We have outstanding stock-based compensation awards that were granted under the amended and restated 2005 Long-Term Incentive Plan (the 2005 LTIP), the 2018 Long-Term Incentive Plan (the 2018 LTIP) and the 2020 Long-Term Incentive Plan, as amended (the 2020 LTIP). The 2005 LTIP, the 2018 LTIP and the 2020 LTIP are collectively referred to as the LTIP. 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.

Under the LTIP, the board of directors grants restricted stock units and performance stock units to certain employee participants (collectively, the stock units). 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 is the market price of the underlying common stock on the date of grant. The fair value of performance stock units is determined using the market price of the underlying common stock on the date of grant for units with a performance condition and a Monte Carlo valuation model for units with a market condition.

For grants to most employees prior to 2023, the restricted stock units vest in four equal annual installments. Starting in 2023, most grants of restricted stock units vest in three years. 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 with vesting periods of typically two years or less.

Performance stock units have vesting based upon either a performance condition or a market condition. Performance stock units granted with a performance condition have a cumulative three-year performance objective based on adjusted EBITDA (see Note 9 – Segment Information). For performance stock units granted with a market condition, which applies to all performance stock unit grants made prior to 2023, the applicable objective is based on our total shareholder return relative to the Standard & Poor’s SmallCap 600 Materials Index and has multi-year performance objectives.

Both types of performance stock units have a three-year period for vesting. 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. We have the discretion to settle the award in cash rather than shares, although we currently expect that all awards will be settled by the issuance of shares.

We calculated the fair value of the performance stock unit awards on the date of the grant using assumptions listed below:


	January 2023 Grant			January 2022 Grant			January 2021 Grant
Grant date price per share of stock performance award	$	29.01		$	32.19		$	29.84
Expected volatility		66.30	%		66.90	%		68.70	%
Risk-free interest rate		4.11	%		1.10	%		0.16	%
Look-back period in years		3.00			3.00			3.00
Grant date fair value per share	$	39.51		$	45.19		$	41.50

Dividends declared, if any, on our 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 December 31, 2023:


Performance Period	Minimum Shares		Target Shares		Maximum Shares
Market Condition Units
2021 – 2023		136,560		136,560		136,560
2022 – 2024		97,870		149,246		200,622
2023 – 2025		52,598		105,196		157,794
Performance Condition Units
2023 – 2025		0		189,084		378,168

The minimum, target and maximum shares above reflect the impact from completed performance periods. Performance stock units granted in January 2021 for the 2021 – 2023 performance period vested in January 2024 at 94.7 percent of the original target share amount plus dividend equivalent units.

The following table shows a summary of the status and activity of non-vested stock awards:


	Restricted Stock Units			Performance Stock Units			Total Stock Units			Weighted Average Grant Date Fair Value per Unit
Non-vested at January 1, 2023		524,612			237,032			761,644		$	32.40
Granted		238,544			267,073			505,617		$	30.92
Credited from dividends		6,394			4,604			10,998		$	32.37
Performance share adjustment		0			78,468			78,468		$	42.18
Vested		(222,250	)		0			(222,250	)	$	26.44
Forfeited		(15,961	)		(6,414	)		(22,375	)	$	32.00
Non-vested at December 31, 2023		531,339			580,763			1,112,102		$	33.62

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. No stock options were granted in 2023.

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


	January 2022 Grant			January 2021 Grant			March 2020 Grant
Grant date price per share of stock option award	$	32.19		$	29.84		$	19.63
Expected life in years		6.76			6.64			6.40
Expected volatility		54.50	%		54.80	%		42.85	%
Risk-free interest rate		1.52	%		0.59	%		0.87	%
Grant date fair value per share	$	17.58		$	15.79		$	8.42

Prior to February 2022, we had not declared a dividend since 2014. The expected life in years is based on our historical exercise data of previously granted options. Expected volatility is based on the historical volatility of our common stock. 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:


	Options			Weighted Average Exercise Price per Option		Weighted Average Remaining Contractual Term (in years)		Aggregate Intrinsic Value (in millions)
Outstanding at December 31, 2022		1,122,136		$	27.05
Exercised		(365,237	)	$	24.11
Expired		(50,031	)	$	42.16
Outstanding at December 31, 2023		706,868		$	27.51		5.02	$	16.8
Exercisable at December 31, 2023		545,392		$	27.29		4.35	$	13.0

The following table presents total stock-based compensation expense recognized under our LTIP and employee stock purchase plan:


	Year Ended December 31,
	2023		2022		2021
(Dollars in millions)
Stock-based compensation expense recognized:
Selling, general and administrative expenses	$	17.3	$	13.2	$	13.0
Less related income tax benefit		4.8		4.4		3.7
Decrease in net income attributable to Koppers	$	12.5	$	8.8	$	9.3
Intrinsic value of exercised stock options	$	6.4	$	0.0	$	2.2
Cash received from the exercise of stock options	$	8.8	$	0.0	$	2.3

As of December 31, 2023, total future compensation expense related to non-vested stock-based compensation arrangements totaled $21.7 million and the weighted-average period over which this expense is expected to be recognized is approximately 21 months.