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Stock-Based Compensation (Tables)
 12 Months Ended
Dec. 31, 2023
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Stock Option Activity
The following summarizes stock option activity: 
 Option SharesWeighted Average Exercise Price
(in millions, except per share data)202320222021202320222021
Outstanding, at beginning of year1.2 1.4 2.0 $27.40 $23.58 $17.52 
Granted0.1 0.2 0.2 51.81 35.80 42.84 
Exercised(0.3)(0.4)(0.8)23.70 16.09 12.12 
Canceled or expired— — — 41.45 33.89 30.76 
Outstanding, at end of year1.0 1.2 1.4 $31.65 $27.40 $23.58 
Exercisable, at end of year0.7 0.8 1.0 $26.35 $23.60 $19.15 
Summary of Information Concerning Stock Options Outstanding
The following table summarizes information for stock options outstanding as of December 31, 2023 under all plans:
 Options OutstandingOptions Exercisable
Range of Exercise PricesSharesWeighted Average
Remaining Life		Weighted Average
Exercise Price		SharesWeighted Average
Exercise Price
 (in millions)(in years)(in millions) 
$10.01 — 15.00
0.1 2.2$12.77 0.1 $12.77 
15.01 — 20.00
0.1 2.816.85 0.1 16.85 
20.01 — 25.00
0.1 4.123.14 0.1 23.14 
25.01 — 30.00
0.3 5.627.58 0.3 27.58 
35.01 — 40.00
0.2 8.135.80 — 35.80 
40.01 — 45.00
0.1 7.142.86 0.1 42.86 
50.01 — 55.00
0.1 9.351.81 — — 
1.0 6.0$31.65 0.7 $26.35 
Summary of Restricted Stock Grants
The following table summarizes restricted stock activity for the year ended December 31, 2023:
Number of
Restricted Shares		Weighted Average
Price per Share
 (in millions) 
Outstanding and non-vested, at December 31, 20220.3 $34.93 
Granted— 52.76 
Vested(0.1)30.44 
Forfeited— 39.23 
Outstanding and non-vested, at December 31, 20230.2 $43.03 
Equity Option  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Assumptions Used to Calculate Fair Value
The fair value of each option grant was estimated using the Black-Scholes option pricing model with the following weighted average assumptions:
202320222021
Expected dividend yield0.8 %1.0 %0.8 %
Expected volatility32.7 %32.7 %33.0 %
Risk-free interest rate3.3 %3.0 %1.1 %
Expected option life in years5.66.96.4
PSUs  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Schedule of Share-based Compensation, Activity
The following table summarizes PSU activity for the year ended December 31, 2023:
Number of PSUsWeighted Average Price per Share
(in millions)
Outstanding and non-vested, at December 31, 20220.2 $39.83 
Granted (a)
0.1 51.31 
Vested (0.1)42.85 
Forfeited— 42.19 
Outstanding and non-vested, at December 31, 20230.2 $44.23 
(a) Includes the effect of the PSUs granted in 2021 being earned at 132% of target.
Assumptions used to Calculate PSU Fair Value As the PSUs granted in 2023 and 2022 contain a market condition, the Company utilized a Monte Carlo simulation model to determine the respective grant date fair values, using the following assumptions:
PSUs granted in 2023Annual Expected Stock Price VolatilityAnnual Expected Dividend YieldRisk-Free Interest RateCorrelation Between TSR for Federal Signal Corporation and the Applicable S&P Index
Federal Signal Corporation29.8 %0.8 %3.6 %48.0 %
Peer Group within S&P 600 Capital Goods Index44.4 %n/a3.6 %n/a
PSUs granted in 2022Annual Expected Stock Price VolatilityAnnual Expected Dividend YieldRisk-Free Interest RateCorrelation Between TSR for Federal Signal Corporation and the Applicable S&P Index
Federal Signal Corporation34.4 %1.0 %2.8 %52.3 %
Peer Group within S&P 600 Capital Goods Index50.5 %n/a2.8 %n/a