Employee compensation plans (Tables)

12 Months Ended

Dec. 31, 2021

Share-based Payment Arrangement [Abstract]

Summarizes of Company's Non-Vested ESP/EIP Awards

The following table summarizes the status of the Company's non-vested restricted Class A Stock awards under the OIP for the year ended December 31, 2021:

	Number of Class A Shares Subject to Restricted Stock  Awards	Weighted Average Fair Value		Weighted Average Remaining Contractual Life
Nonvested at beginning of year	1,328,877	$	22.63	1.9 years
Granted	631,390	29.66		2.9 years
Vested	(376,139)	17.79		—
Forfeited	(41,412)	25.95		—
Nonvested at end of year	1,542,716	$	26.59	2.2 years

Stock Appreciation Rights

The following table summarizes the status of the Company's outstanding OARs awards as of December 31, 2021:

Grant Date	Number of OARs Outstanding	Strike Price		Remaining Contractual Life	Fair Value as of December 31, 2021
January 6, 2017	367,320	$	18.90	5 days	$	27.47
January 5, 2018	436,010	27.05		1 year	19.22
January 11, 2019	509,216	26.45		2 years	21.49
January 10, 2020	522,720	27.54		3 years	20.90
January 11, 2021	623,380	32.16		4 years	18.59
Total OARs Outstanding	2,458,646
Total weighted average values		$	27.11	3.1 years	$	21.12

Schedule of Assumptions Used

The fair value as of December 31, 2021 for each of the OARs was estimated using the Black-Scholes model with the following assumptions:

	Grant Date
	January 6, 2017			January 5, 2018			January 11, 2019			January 10, 2020			January 11, 2021
Expected term (1)	5 days			1 year			2 years			3 years			4 years
Expected volatility factor (2)	20.602		%	35.942		%	45.514		%	39.569		%	36.701		%
Risk-free interest rate (3)	0.002		%	0.380		%	0.738		%	0.964		%	1.164		%
Quarterly dividends (4)	$	0.54		$	0.54		$	0.54		$	0.54		$	0.54

    (1) The expected term was determined based on the remaining life of the actual awards.

(2) The volatility factor was measured using the weighted average of historical daily price changes of the

Company's Class A Stock over a historical period commensurate to the expected term of the awards.

(3) The risk-free interest rate was based on periods equal to the expected term of the awards based on the

U.S. Treasury yield curve in effect at December 31, 2021.

(4) Quarterly dividends were used to compute the expected annual dividend yield.