Stock-based compensation

Accounting for stock-based compensation requires that the cost resulting from all stock-based payments be recognized in the financial statements based on the grant date fair value of the award. Our stock-based compensation primarily consists of stock options, restricted stock units (RSUs), performance-based restricted stock units (PRSUs) and stock-settled stock appreciation rights (SARs).

Beginning with the 2018 grant, RSU and PRSU awards are credited with dividend equivalent units on each date that a cash dividend is paid to holders of Common Stock. The fair value of the RSU and PRSU awards granted in 2018 was determined as the closing stock price on the date of grant. Prior to 2018, RSU and PRSU awards were not credited with dividend equivalent units and the fair value was determined by reducing the stock price on the date of grant by the present value of the estimated dividends to be paid during the vesting period. The estimated dividends were based on Caterpillar's quarterly dividend per share at the time of grant.

We recognized pretax stock-based compensation expense of $50 million and $49 million for the three months ended March 31, 2018 and 2017, respectively.

The following table illustrates the type and fair value of the stock-based compensation awards granted during the three months ended March 31, 2018 and 2017, respectively:




	Three Months Ended March 31, 2018					Three Months Ended March 31, 2017
	Shares Granted	Weighted-Average Fair Value Per Share		Weighted-Average Grant Date Stock Price		Shares Granted	Weighted-Average Fair Value Per Share		Weighted-Average Grant Date Stock Price
Stock options	1,566,788	$	46.18	$	151.12	2,701,644	$	25.01	$	95.66
RSUs	676,228	$	151.12	$	151.12	906,068	$	89.76	$	95.63
PRSUs	339,559	$	151.12	$	151.12	437,385	$	86.78	$	95.66

The following table provides the assumptions used in determining the fair value of the stock-based awards for the three months ended March 31, 2018 and 2017, respectively:




	Grant Year
	2018	2017
Weighted-average dividend yield	2.70%	3.42%
Weighted-average volatility	30.2%	29.2%
Range of volatilities	21.5-33.0%	22.1-33.0%
Range of risk-free interest rates	2.02-2.87%	0.81-2.35%
Weighted-average expected lives	8 years	8 years

As of March 31, 2018, the total remaining unrecognized compensation expense related to nonvested stock-based compensation awards was $327 million, which will be amortized over the weighted-average remaining requisite service periods of approximately 2.0 years.