Income approach: relief from royalty, multi-period and single-period excess earnings, incremental cash flow, and contributory asset charges. Method selects the formula. Use for the income-approach arithmetic: relief_from_royalty for IP with observable royalty rates, and excess earnings (mpeem or single_period_excess_earnings) for the residual intangible. For a complete asset-specific valuation of customer, technology, IP or workforce assets, prefer the dedicated valuation_customer, valuation_technology, valuation_ip and valuation_human_capital tools. For royalty-rate inputs use valuation_royalty_analysis; for asset-specific income valuations use valuation_customer, valuation_technology, valuation_ip or valuation_human_capital; for cost or market indications use valuation_cost_approach and valuation_market_approach. Per method: relief_from_royalty needs revenue_projections + royalty_rate + discount_rate + tax_rate + useful_life (optional: tab_enabled); mpeem needs cash_flow_projections + contributory_asset_charges + discount_rate + tax_rate (optional: tab_enabled); single_period_excess_earnings needs normalized_earnings + contributory_asset_charges + capitalization_rate; incremental_cashflow needs cash_flows_with + cash_flows_without + discount_rate; contributory_asset_charges needs assets. cash_flow_projections and contributory_asset_charges must be period-aligned; cash_flows_with and cash_flows_without must be equal length. Only method is required; other parameters are method-dependent, so supply those named for the selected method and omit the rest (documented defaults apply where defined). Pure arithmetic: no I/O and no external calls, and numeric results are returned rounded to 2 decimals. Parameters belonging to other methods of this tool are accepted and ignored. Supplying an unknown method, or leaving unset a parameter that the chosen method requires, returns an error instead of a value.