NOTE K—EQUITY-BASED COMPENSATION

Equity-based compensation expense was $14,633, $15,648, and $14,955 for fiscal years 2020, 2019, and 2018, respectively. The related tax benefit for these periods was $2,472, $2,732, and $2,777, respectively.

The following table shows the remaining unrecognized compensation expense on a pre-tax basis for all types of unvested equity awards outstanding as of January 2, 2021. This table does not include an estimate for future grants that may be issued.

The cost above is expected to be recognized over a weighted-average period of 1.7 years.

The Company’s 2015 Equity Incentive Award Plan (the “2015 Plan”) allows for the grant of various equity awards including stock-settled stock appreciation rights, stock options, restricted stock units, deferred stock units, and other types of equity-based awards to the Company’s officers, key employees, and non-employee directors. Prior to the approval of the 2015 plan, the Company maintained a 2006 Equity Incentive Award Plan (the “2006 Plan”), which expired in April of 2016. The 2015 Plan replaced the 2006 Plan for all future grants, and no new awards have been granted under the 2006 Plan.

At the inception of the 2015 Plan, 13,839 awards had been granted under the 2006 Plan, of which 13,595 were stock-settled stock appreciation rights, 15 were stock options, and 229 were deferred stock units. In addition, at the inception of the 2015 Plan, 2,551 awards had been forfeited. Under the 2015 Plan, 10,000 shares have been authorized. As of  January 2, 2021, 3,506 awards had been granted under the 2015 Plan, of which 2,912 were stock-settled stock appreciation rights, and 593 were restricted stock awards. Also, as of  January 2, 2021, a total of 1,087 awards had been forfeited and added back to the number of shares available for issuance under the 2015 Plan.

Stock-Settled Stock Appreciation Rights

The Company uses the Black-Scholes option pricing model to estimate the fair value of its stock-settled stock appreciation rights. The weighted-average fair value of stock-settled stock appreciation rights granted in 2020 and 2019 was $17.65 and $35.41, respectively. There were no stock-settled stock appreciation rights granted in 2018.

Stock-settled stock appreciation rights granted to officers and key employees upon hire or promotion to such a position, or annually for existing participants, generally vest 25% each year on the anniversary of the grant date and expire 4.5 years from the date of grant.

Following is a table that includes the weighted-average assumptions that the Company used to calculate fair value of stock-settled stock appreciation rights that were granted during the periods indicated.

(1) The Company utilizes historical volatility of the trading price of its common stock.

(2) Risk-free interest rate is based on the U.S. Treasury yield curve with respect to the expected life of the award.

(3) Depending upon the terms of the award, one of two methods will be used to calculate expected life:

(i) a weighted-average that includes historical settlement data of the Company’s equity awards and a

hypothetical holding period, or (ii) the simplified method.

(4) The Company historically has not paid and currently has no plan to pay dividends.

(5) Exercise price is the closing price of the Company's common stock on the date of grant.

A summary of the Company’s stock-settled stock appreciation right activity is as follows:

* Aggregate intrinsic value is defined as the difference between the current market value at the reporting date (the closing price of the Company’s common stock on the last trading day of the period) and the exercise price of awards that were in-the-money. The closing price of the Company’s common stock at January 2, 2021, and December 28, 2019, was $77.10 and $80.00, respectively.

The total intrinsic value of stock-settled stock appreciation rights exercised was $7,881, $4,937, and $46,224, for the years ended 2020, 2019, and 2018, respectively. The total fair value of stock-settled stock appreciation rights that vested was $3,532, $15,940, and $17,614, for the years ended 2020, 2019, and 2018 respectively.

During the years ended  January 2, 2021, December 28, 2019, and December 29, 2018, certain employees elected to receive a net amount of shares upon the exercise of stock-settled stock appreciation rights in order to satisfy the Company’s tax withholding obligation. This resulted in a reduction to additional paid-in capital of $170 and $154 for the years ended 2019 and 2018, respectively. There was no reduction to additional paid-in capital for the year ended 2020.

Restricted Stock Awards

Restricted stock awards include stock-settled and cash-settled restricted stock units granted to the Company’s officers and key employees, and deferred stock units granted to non-employee directors. Restricted stock units are granted to officers and key employees upon hire or promotion to such a position, or annually for existing participants, and generally vest 25% each year on the anniversary of the grant date. Awards of deferred stock units granted to non-employee directors generally vest 25% each quarter, commencing on the first vest date anniversary following the final vesting of the previous award. Upon vesting, holders of stock-settled restricted stock units and deferred stock units are entitled to receive shares of the Company’s common stock on a one-for-one basis. Holders of cash-settled restricted stock units are entitled to receive cash payments equivalent to the number of awards held, valued at the closing market price on the vest date. The fair value of restricted stock awards is determined based on the Company’s closing stock price on the date of grant. Cash-settled restricted stock units are accounted for as liability awards and fair value is remeasured to current fair value at each reporting date until the award is settled at vesting. Restricted stock awards are full-value shares at the date of grant, vesting over the periods of service, and do not have expiration dates.

A summary of the Company’s stock-settled restricted stock unit activity is as follows:

During the year ended January 2, 2021, certain employees elected to receive a net amount of shares upon the release of restricted stock units in order to satisfy the Company’s tax withholding obligation. This resulted in a reduction to additional paid-in capital of $2,367, $1,817, and $655 for the years ended 2020, 2019, and 2018, respectively, reflected as a financing activity in the Company’s consolidated statements of cash flows.

The total fair value of restricted stock units that vested was $7,732, $6,050, and $2,395, for the years ended 2020, 2019, and 2018, respectively.

A summary of the Company’s cash-settled restricted stock unit activity is as follows:

The weighted-average fair value of liability awards outstanding was $76, $103, and $98 for the years ended 2020, 2019, and 2018, respectively.

The number of deferred stock units vested and unreleased totaled 23, 23, and 24 for the years ended 2020, 2019, and 2018, respectively. The total fair value of deferred stock units that vested was $290 for the year ended 2018. There were no deferred stock units that vested in 2020 and 2019.