Stock-Based Compensation Plans - Assumptions Used in Black - Scholes Model for Each Grant (Details) |
6 Months Ended | |
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Jul. 31, 2026 |
Jul. 31, 2025 |
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| Stock-Based Compensation Plans | ||
| Expected volatility (%) | 29.30% | 28.30% |
| Risk-free rate (%) | 3.10% | 2.80% |
| Expected option life (years) | 5 years | 5 years |
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- References No definition available.
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- Definition The estimated measure of the percentage by which a share price is expected to fluctuate during a period. Volatility also may be defined as a probability-weighted measure of the dispersion of returns about the mean. The volatility of a share price is the standard deviation of the continuously compounded rates of return on the share over a specified period. That is the same as the standard deviation of the differences in the natural logarithms of the stock prices plus dividends, if any, over the period. Reference 1: http://www.xbrl.org/2003/role/disclosureRef
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- Definition The risk-free interest rate assumption that is used in valuing an option on its own shares. Reference 1: http://www.xbrl.org/2003/role/disclosureRef
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- Definition Expected term of award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. Reference 1: http://www.xbrl.org/2003/role/disclosureRef
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