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 2019, we issued stock options, time-lapse restricted stock units, TSR performance restricted stock units and FCF performance restricted stock units. We have not issued EPS performance restricted stock units in 2019.

Total pre-tax stock-based compensation expense and tax-related benefits recognized in the Consolidated Statements of Earnings were as follows:



	Three Months Ended
	October 28, 2018		October 29, 2017
Total pre-tax stock-based compensation expense	$	14	$	14
Tax-related benefits	$	3	$	5

The following table summarizes stock option activity as of October 28, 2018:



	Options		Weighted- Average Exercise Price		Weighted- Average Remaining Contractual Life	Aggregate Intrinsic Value
	(Options in thousands)				(In years)
Outstanding at July 29, 2018	1,537		$	50.36
Granted	264		$	36.60
Exercised	—		$	—
Terminated	(74	)	$	49.05
Outstanding at October 28, 2018	1,727		$	48.31	7.6	$	—
Exercisable at October 28, 2018	1,035		$	50.88	6.6	$	—

No options were exercised during the three-month period ended October 29, 2017. We measure the fair value of stock options using the Black-Scholes option pricing model. The expected term of options granted was based on the weighted average time of vesting and the end of the contractual term. We utilized this simplified method as we do not have sufficient historical exercise data to provide a reasonable basis upon which to estimate the expected term.

The assumptions and grant-date fair values for grants in 2019 and 2018 were as follows:



	2019	2018
Risk-free interest rate	2.99%	2.06%
Expected dividend yield	3.78%	2.95%
Expected volatility	25.98%	19.60%
Expected term	6 years	6 years
Grant-date fair value	$6.77	$6.67

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 October 28, 2018, total remaining unearned compensation related to nonvested stock options was $2, which will be amortized over the weighted-average remaining service period of 1.4 years.

The following table summarizes time-lapse restricted stock units and EPS performance restricted stock units as of October 28, 2018:



	Units		Weighted- Average Grant-Date Fair Value
	(Restricted stock units in thousands)
Nonvested at July 29, 2018	1,652		$	47.01
Granted	1,134		$	36.38
Vested	(522	)	$	50.10
Forfeited	(94	)	$	43.03
Nonvested at October 28, 2018	2,170		$	40.88

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 expense EPS performance restricted stock units on a graded-vesting basis, except for awards issued to retirement-eligible participants, which we expense on an accelerated basis. There were 66 thousand EPS performance target grants outstanding at October 28, 2018, with a weighted-average grant-date fair value of $49.10. The actual number of EPS performance restricted stock units issued at the vesting date could range from 0% to 100% of the initial grant, depending on actual performance achieved. We estimate expense based on the number of awards expected to vest.

As of October 28, 2018, total remaining unearned compensation related to nonvested time-lapse restricted stock units and EPS performance restricted stock units was $60, which will be amortized over the weighted-average remaining service period of 2.0 years. The fair value of restricted stock units vested during the three-month periods ended October 28, 2018, and October 29, 2017, was $19, and $29, respectively. The weighted-average grant-date fair value of the restricted stock units granted during the three-month period ended October 29, 2017, was $46.88.

In 2019, we issued approximately 351 thousand FCF performance restricted stock units for which vesting is contingent upon the 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 will be 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 will be based upon the quoted price of our stock at the date of grant. We will expense FCF performance restricted stock units over the requisite service period of each objective.

The following table summarizes TSR performance restricted stock units as of October 28, 2018:



	Units		Weighted- Average Grant-Date Fair Value
	(Restricted stock units in thousands)
Nonvested at July 29, 2018	1,664		$	46.66
Granted	351		$	31.21
Vested	—		$	—
Forfeited	(629	)	$	58.39
Nonvested at October 28, 2018	1,386		$	37.41

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:



	2019	2018
Risk-free interest rate	2.84%	1.58%
Expected dividend yield	3.78%	2.95%
Expected volatility	24.32%	19.07%
Expected term	3 years	3 years

We recognize compensation expense on a straight-line basis over the service period. As of October 28, 2018, total remaining unearned compensation related to TSR performance restricted stock units was $25, which will be amortized over the weighted-average remaining service period of 2.1 years. In the first quarter of 2019, 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 27, 2018. In the first quarter of 2018, recipients of TSR performance restricted stock units earned 125% of the initial grants based upon our TSR ranking in a performance peer group during a three-year period ended July 28, 2017. As a result, approximately 160 thousand additional shares were awarded. The fair value of TSR performance restricted stock units vested during the three-month period ended October 29, 2017, was $38. The grant-date fair value of the TSR performance restricted stock units granted during 2018 was $39.39.

The excess tax deficiencies of $2 in the three-month period ended October 28, 2018, and the excess tax benefits of $5 in the three-month period ended October 29, 2017, on vested restricted stock were presented as cash flows from operating activities.