Authorized shares of common and preferred stock and stock-based compensation plans (Tables)

9 Months Ended

Sep. 30, 2020

Share-based Payment Arrangement [Abstract]

Share-based Payment Arrangement, Performance Shares, Activity

The key assumptions used in valuing these market-based awards are as follows:

	Nine Months Ended
	(unaudited)
	September 30, 2020	September 30, 2019
Number of simulations	100,000	100,000
Expected volatility	27.41%	26.08%
Expected life in years	2.92 years	2.94 years
Risk-free interest rate	1.38%	2.52%
Dividend yield	2.32%	1.96%