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Stock-based Compensation (Tables)
12 Months Ended
Sep. 30, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Assumptions Used in Black-Scholes Option Valuation Model
 Year Ended September 30,
 202020192018
Expected life of option (years)6.56.46.5
Risk-free interest rate1.67%2.77%2.28%
Expected volatility of the Company’s stock22.40%21.80%23.70%
Expected dividend yield on the Company’s stock2.49%3.29%2.78%
Summary of Stock Option Activity
A summary of stock option activity at September 30, 2020, and changes for the year then ended, is presented below:
Weighted
Average
Option Price
Shares
Subject to
Option
Weighted
Average
Remaining
Contractual
Life (years)
Aggregate
Intrinsic
Value
(in millions)
Outstanding, September 30, 2019$35.07 12,369,749 
Granted41.67 1,347,310 
Exercised28.80 (2,504,516)
Forfeited or expired38.30 (1,097,638)
Outstanding, September 30, 2020$37.14 10,114,905 4.9$46 
Exercisable, September 30, 2020$36.98 7,473,203 3.6$36 
Assumptions Used in Black-Scholes Stock Appreciation Rights Valuation Model
The assumptions used to determine the fair value of the SAR awards at September 30, 2020 were as follows:
Expected life of SAR (years)
0.4 - 2.5
Risk-free interest rate
0.11% - 0.18%
Expected volatility of the Company’s stock22.40%
Expected dividend yield on the Company’s stock2.49%
Summary of Stock Appreciation Rights Activity
A summary of SAR activity at September 30, 2020, and changes for the year then ended, is presented below:
Weighted
Average
SAR Price
Shares
Subject to
SAR
Weighted
Average
Remaining
Contractual
Life (years)
Aggregate
Intrinsic
Value
(in millions)
Outstanding, September 30, 2019$28.67 368,009 
Exercised26.88 (129,277)
Forfeited or expired25.47 (26,095)
Outstanding, September 30, 2020$30.14 212,637 1.8$
Exercisable, September 30, 2020$30.14 212,637 1.8$
Summary of Nonvested Restricted Stock Awards
A summary of non-vested restricted stock awards at September 30, 2020, and changes for the fiscal year then ended, is presented below:
Weighted
Average
Price
Shares/Units
Subject to
Restriction
Non-vested, September 30, 2019$35.98 3,333,076 
Granted41.38 2,053,292 
Vested37.39 (1,634,306)
Forfeited37.47 (522,183)
Non-vested, September 30, 2020$38.58 3,229,879 
Schedule of share-based payment award, performance share, valuation assumptions
 Year Ended September 30,
 202020192018
Risk-free interest rate1.60%2.76%1.92%
Expected volatility of the Company’s stock21.80%22.90%21.70%
Summary of Nonvested PSUs
A summary of the status of the Company’s non-vested PSUs at September 30, 2020, and changes for the fiscal year then ended, is presented below:
Weighted
Average
Price
Shares/Units
Subject to
PSU
Non-vested, September 30, 2019$39.82 1,825,519 
Granted42.48 476,939 
Vested44.98 (515,975)
Forfeited38.87 (168,539)
Non-vested, September 30, 2020$39.06 1,617,944