Stock-Based Compensation

On May 8, 2015 (the "Effective Date"), the 2015 Long-Term Incentive Plan (the "2015 Plan") was approved by shareholders. As of the Effective Date, no additional awards will be granted to employees under the 2011 Long-Term Incentive Plan (the "2011 Plan"). The significant terms of stock options and restricted stock units ("RSUs") were not changed under the 2015 Plan. Stock options and RSUs are issued to officers and/or other management employees under these plans. Stock options generally vest over a four-year period and have an expiration of ten years from the issuance date. RSUs generally "cliff" vest after a three-year period and include units with and without performance criteria. RSUs with performance criteria provide for full "cliff" vesting after three years if the Compensation Committee certifies that the performance goals have been met. Upon vesting, the holder will receive one share of common stock of the Company for each vested RSU.

Commencing in February 2013, the Company began issuing shares from treasury stock to cover the exercised options and vested RSUs. Prior to February 2013, the Company generally issued new shares from its authorized but unissued share pool. As of December 31, 2018, approximately 13 million shares of ITW common stock were reserved for issuance under these plans.

The Company records compensation expense for the grant date fair value of stock awards over the remaining service periods of those awards. The following table summarizes the Company’s stock-based compensation expense:



In millions	2018			2017			2016
Pre-tax compensation expense	$	40		$	36		$	39
Tax benefit	(5		)	(9		)	(13		)
Total stock-based compensation expense, net of tax	$	35		$	27		$	26

The following table summarizes activity related to non-vested RSUs during 2018:



Shares in millions	Number of Shares		Weighted-Average Grant-Date Fair Value
Unvested, January 1, 2018	0.6		$99.87
Granted	0.2		162.49
Vested	(0.3	)	92.71
Unvested, December 31, 2018	0.5		121.24

The following table summarizes stock option activity for the year ended December 31, 2018:



In millions except exercise price and contractual terms	Number of Shares		Weighted-Average Exercise Price	Weighted-Average Remaining Contractual Term	Aggregate Intrinsic Value
Under option, January 1, 2018	4.5		$80.88
Granted	0.5		163.36
Exercised	(0.4	)	61.22
Under option, December 31, 2018	4.6		90.56	5.6	$165
Exercisable, December 31, 2018	3.2		74.08	4.6	$168

Effective with the 2017 grant, issued RSUs provide for dividend equivalents payable in additional RSUs for dividends that would have been paid during the vesting period. Accordingly, the fair value of RSUs issued in 2018 and 2017 was equal to the common stock fair market value on the date of the grant. For grants prior to 2017, the fair value of RSUs was determined by reducing the closing market price on the date of the grant by the present value of projected dividends over the vesting period. Stock option exercise prices are equal to the common stock fair market value on the date of grant. The Company uses a binomial option pricing model to estimate the fair value of the stock options granted. The following summarizes the assumptions used in the models:



	2018	2017	2016
Risk-free interest rate	2.07-3.06%	0.91-2.61%	0.56-1.86%
Weighted-average volatility	22.0%	22.0%	24.0%
Dividend yield	2.10%	2.22%	2.12%
Expected years until exercise	7.5-8.4	7.2-7.9	6.9-7.7

Lattice-based option valuation models, such as the binomial option pricing model, incorporate ranges of assumptions for inputs. The risk-free rate of interest for periods within the contractual life of the option is based on a zero-coupon U.S. government instrument over the contractual term of the equity instrument. Expected volatility is based on implied volatility from traded options on the Company’s stock and historical volatility of the Company’s stock. The Company uses historical data to estimate option exercise timing and employee termination rates within the valuation model. The weighted-average dividend yield is based on historical information. The expected term of options granted is derived from the output of the option valuation model and represents the period of time that options granted are expected to be outstanding. The ranges presented result from separate groups of employees assumed to exhibit different exercise behavior.

The weighted-average grant-date fair value of stock options granted during 2018, 2017 and 2016 was $38.34, $26.83 and $20.02 per share, respectively. The aggregate intrinsic value of stock options exercised during the years ended December 31, 2018, 2017 and 2016 was $33 million, $132 million and $89 million, respectively. As of December 31, 2018, there was $10 million of total unrecognized compensation cost related to unvested stock options. That cost is expected to be recognized over a weighted-average period of 2.1 years. Exercise of stock options during the years ended December 31, 2018, 2017 and 2016 resulted in cash receipts of $22 million, $84 million and $84 million, respectively. The total fair value of vested stock option awards during the years ended December 31, 2018, 2017 and 2016 was $15 million, $13 million and $12 million, respectively.

As of December 31, 2018, there was $30 million of total unrecognized compensation cost related to unvested RSUs. That cost is expected to be recognized over a weighted-average remaining contractual life of 1.8 years. The total fair value of vested RSU awards during the years ended December 31, 2018, 2017 and 2016 was $19 million, $19 million and $21 million, respectively.