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Stock-Based Compensation (Tables) | 12 Months Ended
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Dec. 31, 2024
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |
Stock Option Activity | The following summarizes stock option activity:
| Option Shares |  | Weighted Average Exercise Price
(in millions, except per share data) | 2024 |  | 2023 |  | 2022 |  | 2024 |  | 2023 |  | 2022
Outstanding, at beginning of year | 1.0 |  |  | 1.2 |  |  | 1.4 |  |  | $ | 31.65 |  |  | $ | 27.40 |  |  | $ | 23.58 |
Granted | 0.1 |  |  | 0.1 |  |  | 0.2 |  |  | 82.58 |  |  | 51.81 |  |  | 35.80 |
Exercised | (0.1) |  |  | (0.3) |  |  | (0.4) |  |  | 29.10 |  |  | 23.70 |  |  | 16.09 |
Canceled or expired | — |  |  | — |  |  | — |  |  | 48.29 |  |  | 41.45 |  |  | 33.89 |
Outstanding, at end of year | 1.0 |  |  | 1.0 |  |  | 1.2 |  |  | $ | 36.58 |  |  | $ | 31.65 |  |  | $ | 27.40 |
Exercisable, at end of year | 0.8 |  |  | 0.7 |  |  | 0.8 |  |  | $ | 29.21 |  |  | $ | 26.35 |  |  | $ | 23.60 |
Summary of Information Concerning Stock Options Outstanding | The following table summarizes information for stock options outstanding as of December 31, 2024 under all plans:
| Options Outstanding |  | Options Exercisable
Range of Exercise Prices | Shares |  | Weighted Average Remaining Life |  | Weighted Average Exercise Price |  | Shares |  | Weighted Average Exercise Price
| (in millions) |  | (in years) |  |  |  | (in millions) |  |
$10.01 — 15.00 | 0.1 |  |  | 1.3 |  | $ | 12.66 |  |  | 0.1 |  |  | $ | 12.66 |
15.01 — 20.00 | 0.1 |  |  | 2.0 |  | 16.87 |  |  | 0.1 |  |  | 16.87 |
20.01 — 25.00 | 0.1 |  |  | 3.4 |  | 23.14 |  |  | 0.1 |  |  | 23.14 |
25.01 — 30.00 | 0.2 |  |  | 4.8 |  | 27.59 |  |  | 0.2 |  |  | 27.59 |
35.01 — 40.00 | 0.2 |  |  | 7.3 |  | 35.80 |  |  | 0.1 |  |  | 35.80 |
40.01 — 45.00 | 0.1 |  |  | 6.2 |  | 42.86 |  |  | 0.1 |  |  | 42.86 |
50.01 — 55.00 | 0.1 |  |  | 8.3 |  | 51.81 |  |  | 0.1 |  |  | 51.81 |
80.01 — 85.00 | 0.1 |  |  | 9.3 |  | 82.31 |  |  | — |  |  | — |
| 1.0 |  |  | 5.6 |  | $ | 36.58 |  |  | 0.8 |  |  | $ | 29.21 |
Summary of Restricted Stock Grants | The following table summarizes restricted stock activity in each of the three years in the period ended December 31, 2024:
| Number of Restricted Shares |  | Weighted Average Price per Share
| (in millions) |  |
Outstanding and non-vested, at December 31, 2021 | 0.2 |  |  | $ | 32.15 |
Granted | 0.2 |  |  | 35.60 |
Vested | (0.1) |  |  | 28.35 |
Forfeited | — |  |  | 34.99 |
Outstanding and non-vested, at December 31, 2022 | 0.3 |  |  | $ | 34.93 |
Granted | — |  |  | 52.76 |
Vested | (0.1) |  |  | 30.44 |
Forfeited | — |  |  | 39.23 |
Outstanding and non-vested, at December 31, 2023 | 0.2 |  |  | $ | 43.03 |
Granted | 0.1 |  |  | 83.69 |
Vested | (0.1) |  |  | 43.83 |
Forfeited | — |  |  | 44.68 |
Outstanding and non-vested, at December 31, 2024 | 0.2 |  |  | $ | 53.18 |
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:
| 2024 |  | 2023 |  | 2022
Expected dividend yield | 0.6 | % |  | 0.8 | % |  | 1.0 | %
Expected volatility | 31.6 | % |  | 32.7 | % |  | 32.7 | %
Risk-free interest rate | 4.6 | % |  | 3.3 | % |  | 3.0 | %
Expected option life in years | 5.4 |  | 5.6 |  | 6.9
PSUs |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |
Schedule of Share-based Compensation, Activity | The following table summarizes PSU activity in each of the three years in the period ended December 31, 2024:
| Number of PSUs |  | Weighted Average Price per Share
| (in millions) |  |
Outstanding and non-vested, at December 31, 2021 | 0.2 |  |  | $ | 34.87 |
Granted (a) | 0.1 |  |  | 35.82 |
Vested | (0.1) |  |  | 28.04 |
Forfeited | — |  |  | 37.97 |
Outstanding and non-vested, at December 31, 2022 | 0.2 |  |  | $ | 39.83 |
Granted (b) | 0.1 |  |  | 51.31 |
Vested | (0.1) |  |  | 42.85 |
Forfeited | — |  |  | 42.19 |
Outstanding and non-vested, at December 31, 2023 | 0.2 |  |  | $ | 44.23 |
Granted (c) | 0.2 |  |  | 51.33 |
Vested | (0.3) |  |  | 36.29 |
Forfeited | — |  |  | 49.42 |
Outstanding and non-vested, at December 31, 2024 | 0.1 |  |  | $ | 65.57 |
(a) Includes the effect of the PSUs granted in 2020 being earned at 125% of target. (b) Includes the effect of the PSUs granted in 2021 being earned at 132% of target. (c) Includes the effect of the PSUs granted in 2022 being earned at 228% of target.
Assumptions used to Calculate PSU Fair Value | As the PSUs granted in 2024, 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 2024 | Annual Expected Stock Price Volatility |  | Annual Expected Dividend Yield |  | Risk-Free Interest Rate |  | Correlation Between TSR for Federal Signal Corporation and the Applicable S&P Index
Federal Signal Corporation | 26.9 | % |  | 0.6 | % |  | 4.8 | % |  | 40.9 | %
Peer Group within S&P 600 Capital Goods Index | 40.3 | % |  | n/a |  | 4.8 | % |  | n/a
PSUs granted in 2023 | Annual Expected Stock Price Volatility |  | Annual Expected Dividend Yield |  | Risk-Free Interest Rate |  | Correlation Between TSR for Federal Signal Corporation and the Applicable S&P Index
Federal Signal Corporation | 29.8 | % |  | 0.8 | % |  | 3.6 | % |  | 48.0 | %
Peer Group within S&P 600 Capital Goods Index | 44.4 | % |  | n/a |  | 3.6 | % |  | n/a
PSUs granted in 2022 | Annual Expected Stock Price Volatility |  | Annual Expected Dividend Yield |  | Risk-Free Interest Rate |  | Correlation Between TSR for Federal Signal Corporation and the Applicable S&P Index
Federal Signal Corporation | 34.4 | % |  | 1.0 | % |  | 2.8 | % |  | 52.3 | %
Peer Group within S&P 600 Capital Goods Index | 50.5 | % |  | n/a |  | 2.8 | % |  | n/a

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