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Stock-Based Compensation (Tables)
 12 Months Ended
Dec. 31, 2020
Stock-based compensation  
Schedule of compensation expense
Stock-based compensation cost by award type follows:
(in millions)202020192018
Stock option awards$11.2 $10.8 $11.0 
Restricted stock awards8.9 7.4 7.7 
Performance share awards7.9 6.0 7.4 
Restricted stock units1.4 1.3 1.4 
Stock appreciation rights3.4 8.6 — 
Total stock-based compensation cost incurred32.8 34.1 27.5 
Capitalized cost during the period(4.5)(10.6)(1.3)
Amortization of capitalized cost during the period1.6 7.9 0.8 
Total stock-based compensation expense$29.9 $31.4 $27.0 
Income tax benefit$9.6 $12.9 $10.6 
Schedule of weighted-average assumptions for equity awards The weighted average assumptions used in the determination of fair value for stock options follows:
(in millions, except per share amounts)2020201920182018
One-time Grant
Expected dividend yield1.3 %1.6 %1.4 %1.4 %
Expected term (in years)
4.84.95.53.9
Expected volatility21.9 %21.3 %23.1 %20.7 %
Risk-free interest rate1.4 %2.5 %2.6 %2.6 %
Weighted-average grant date fair value (per share)
$29.29 $21.07 $23.71 $21.91 
Fair value of options granted$11.6 $9.7 $9.1 $13.6 
Schedule of stock option activity under the Company's stock option awards
A summary of stock options outstanding and activity follows:
Number of Shares
(in thousands)
Weighted-Average Exercise Price
(per share)
Weighted-Average Contractual Term
(in years)
Aggregate Intrinsic Value
(in millions)
Outstanding as of December 31, 20191,825 $101.95 
Options granted395 159.49 
Options exercised(229)95.49 
Options forfeited / expired(165)119.11 
Outstanding as of December 31, 20201,826 114.03 7.0$78.8 
Vested and exercisable as of December 31, 2020768 98.25 5.4$44.5 
Additional information related to stock option activity during the years ended December 31 follows:
(in millions)202020192018
Intrinsic value of options exercised$11.9 $25.4 $18.4 
Fair value of options vested$7.9 $6.3 $10.2 
Schedule of activity related to restricted stock
Information related to restricted stock during the years ended December 31 follows:
202020192018
Weighted-average grant date fair value (per share)$147.78 $112.70 $114.27 
A summary of restricted stock outstanding and activity follows:
Number of Shares
(in thousands)
Weighted-Average Grant Date Fair Value
(per share)
Weighted-Average Contractual Term
(in years)
Aggregate Intrinsic Value
(in millions)
Outstanding as of December 31, 2019173 $109.62 
Shares granted69 147.78 
Shares vested(66)114.39 
Shares forfeited(10)123.70 
Outstanding as of December 31, 2020166 122.88 0.8$26.0 
Additional information related to restricted stock award activity during the years ended December 31 follows:
(in millions)202020192018
Intrinsic value of restricted stock exercised$9.6 $5.6 $11.7 
Fair value of restricted stock vested$7.5 $4.6 $9.8 
Additional information related to restricted stock unit activity during the years ended December 31 follows:
(in thousands, except per share amounts)202020192018
Restricted stock units granted8 12 13 
Weighted-average grant date fair value (per share) (1)
$161.41 $110.79 $108.72 
(1)Restricted stock units' fair value is based on the closing market price of the stock on the respective dates of the grants.
Schedule of activity related to performance shares
Information related to performance shares during the years ended December 31 follows:
202020192018
Weighted-average grant date fair value (per share)$222.50 $149.27 $140.20 
A summary of performance shares outstanding and activity follows:
Number of Shares
(in thousands)
Weighted-Average Grant Date Fair Value
(per share)
Weighted-Average Contractual Term
(in years)
Aggregate Intrinsic Value
(in millions)
Outstanding as of December 31, 2019143 $143.94 
Awards granted46 222.50 
Awards vested(80)141.79 
Awards converted36 141.81 
Awards forfeited(9)167.03 
Outstanding as of December 31, 2020136 170.34 0.9$21.2 
Additional information related to performance share activity during the years ended December 31 follows:
(in millions)202020192018
Intrinsic value of performance share awards exercised$12.9 $5.0 $5.3 
Fair value of performance share awards vested$11.3 $5.9 $5.2 
Schedule of activity related to stock appreciation rights
A summary of stock appreciation awards outstanding and activity follows:
Number of Shares
(in thousands)
Weighted-Average Exercise Price
(per share)
Weighted-Average Contractual Term
(in years)
Aggregate Intrinsic Value
(in millions)
Outstanding as of December 31, 2019362 $106.85 
Awards exercised(3)106.85 
Awards forfeited(78)106.85 
Outstanding as of December 31, 2020281 106.85 0.3$13.9 
Stock appreciation rights  
Stock-based compensation  
Schedule of weighted-average assumptions for equity awards The weighted average assumptions used in the December 31, 2020 determination of fair value for stock appreciation rights follows:
(in millions, except per share amounts)2018 One-time Grant
Expected dividend yield1.5 %
Expected term (in years)0.3
Expected volatility30.1 %
Risk-free interest rate0.1 %
Weighted-average grant date fair value (per share)$48.24 
Fair value of stock appreciation rights granted$13.5