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Stock-based Compensation
 3 Months Ended
Nov. 01, 2020
Share-based Payment Arrangement [Abstract]  
Stock-based Compensation Stock-based Compensation
We provide compensation benefits by issuing stock options, unrestricted stock and restricted stock units (including time-lapse restricted stock units, EPS performance restricted stock units, total shareholder return (TSR) performance restricted stock units, and free cash flow (FCF) performance restricted stock units). In 2021, we issued time-lapse restricted stock units, unrestricted stock and TSR performance restricted stock units. We have not issued stock options, FCF performance restricted stock units, or EPS performance restricted stock units in 2021.
In determining stock-based compensation expense, we estimate forfeitures expected to occur. Total pre-tax stock-based compensation expense and tax-related benefits recognized in Earnings from continuing operations were as follows:
Three Months Ended
 November 1,
2020		October 27,
2019
Total pre-tax stock-based compensation expense$16 $13 
Tax-related benefits$3 $3 
Total pre-tax stock-based compensation expense and tax-related benefits recognized in Earnings (loss) from discontinued operations were as follows:
Three Months Ended
 October 27,
2019
Total pre-tax stock-based compensation expense$1 
Tax-related benefits$— 
The following table summarizes stock option activity as of November 1, 2020:
OptionsWeighted-
Average
Exercise
Price		Weighted-
Average
Remaining
Contractual
Life		Aggregate
Intrinsic
Value
(Options in
thousands)		 (In years) 
Outstanding at August 2, 20201,423 $45.42 
Granted— $— 
Exercised— $— 
Terminated— $— 
Outstanding at November 1, 20201,423 $45.42 6.7$6 
Exercisable at November 1, 20201,069 $48.74 6.2$2 
The total intrinsic value of options exercised during the three-month period ended October 27, 2019 was not material. We measured the fair value of stock options using the Black-Scholes option pricing model.
We expense stock options on a straight-line basis over the vesting period, except for awards issued to retirement eligible participants, which we expense on an accelerated basis. As of November 1, 2020, total remaining unearned compensation related to nonvested stock options was $1, which will be amortized over the weighted-average remaining service period of 1.2 years.
The following table summarizes time-lapse restricted stock units, EPS performance restricted stock units and FCF performance restricted stock units as of November 1, 2020:
UnitsWeighted-Average Grant-Date Fair Value
 (Restricted stock
units in thousands)		 
Nonvested at August 2, 20201,866 $43.18 
Granted875 $48.43 
Vested(715)$42.82 
Forfeited(62)$47.10 
Nonvested at November 1, 20201,964 $45.54 
We determine the fair value of time-lapse restricted stock units and EPS performance restricted stock units based on the quoted price of our stock at the date of grant. We expense time-lapse restricted stock units on a straight-line basis over the vesting period, except for awards issued to retirement-eligible participants, which we expense on an accelerated basis. We expensed EPS performance restricted stock units on a graded-vesting basis, except for awards issued to retirement-eligible participants, which we expensed on an accelerated basis. The actual number of EPS performance restricted stock units issued at the vesting date was either 0% or 100% of the initial grant, depending on actual performance achieved. We estimated expense based on the number of awards expected to vest. As of November 1, 2020, there were no EPS performance target grants outstanding.
In 2019, we issued approximately 388 thousand FCF performance restricted stock units for which vesting is contingent upon achievement of free cash flow (defined as Net cash provided by operating activities less capital expenditures and certain investing and financing activities) compared to annual operating plan objectives over a three-year period. An annual objective was established each fiscal year for three consecutive years. Performance against these objectives will be averaged at the end of the three-year period to determine the number of underlying units that will vest at the end of the three years. The actual number of FCF performance restricted stock units issued at the vesting date could range from 0% to 200% of the initial grant depending on actual performance achieved. The fair value of FCF performance restricted stock units is based upon the quoted price of our stock at the date of grant. We expense FCF performance restricted stock units over the requisite service period of each objective. As of November 1, 2020, we have granted all of the issued FCF performance restricted stock units, which are included in the table above. There were 246 thousand FCF performance target grants outstanding at November 1, 2020, with a weighted-average grant-date fair value of $44.10.
As of November 1, 2020, total remaining unearned compensation related to nonvested time-lapse restricted stock units and FCF performance restricted units was $60, which will be amortized over the weighted-average remaining service period of 1.9 years. The fair value of restricted stock units vested during the three-month periods ended November 1, 2020, and October 27,
2019, was $34, and $30, respectively. The weighted-average grant-date fair value of the restricted stock units granted during the three-month period ended October 27, 2019 was $46.79.
The following table summarizes TSR performance restricted stock units as of November 1, 2020:
UnitsWeighted-Average Grant-Date Fair Value
 (Restricted stock
units in thousands)		 
Nonvested at August 2, 20201,254 $47.83 
Granted521 $54.93 
Vested(236)$39.39 
Forfeited(252)$40.35 
Nonvested at November 1, 20201,287 $53.71 
We estimated the fair value of TSR performance restricted stock units at the grant date using a Monte Carlo simulation.
Assumptions used in the Monte Carlo simulation were as follows:
 20212020
Risk-free interest rate0.15%1.48%
Expected dividend yield2.85%2.95%
Expected volatility29.99%27.01%
Expected term3 years3 years
We recognize compensation expense on a straight-line basis over the service period, except for awards issued to retirement eligible participants, which we expense on an accelerated basis. As of November 1, 2020, total remaining unearned compensation related to TSR performance restricted stock units was $41, which will be amortized over the weighted-average remaining service period of 2.2 years. In the first quarter of 2021, recipients of TSR performance restricted stock units earned 50% of the initial grants based upon our TSR ranking in a performance peer group during a three-year period ended July 31, 2020. In the first quarter of 2020, recipients of TSR performance restricted stock units earned 0% of the initial grants based upon our TSR ranking in a performance peer group during a three-year period ended July 26, 2019. The fair value of TSR performance restricted stock units vested during the three-month period ended November 1, 2020 was $11. The grant-date fair value of the TSR performance restricted stock units granted during 2020 was $63.06.
The excess tax benefits of $1 in the three-month periods ended November 1, 2020 and October 27, 2019 on the exercise of stock options and vested restricted stock were presented as cash flows from operating activities. Cash received from the exercise of stock options was $1 for the three-month period ended October 27, 2019 and is reflected in cash flows from financing activities in the Consolidated Statements of Cash Flows.