
	2022		2021		2020
	(in millions)
Stock-based compensation expense by line item:
Cost of sales	$	9.4	$	6.3	$	5.6
Research and development expenses	297.9		268.3		262.7
Selling, general and administrative expenses	184.0		166.8		161.2
Total stock-based compensation expense included in costs and expenses	491.3		441.4		429.5
Income tax effect	(144.1)		(82.9)		(147.0)
Total stock-based compensation included in costs and expenses, net of tax	$	347.2	$	358.5	$	282.5


	2022		2021		2020
	(in millions)
Stock-based compensation expense by type of award:
Restricted stock units (including PSUs)	$	456.1	$	384.3	$	360.4
Stock options	17.6		36.8		59.7
ESPP share issuances	16.7		24.4		13.0
Stock-based compensation expense related to inventories	0.9		(4.1)		(3.6)
Total stock-based compensation expense included in costs and expenses	$	491.3	$	441.4	$	429.5

We capitalize a portion of our stock-based compensation expense to inventories, all of which is attributable to employees who support the manufacturing of our products.

The following table sets forth our unrecognized stock-based compensation expense as of December 31, 2022, by type of award and the weighted-average period over which that expense is expected to be recognized:


	As of December 31, 2022
	Unrecognized Expense		Weighted-average Recognition Period
	(in millions)		(in years)
Type of award:
Restricted stock units (including PSUs)	$	477.9	1.93
Stock options	2.2		0.42
ESPP share issuances	11.3		0.61
Total unrecognized stock-based compensation expense	$	491.4

In each of the three years ended December 31, 2022, we issued stock options to our non-employee directors. We use the Black-Scholes option pricing model to estimate the fair value of stock options at the grant date. The Black-Scholes option pricing model uses the option exercise price as well as estimates and assumptions related to the expected price volatility of our stock, the rate of return on risk-free investments, the expected period during which the options will be outstanding, and the expected dividend yield for our stock to estimate the fair value of a stock option on the grant date. The options granted during 2022, 2021 and 2020 had a weighted-average grant-date fair value per share of $89.65, $65.94 and $88.37,

The fair value of each option granted during 2022, 2021 and 2020 was estimated on the date of grant using the Black-Scholes option pricing model with the following weighted-average assumptions:


	2022	2021	2020
Stock options granted	20,079	27,302	22,636

Expected stock price volatility	34.03%	35.03%	35.87%
Risk-free interest rate	2.93%	0.86%	0.43%
Expected term of options (in years)	4.36	4.50	4.67
Expected annual dividends	—	—	—

•Expected stock price volatility: Expected stock price volatility is calculated using the trailing one-month average of daily implied volatilities prior to the grant date. Implied volatility is based on options to purchase our stock with remaining terms of greater than one year that are regularly traded in the market.

•Risk-free interest rate: We base the risk-free interest rate on the interest rate payable on U.S. Treasury securities in effect at the time of grant for a period that is commensurate with the assumed expected option term.

•Expected term of options: The expected term of options represents the period of time options are expected to be outstanding. We use historical data to estimate employee exercise and post-vest termination behavior. We believe that all groups of employees exhibit similar exercise and post-vest termination behavior and therefore do not stratify employees into multiple groups in determining the expected term of options.

•Expected annual dividends: The estimate for annual dividends is $0.00 because we have not historically paid, and do not intend for the foreseeable future to pay, a dividend.

As described in Note N, “Common Stock, Preferred Stock and Equity Plans,” we grant PSUs to certain members of senior management. Our financial-based PSUs vest in three equal installments over a three-year period and are expensed ratably over that same period based upon an assessment of the likely level of achievement. Our non-financial based PSUs cliff vest at the end of the three-year performance period and are expensed on a straight-line basis over that same period based upon an assessment of the likely level of achievement.

The weighted-average fair value of each purchase right granted during 2022, 2021 and 2020 was $79.36, $51.71 and $65.88, respectively. The following table reflects the weighted-average assumptions used in the Black-Scholes option pricing model for 2022, 2021 and 2020:


	2022	2021	2020
Expected stock price volatility	33.55%	34.06%	37.70%
Risk-free interest rate	4.05%	0.05%	0.11%
Expected term (in years)	0.71	0.69	0.71
Expected annual dividends	—	—	—

The weighted-average assumptions used in our Black-Scholes option pricing model were determined utilizing calculations similar to those described under Stock Options above.