.6 million as of December 31, 2019, is to be recognized over a weighted-average period of 1.3 years.

The stock appreciation rights are classified as liability awards and are measured at fair value at each balance sheet date. The Company utilizes the BSM option pricing model to determine the fair value of its stock appreciation rights. The BSM relies on certain assumptions to estimate a stock appreciation right's fair value. The weighted average assumptions used in the December 31, 2019 determination of fair value for stock appreciation rights follows:


(in millions, except per share amounts)	2018 One-time Grant
Expected dividend yield	1.3		%
Expected term (in years)	1.3
Expected volatility	24.3		%
Risk-free interest rate	1.6		%
Weighted-average grant date fair value (per share)	$	55.76
Fair value of stock appreciation rights granted	$	27.5

The expected life of stock appreciation rights is based on the time from the valuation date to the vest date. The expected volatility is based on historical volatility as well as implied volatility of the Company’s call options. The risk-free interest rate is based on rates of U.S. Treasury issues with a remaining life equal to the expected life of the stock appreciation right. The expected dividend yield is based on the latest quarterly dividend payment per share, annualized, divided by the average three-month stock price as of the date of grant.


	Number of Shares (in thousands)	Weighted-Average Exercise Price (per share)		Weighted-Average Contractual Term (in years)	Aggregate Intrinsic Value (in millions)
Outstanding as of December 31, 2018	—	$	—
Awards granted	493	106.85
Awards forfeited	(131)	106.85
Outstanding as of December 31, 2019	362	106.85		1.3	$	19.9

Certain employees are eligible to participate in the Company’s Non-qualified Deferred Compensation Plan (the “Deferred Compensation Plan”). Participants may elect to defer all or part of their restricted and performance shares. Participants have elected to defer 86 thousand and 202 thousand shares of Company common stock as of December 31, 2019 and 2018, respectively. Company stock held for future issuance of vested awards is classified as deferred compensation equity in the Consolidated Balance Sheets and is recorded at grant date fair value. Such deferred shares are included in basic earnings per share.