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Stock-based Compensation (Tables)
 6 Months Ended
Jun. 30, 2021
Stock-based compensation [Abstract]  
Stock-Based Compensation

Information regarding stock-based compensation appears in the table below:

Three Months Ended

Six Months Ended

June 30,

June 30,

Millions

2021

2020

2021

2020

Stock-based compensation, before tax:

Stock options

$

4 

$

4 

$

8 

$

8 

Retention awards

18 

14 

34 

32 

Total stock-based compensation, before tax

$

22 

$

18 

$

42 

$

40 

Excess tax benefits from equity compensation plans

$

2 

$

2 

$

17 

$

35 
Stock Options Weight Average Assumptions The table below shows the annual weighted-average assumptions used for valuation purposes:

Weighted-Average Assumptions

2021

2020

Risk-free interest rate

0.4%

1.5%

Dividend yield

1.9%

2.1%

Expected life (years)

4.6 

4.9 

Volatility

28.3%

23.4%

Weighted-average grant-date fair value of options granted

$

39.97 

$

32.20 

 
Stock Options Activity A summary of stock option activity during the six months ended June 30, 2021, is presented below:

Options (thous.)

Weighted-Average
‎Exercise Price

Weighted-Average Remaining Contractual Term

Aggregate Intrinsic Value (millions)

Outstanding at January 1, 2021

2,569 

$

132.49 

6.4 

yrs.

$

195 

Granted

387 

204.45 

N/A

N/A

Exercised

(341)

122.63 

N/A

N/A

Forfeited or expired

(53)

152.07 

N/A

N/A

Outstanding at June 30, 2021

2,562 

$

144.27 

6.5 

yrs.

$

194 

Vested or expected to vest at June 30, 2021

2,537 

$

143.78 

6.5 

yrs.

$

193 

Options exercisable at June 30, 2021

1,725 

$

123.50 

5.4 

yrs.

$

166 

 
Stock Option Exercises Additional information regarding stock option exercises appears in the following table:

Three Months Ended

Six Months Ended

June 30,

June 30,

Millions

2021

2020

2021

2020

Intrinsic value of stock options exercised

$

9 

$

17 

$

32 

$

65 

Cash received from option exercises

4 

18 

34 

51 

Treasury shares repurchased for employee taxes

(1)

(4)

(7)

(12)

Tax benefit realized from option exercises

2 

3 

6 

14 

Aggregate grant-date fair value of stock options vested

-

-

14 

14 

 
Retention Awards Activity Changes in our retention awards during the six months ended June 30, 2021, were as follows:

Shares
‎(thous.)

Weighted-Average
‎Grant-Date Fair Value

Nonvested at January 1, 2021

1,476 

$

141.06 

Granted

284 

204.87 

Vested

(410)

107.88 

Forfeited

(39)

161.63 

Nonvested at June 30, 2021

1,311 

$

164.65 

 
Performance Based Units Activity

Changes in our performance retention awards during the six months ended June 30, 2021, were as follows:

Shares
‎(thous.)

Weighted-Average
‎Grant-Date Fair Value

Nonvested at January 1, 2021

773 

$

148.17 

Granted

227 

204.45 

Vested

(140)

129.60 

Unearned

(150)

128.78 

Forfeited

(28)

183.78 

Nonvested at June 30, 2021

682 

$

173.52