Time value of money: discount or compound a single sum, value level and growing annuities and perpetuities, and compute a terminal value by Gordon growth or exit multiple. Method selects the formula. Use to move cash flows through time or to value a terminal value in a DCF; combine with a rate from valuation_discount_rate. For uneven multi-period cash flows use valuation_income_methods; for rate construction use valuation_discount_rate. Per method: present_value needs future_value + discount_rate + periods; future_value needs present_value + discount_rate + periods; annuity_pv needs payment + discount_rate + periods; perpetuity_pv needs payment + discount_rate; growing_annuity_pv needs payment + discount_rate + growth_rate + periods; terminal_value_gordon_growth needs final_year_cashflow + perpetual_growth_rate + discount_rate; terminal_value_exit_multiple needs final_year_cashflow + exit_multiple. Rates and growth are decimals (0.10 = 10%); for terminal_value_gordon_growth the discount rate must exceed the perpetual growth rate. 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.

Construct discount and capitalization rates: build-up, CAPM, WACC, tax-amortization benefit, control premium, Finnerty DLOM, and currency/country-risk adjustment. Method selects the formula. Use to derive the rate that feeds every income-based method; build_up and capm estimate cost of equity, wacc blends debt and equity. For a cross-border rate with currency and country premia use method currency_adjusted; for the cash flows the rate discounts use valuation_time_value. Per method: build_up needs risk_free_rate + equity_risk_premium (optional: size_premium, industry_risk_premium, specific_risk_premium); capm needs risk_free_rate + beta + market_return; wacc needs equity_value + debt_value + cost_of_equity + cost_of_debt + tax_rate; tax_amortization_benefit needs discount_rate + useful_life + tax_rate + asset_value; control_premium needs minority_price + control_price; dlom_finnerty needs restricted_period + volatility + risk_free_rate; currency_adjusted needs base_rate (optional: currency_risk_premium, country_risk_premium). All rates and premiums are decimals; wacc requires both equity_value and debt_value, and dlom_finnerty volatility is an annualized decimal. 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.

Cost approach: depreciated reproduction cost from a cost breakdown and depreciated replacement cost with equivalent utility, both reduced by obsolescence. Method selects the formula. Use when no income or market evidence exists, or to corroborate income and market indications for internally developed intangibles. For income-based indications use valuation_income_methods; for market evidence use valuation_market_approach. Per method: reproduction_cost needs development_costs (optional: obsolescence_factors); replacement_cost needs current_cost (optional: obsolescence_factors). obsolescence_factors values are decimals that are summed and applied to the cost base; omit them for no obsolescence. 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.

Market approach: value from comparable transaction revenue multiples or capitalize a royalty stream into a perpetuity value. Method selects the formula. Use when reliable comparable transactions or royalty rates exist for the subject asset. For income-based excess earnings use valuation_income_methods; for royalty-rate selection and adjustment use valuation_royalty_analysis. Per method: comparable_transactions needs comparables + subject_revenue (optional: adjustments); royalty_capitalization needs revenue + royalty_rate + discount_rate. Each comparable is {revenue, multiple}; comparable_transactions applies the comparable multiple to subject_revenue. 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.

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.

Intellectual property: risk-adjusted patent value, trademark/brand value, copyright income value, and trade-secret value under secrecy risk. Method selects the formula. Use to value a specific IP right; patent weights projected cash flows by probability of success, trademark uses brand strength to set the royalty. For technology, software, data, and platform assets use valuation_technology; for customer and workforce assets use valuation_customer and valuation_human_capital. Per method: patent needs remaining_life + cash_flow_projections + probability_of_success + discount_rate (optional: comparable_license_rates); trademark needs revenue + profit_margin + brand_strength_index + discount_rate + useful_life (optional: brand_method); copyright needs projected_revenue + useful_life + discount_rate + royalty_rate; trade_secret needs development_cost + economic_life + competitive_advantage_period + discount_rate + secrecy_probability. cash_flow_projections for patent run over remaining_life. 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.

Technology assets: developed technology under life-cycle risk, software under cost and income, data assets with a quality adjustment, and platforms with network effects. Method selects the formula. Use for developed technology, software, data, and platform intangibles; developed_technology and software blend cost and income evidence. For patents, trademarks, copyrights, and trade secrets use valuation_ip; for customer relationships use valuation_customer. Per method: developed_technology needs rd_costs + life_cycle_stage + competitive_advantage + discount_rate + cash_flow_projections; software needs development_cost + maintenance_cost + user_base + revenue_model + useful_life + discount_rate; data_asset needs acquisition_cost + quality_score + revenue_contribution + useful_life + discount_rate; platform needs network_size + network_effects_coefficient + revenue_per_user + growth_rate + discount_rate. cash_flow_projections for developed_technology run over the remaining useful life. 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.

Customer-related intangibles: customer relationships with attrition, distribution networks by channel profitability, and non-compete agreements on protected profits. Method selects the formula. Use for customer relationships, distribution networks, and non-compete assets; customer_relationships projects multi-period revenue with a retention rate. For the workforce and key-person assets use valuation_human_capital; for technology assets use valuation_technology. Per method: customer_relationships needs customer_count + avg_revenue_per_customer + retention_rate + profit_margin + discount_rate + projection_period; distribution_network needs channel_count + revenue_per_channel + channel_margin + useful_life + discount_rate; non_compete needs protected_revenue + profit_margin + term + enforcement_probability + discount_rate. retention_rate and enforcement_probability are in [0,1]; projection_period sets the number of discounted periods. 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.

Human capital: assembled-workforce value by replacement cost and key-person value from revenue contribution and departure risk. Method selects the formula. Use for assembled workforce and key-person intangibles; assembled_workforce nets training and attrition into a replacement cost. For customer-related assets use valuation_customer; for technology assets use valuation_technology. Per method: assembled_workforce needs employee_count + avg_replacement_cost + training_cost + productivity_factor + attrition_rate; key_person needs revenue_contribution + replacement_cost + departure_probability + discount_rate. attrition_rate is in [0,1]; productivity_factor scales the replacement cost (1.0 = parity). 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.

Goodwill and purchase price allocation: goodwill as the residual, a full PPA waterfall across identified intangibles, and useful-life estimation. Method selects the formula. Use for ASC 805 / IFRS 3 business combinations; purchase_price_allocation allocates consideration to identified intangibles with the remainder to goodwill. For subsequent goodwill and intangible impairment testing use valuation_impairment; for individual intangible fair values feed valuation_ip, valuation_technology or valuation_customer into the allocation. Per method: goodwill needs purchase_price + fair_value_net_identifiable_assets; purchase_price_allocation needs purchase_price + tangible_assets_fv + identified_intangibles (optional: liabilities_fv); useful_life needs asset_type (optional: legal_life, economic_factors, obsolescence_rate). identified_intangibles values are summed before goodwill is taken as the residual; liabilities_fv reduces net identifiable assets. 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.

Impairment testing: goodwill impairment and intangible impairment under US GAAP (ASC 350) or IFRS (IAS 36). Method selects the formula. Use for annual or triggering-event impairment testing; goodwill_impairment compares a reporting unit's carrying value with its fair value. To compute the initial goodwill or allocation use valuation_goodwill_ppa; for the underlying asset fair values use the relevant asset-type tool. Per method: goodwill_impairment needs carrying_value + fair_value (optional: reporting_unit, standard); intangible_impairment needs carrying_value (optional: fair_value, recoverable_amount, standard). fair_value is required for ASC350; recoverable_amount is required for IAS36. 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.

Royalty analysis: benchmark royalty-rate ranges by IP type and industry, adjust a base rate for deal factors, and apply the 25% rule of thumb. Method selects the formula. Use to select and support a royalty rate before a relief-from-royalty or royalty-capitalization valuation. To apply the chosen rate in a valuation use valuation_income_methods (relief_from_royalty) or valuation_market_approach (royalty_capitalization); for transfer-pricing pricing use valuation_compliance. Per method: benchmark needs ip_type + industry (optional: comparable_database); adjust needs base_royalty_rate + adjustment_factors; twenty_five_percent_rule needs licensee_expected_profit (optional: profit_attribution_to_ip). adjustment_factors multiply the base rate, so values above 1.0 raise the rate. 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.

Uncertainty analysis: Monte Carlo valuation, Monte Carlo sensitivity ranking, decision-tree expected values, and one-at-a-time sensitivity analysis. Method selects the formula. Use to quantify and stress the uncertainty around a point valuation; monte_carlo simulates all listed inputs, monte_carlo_sensitivity ranks the drivers. For a single deterministic point value use the relevant valuation tool; sensitivity_analysis varies one parameter of a core function only. Per method: monte_carlo needs input_distributions (optional: iterations, seed); monte_carlo_sensitivity needs base_params + distributions (optional: iterations, seed); decision_tree needs tree; sensitivity_analysis needs function_name + parameter_name + parameter_range + fixed_parameters. monte_carlo_sensitivity requires iterations between 1000 and 100000. 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.

Transfer pricing and litigation: the Comparable Uncontrolled Price arm's-length range and patent infringement damages with pre-judgment interest. Method selects the formula. Use for OECD transfer-pricing pricing of intercompany intangibles and for patent infringement damages awards. For royalty-rate benchmarking to set a rate use valuation_royalty_analysis; for the substantive asset valuation use valuation_ip or valuation_income_methods. Per method: cup_transfer_price needs controlled_price + uncontrolled_prices; patent_infringement_damages needs lost_profits_or_royalty + infringement_period + discount_rate + prejudgment_interest_rate. uncontrolled_prices must contain at least one comparable price for the arm's-length range. 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.