8. Stock-based Compensation

The amended and restated 2005 Long-Term Incentive Plan (the “LTIP”) provides for the grant to eligible persons of stock options, stock appreciation rights, restricted stock, restricted stock units, performance shares, performance awards, dividend equivalents and other stock-based awards, which are collectively referred to as the awards.

Restricted Stock Units and Performance Stock Units

Under the LTIP, the board of directors grants restricted stock units and performance stock units to certain employee participants (collectively, the “stock units”). For grants to most employees, the restricted stock units vest in four equal annual installments. Restricted stock units that have one-year vesting periods are also issued under the LTIP to members of the board of directors in connection with annual director compensation and, from time to time, are issued to employees in connection with employee compensation with vesting periods of two years or less.

Compensation expense for non-vested stock units is recorded over the vesting period based on the fair value at the date of grant. The fair value of restricted stock units and performance stock units with a performance condition is the market price of the underlying common stock on the date of grant.

Performance stock units granted prior to 2016 have vesting based upon a performance condition. These performance stock units generally have three-year performance objectives and all performance stock units have a three-year period for vesting (if the applicable performance objective is achieved). For awards granted prior to 2016, the applicable performance objective is based upon a multi-year cumulative value creation calculation that considers the Company’s financial performance commencing on the first day of each grant year. The number of performance stock units granted represents the target award and participants have the ability to earn between zero and 200 percent (depending on the grant date) of the target award based upon actual performance. If minimum performance criteria are not achieved, no performance stock units will vest. Performance stock units granted in 2015 exceeded the maximum value creation and vested at 200 percent in March 2018.

Performance stock units granted in 2016 and thereafter have vesting based upon a market condition. These performance stock units have a three-year performance objective and a three-year period for vesting (if the applicable performance objective is achieved). The applicable performance objective is based on the Company’s total shareholder return relative to the Standard & Poor’s SmallCap 600 Materials Index. The number of performance stock units granted represents the target award and participants have the ability to earn between zero and 200 percent of the target award based upon actual performance. If minimum performance criteria are not achieved, no performance stock units will vest. The Company has the discretion to settle the award in cash rather than shares, although the Company currently expects that all awards will be settled by the issuance of shares.

Compensation expense for non-vested performance stock units with a market condition is recorded over the vesting period based on the fair value at the date of grant. The Company calculated the fair value of the awards on the date of grant using the Monte Carlo valuation model and the assumptions listed below:

	March 2018 Grant			March 2017 Grant			March 2016 Grant
Grant date price per share of performance award	$	41.60		$	44.10		$	18.11
Expected dividend yield per share		0.00	%		0.00	%		0.00	%
Expected volatility		39.40	%		43.50	%		40.86	%
Risk-free interest rate		2.35	%		1.54	%		0.96	%
Look-back period in years		2.84			2.83			2.84
Grant date fair value per share of performance award	$	47.12		$	64.02		$	23.70

Dividends declared, if any, on the Company’s common stock during the period prior to vesting of the stock units are credited at equivalent value as additional stock units and become payable as additional common shares upon vesting. In the event of termination of employment, other than retirement, death or disability, any non-vested stock units are forfeited, including additional stock units credited from dividends. In the event of termination of employment due to retirement, death or disability, pro-rata vesting of the stock units over the service period will result. There are special vesting provisions for the stock units related to a change in control.

The following table shows a summary of the performance stock units as of March 31, 2018:

Performance Period	Minimum Shares		Target Shares		Maximum Shares
2016 – 2018		0		256,628		513,256
2017 – 2019		0		115,098		230,196
2018 – 2020		0		123,133		246,266

The following table shows a summary of the status and activity of non-vested stock units for the three months ended March 31, 2018:

	Restricted Stock Units			Performance Stock Units			Total Stock Units			Weighted Average Grant Date Fair Value per Unit
Non-vested at December 31, 2017		238,140			581,551			819,691		$	29.14
Granted		85,346			124,262			209,608		$	44.78
Performance share adjustment		0			204,866			204,866		$	17.57
Vested		(73,576	)		(409,732	)		(483,308	)	$	18.64
Forfeited		(3,965	)		(6,088	)		(10,053	)	$	37.74
Non-vested at March 31, 2018		245,945			494,859			740,804		$	37.09

Stock Options

Stock options to most executive officers vest and become exercisable in four equal annual installments. The stock options have a term of ten years. In the event of termination of employment, other than retirement, death or disability, any non-vested options are forfeited. In the event of termination of employment due to retirement, death or disability, pro-rata vesting of the options over the service period will result. There are special vesting provisions for the stock options related to a change in control.

Compensation expense for non-vested stock options is recorded over the vesting period based on the fair value at the date of grant. The Company calculated the fair value of stock options on the date of grant using the Black-Scholes-Merton model and the assumptions listed below:

	March 2018 Grant			March 2017 Grant			March 2016 Grant			March 2015 Grant
Grant date price per share of stock option award	$	41.60		$	44.10		$	18.11		$	17.57
Expected dividend yield per share		0.00	%		0.00	%		0.00	%		3.40	%
Expected life in years		5.73			5.77			5.96			5.75
Expected volatility		37.05	%		39.70	%		40.86	%		42.27	%
Risk-free interest rate		2.67	%		2.13	%		1.45	%		1.73	%
Grant date fair value per share of option award	$	16.38		$	17.90		$	7.41		$	5.20

The Company suspended its dividend in February 2015 and does not expect to declare any dividends for the foreseeable future. The expected life in years is based on historical exercise data of options previously granted by the Company. Expected volatility is based on the historical volatility of the Company’s common stock and the historical volatility of certain other similar public companies. The risk-free interest rate is based on U.S. Treasury bill rates for the expected life of the option.

The following table shows a summary of the status and activity of stock options for the three months ended March 31, 2018:

	Options			Weighted Average Exercise Price per Option		Weighted Average Remaining Contractual Term (in years)		Aggregate Intrinsic Value (in millions)
Outstanding at December 31, 2017		942,537		$	27.59
Granted		139,012		$	41.60
Exercised		(32,568	)	$	39.41
Outstanding at March 31, 2018		1,048,981		$	29.08		6.49	$	13.1
Exercisable at March 31, 2018		653,320		$	27.88		5.55	$	8.8

Stock Compensation Expense

Total stock-based compensation expense recognized for three months ended March 31, 2018 and 2017 is as follows:

	Three Months Ended March 31,
	2018		2017
(Dollars in millions)
Stock-based compensation expense recognized:
Selling, general and administrative expenses	$	2.9	$	2.3
Less related income tax benefit		1.0		0.9
Decrease in net income attributable to Koppers	$	1.9	$	1.4
Intrinsic value of exercised stock options	$	0.2	$	0.7
Cash received from the exercise of stock options	$	0.9	$	1.6

As of March 31, 2018, total future gross compensation expense related to non-vested stock-based compensation arrangements, which are expected to vest, totaled $23.7 million and the weighted-average period over which this cost is expected to be recognized is approximately 30 months.