valuation_advanced

Advanced techniques: Black-Scholes call value, binomial-tree option value, and scenario analysis. Method selects the technique. For a quick expected value over arbitrary outcome lists, prefer valuation_probability with method 'probability_weighted'; scenario_analysis here is for explicit named bull/base/bear scenario tables. Parameters apply per method: black_scholes and binomial need underlying + strike + risk_free_rate + volatility + time_to_maturity (binomial adds steps); scenario_analysis needs scenarios. Not for plain discounted cash flow — for that use valuation_time_value. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
steps	integer	Binomial tree time steps (integer ≥ 1; higher = more accurate).
method*	string	Formula to apply. Options: black_scholes = C = N(d₁)S - N(d₂)Ke^(-rT).; binomial = Cox-Ross-Rubinstein binomial option value.; scenario_analysis = E[V] = Σ pᵢ·Vᵢ over named scenarios.
strike	number	Strike / exercise price K, currency units.
scenarios	array	Scenario objects: {name: str, probability: 0-1, value: currency}; probabilities should sum to 1.
underlying	number	Underlying asset value S, currency units.
volatility	number	Annualised volatility σ as a decimal (0.80 = 80%).
risk_free_rate	number	Risk-free rate as a decimal (e.g. 0.04 for 4%).
time_to_maturity	number	Time to expiry in years T, must be ≥ 0.

Input schema (JSON)

{
  "type": "object",
  "required": [
    "method"
  ],
  "properties": {
    "steps": {
      "type": "integer",
      "default": 50,
      "description": "Binomial tree time steps (integer ≥ 1; higher = more accurate)."
    },
    "method": {
      "enum": [
        "black_scholes",
        "binomial",
        "scenario_analysis"
      ],
      "type": "string",
      "description": "Formula to apply. Options: black_scholes = C = N(d₁)S - N(d₂)Ke^(-rT).; binomial = Cox-Ross-Rubinstein binomial option value.; scenario_analysis = E[V] = Σ pᵢ·Vᵢ over named scenarios."
    },
    "strike": {
      "type": "number",
      "description": "Strike / exercise price K, currency units."
    },
    "scenarios": {
      "type": "array",
      "items": {
        "type": "object"
      },
      "description": "Scenario objects: {name: str, probability: 0-1, value: currency}; probabilities should sum to 1."
    },
    "underlying": {
      "type": "number",
      "description": "Underlying asset value S, currency units."
    },
    "volatility": {
      "type": "number",
      "description": "Annualised volatility σ as a decimal (0.80 = 80%)."
    },
    "risk_free_rate": {
      "type": "number",
      "description": "Risk-free rate as a decimal (e.g. 0.04 for 4%)."
    },
    "time_to_maturity": {
      "type": "number",
      "description": "Time to expiry in years T, must be ≥ 0."
    }
  }
}

valuation_biotech

Risk-adjusted biotech valuation: peak sales, decision-tree expected value, and full pipeline rNPV across drugs. Method selects the model. Use for pharma/drug pipelines; for hardware or deep tech use valuation_hardware. Parameters apply per method: peak_sales needs patient_population + penetration + price; decision_tree needs probabilities + terminal_value; pipeline needs drugs + discount_rate. Not for hardware or deep tech — for that use valuation_hardware. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
drugs	array	Pipeline drugs: {name, peak_sales, probability, years_to_market, multiple(optional)}.
price	number	Price per unit / treatment, currency units.
method*	string	Formula to apply. Options: peak_sales = Peak = population × penetration × price × compliance.; decision_tree = EV = Π pᵢ × terminal value.; pipeline = V = Σ(peak sales × multiple × P_success) / (1+r)^n.
compliance	number	Compliance / adherence rate as a decimal.

valuation_capm

Estimate the cost of capital: standard CAPM, startup-adjusted CAPM with size and illiquidity premiums, portfolio beta from weighted asset betas, and WACC blending after-tax cost of equity and debt. Method selects the formula. Use to derive the discount rate that feeds valuation_time_value and DCF models; for cross-border rates add valuation_international. Parameters apply per method: capm needs risk_free_rate + beta + market_return; startup_capm adds size_premium and liquidity_premium; portfolio_beta needs weights + betas, which must be equal length; wacc needs equity_value + debt_value + cost_of_equity + cost_of_debt + tax_rate. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
beta	number	Systematic risk beta (market = 1.0).
betas	array	Asset betas aligned with weights; typically 0.5–3.0 (market = 1.0).
method*	string	Formula to apply. Options: capm = E(R) = Rf + β·(E(Rm) - Rf).; startup_capm = r = Rf + β·MRP + size premium + illiquidity premium.; portfolio_beta = βp = Σ wᵢ·βᵢ.; wacc = WACC = (E/V)·Re + (D/V)·Rd·(1 − T).
weights	array

valuation_comparables

Market multiples from comparables: P/E, P/S, EV/EBITDA, EV/Revenue, and a regression-adjusted multiple. Method selects the ratio. Use when public comparables exist; for pre-revenue or private startups use valuation_core. Parameters apply per method: pe_ratio needs market_cap + net_income; ps_ratio needs market_cap + revenue; ev_ebitda needs enterprise_value + ebitda; ev_revenue needs enterprise_value + revenue; regression_multiple needs intercept + growth_rate + growth_coefficient (plus optional maturity/stage/geography terms). Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
stage	number	Company stage indicator.
ebitda	number	EBITDA, currency units.
method*	string	Formula to apply. Options: pe_ratio = P/E = market cap / net income.; ps_ratio = P/S = market cap / revenue.; ev_ebitda = EV/EBITDA = enterprise value / EBITDA.; ev_revenue = EV/Revenue = enterprise value / revenue.; regression_multiple = Multiple = β0 + β1·g + β2·M + β3·S + β4·G.
revenue	number	Revenue for the period, currency units.

valuation_core

The textbook's pre-revenue methods: Scorecard, Berkus, Risk-Factor Summation, VC Method (post- and pre-money), and exit terminal value. Use these first for early-stage startups. Method selects the formula, and each method names its own parameters: scorecard needs average_valuation + weights + scores; berkus takes five factor awards; risk_factor needs base_valuation + risk_ratings; vc_post_money needs terminal_value + target_return; vc_pre_money needs post_money + investment; terminal_value needs projected_revenue + multiple; triangulated needs the scorecard inputs plus terminal_value/target_return/investment. Routing: for SAFEs, tokens, ESG, network effects, or data-moat methods use valuation_emerging; for options or bull/base/bear scenario tables use valuation_advanced; for public-comparable multiples use valuation_comparables. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
method*	string	Formula to apply. Options: scorecard = V = V_avg · Σ(wᵢ·sᵢ) across 7 factors.; berkus = V = Σ factor awards, each capped at $500K.; risk_factor = V = V_base + Σ(rᵢ·$250K) over 12 risks.; vc_post_money = Post = Terminal / target ROI.; vc_pre_money = Pre = Post - Investment.; terminal_value = Terminal = projected revenue × multiple.; triangulated = Runs Scorecard and the VC Method together and returns their mean.
scores	array	Factor multipliers aligned with weights (1.0 = average, >1 above average).

valuation_emerging

Modern and alternative valuation: SAFE conversion (discount, cap, expected value), token valuation (equation of exchange, NVT), ESG adjustments (rate, premium, discount), Metcalfe network value, data-moat value, and remote-first premium/NPV. Method selects the model. Use for SAFEs, tokens, ESG, network effects, data moats, and remote-first adjustments; for classic pre-revenue methods use valuation_core. Parameters apply per method: safe_discount needs series_a_price + discount; safe_cap needs cap + series_a_price; safe_expected needs investment + cap + discount + series_a_valuation + series_a_price; token_value needs transaction_volume + price_per_tx + velocity + supply; metcalfe needs n; esg_* need base_valuation + a score; data_moat needs data_volume + data_uniqueness + monetization_rate + competitive_advantage_years. Routing: for classic pre-revenue methods (Scorecard, Berkus, Risk-Factor Summation, VC Method) use valuation_core; for options or scenario tables use valuation_advanced; for public-comparable multiples use valuation_comparables. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
k	integer	Number of events k for the Poisson probability P(X=k); integer ≥ 0.
n	number	Number of users or nodes in the network.
cap	number

valuation_fintech

Value and size fintech business models: payment revenue, lending valuation, payment-processor DCF, and neobank customer-based valuation. Method selects the model. Use for payments, lending, and neobanks; for SaaS-style unit economics use valuation_saas. Parameters apply per method: payment_revenue needs transaction_volume + take_rate; lending needs loan_book + roe + pe_multiple; payment_processor adds growth_rate + discount_rate + terminal_multiple; neobank needs customers + arpu + gross_margin + churn_rate + pe_multiple. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
roe	number	Return on equity as a decimal (0.20 = 20%).
arpu	number	Average revenue per user per month, currency units.
years	integer	Forecast horizon in years; integer ≥ 1.
method*	string	Formula to apply. Options: payment_revenue = Revenue = volume × take rate.; lending = V = loan book × ROE × P/E - NPL reserves.; payment_processor = DCF of payment revenue with a terminal multiple.; neobank = Customer LTV × P/E applied to the customer base.

valuation_hardware

Hardware and deep-tech valuation: TRL-risk-adjusted valuation, gross margin, and break-even volume. Method selects the metric. Use for hardware and deep tech with technology-readiness risk; for drug pipelines use valuation_biotech. Parameters apply per method: trl needs market_size + market_share + margin + multiple + trl_discount; gross_margin needs asp + variable_cost; break_even_volume needs fixed_costs + asp + variable_cost. Not for drug pipelines — for those use valuation_biotech. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
asp	number	Average selling price per unit, currency units.
margin	number	Profit margin as a decimal.
method*	string	Formula to apply. Options: trl = V = market × share × margin × multiple × (1 - TRL discount).; gross_margin = GM = (ASP - COGS) / ASP.; break_even_volume = Units = fixed costs / (ASP - variable cost).
multiple	number	Exit or market multiple applied to the metric.
fixed_costs

valuation_international

Cross-border adjustments: purchasing-power parity, country risk premium, and international CAPM. Method selects the adjustment. Use for cross-border cash flows and country risk; pair with valuation_capm and valuation_time_value. Parameters apply per method: ppp needs spot_rate + inflation_foreign + inflation_domestic; country_risk_premium needs sovereign_yield + us_treasury_yield; intl_capm needs risk_free_rate + beta + mrp + crp. Not for the domestic cost of equity — for that use valuation_capm. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
crp	number	Country risk premium as a decimal.
mrp	number	Market risk premium as a decimal.
beta	number	Systematic risk beta (market = 1.0).
method*	string	Formula to apply. Options: ppp = Eₜ = E₀·(1+π_foreign)/(1+π_domestic).; country_risk_premium = CRP = sovereign yield - US Treasury yield.; intl_capm = r = Rf + β·MRP + CRP.
spot_rate

valuation_marketplace

Marketplace health and valuation: take rate, GMV revenue-multiple valuation, buyer retention, and network density. Method selects the metric. Use for two-sided transaction marketplaces; for subscription software use valuation_saas. Parameters apply per method: take_rate needs revenue + gmv; gmv_multiple needs gmv + multiple; buyer_retention needs buyers_period_1 + buyers_repeat; network_density needs active_buyers + active_sellers + total_users. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
gmv	number	Gross merchandise value (total transaction volume), currency units.
method*	string	Formula to apply. Options: take_rate = Take rate = revenue / GMV.; gmv_multiple = Valuation = GMV × multiple.; buyer_retention = Retention = repeat buyers / base-period buyers.; network_density = Density = active buyers × active sellers / total users.
revenue	number	Revenue for the period, currency units.
multiple	number	Exit or market multiple applied to the metric.

valuation_probability

Compute expected value and probability-weighted outcomes for startup scenarios: discrete E[X], joint probability of sequential events, probability-weighted value, VC portfolio expected return, Poisson event probability, and continuous E[X] over a range. Method selects the formula. Use for probability-weighted central estimates; for named bull/base/bear tables or option pricing use valuation_advanced, and to discount cash flows use valuation_time_value. Parameters apply per method: expected_value_discrete and probability_weighted need outcomes + probabilities; portfolio_return needs weights + returns; poisson needs mean_events + k; expected_value_continuous needs lower + upper. outcomes and probabilities must be equal length, and the probabilities should sum to 1. Routing: use valuation_advanced method 'scenario_analysis' for named bull/base/bear scenario tables, and its black_scholes/binomial methods for option pricing; use this tool for arbitrary outcome lists and probability-weighted central estimates. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
k	integer	Number of events k for the Poisson probability P(X=k); integer ≥ 0.
lower	number	Lower integration bound (standard-normal domain, e.g. -1.0).
upper	number

valuation_saas

SaaS unit economics and valuation: LTV, CAC, MRR, ARR, net revenue retention, magic number, Rule of 40, CAC payback, and ARR revenue-multiple valuation. Method selects the metric. Use for subscription software; for marketplace GMV metrics use valuation_marketplace and for payments/lending use valuation_fintech. Parameters apply per method: ltv needs arpu + gross_margin + churn_rate; cac needs sales_marketing_expense + new_customers; arr needs subscription_values; nrr needs starting_revenue + ending_revenue; revenue_multiple needs arr + revenue_multiple. Not for company-level pre-revenue value — for that use valuation_core. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
arr	number	Annual recurring revenue, currency units.
cac	number	Customer acquisition cost per customer, currency units.
arpu	number	Average revenue per user per month, currency units.
method*	string	Formula to apply. Options: ltv = LTV = ARPU × gross margin / churn.; cac = CAC = S&M expense / new customers.; mrr = MRR = ARR / 12 (reverse of ARR).; arr = ARR = Σ monthly subscriptions × 12.; nrr = NRR = (start + expansion) / start, net of churn.; magic_number = Magic Number = net new ARR / prior-quarter S&M.; rule_of_40 = Score = growth rate + profit margin.; cac_payback = Months to recover CAC from gross profit.; revenue_multiple = Valuation = ARR × multiple.

valuation_stakeholder

Allocate value across stakeholders and equity classes: single-round dilution, OPM common stock, PWERM, liquidation value, M&A synergy, employee-option values, vesting adjustment, cash-vs-equity break-even, and asset-based loan capacity. Method selects the model. Use only after the company-level value is known (from valuation_core, valuation_saas, or valuation_comparables) to split that value across the cap table; for the company value itself do not use this tool. Parameters apply per method: dilution needs ownership_before + investment + post_money; opm needs enterprise_value + liquidation_pref + time_to_exit + volatility; pwerm and employee_option need scenarios; liquidation needs assets + recovery_rates; risk_adjusted_synergy needs revenue_synergies + cost_synergies; vesting_adjusted needs total_value + vested_fraction; max_asset_loan takes collateral values. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
cash	number	Cash and equivalents, currency units.
years	integer	Forecast horizon in years; integer ≥ 1.
assets	object	Map of asset name to book value, e.g. {"cash": 500000}.
method

valuation_time_value

Discount, compound, and forecast value over time: single future value PV, net present value of a cash-flow stream, annuity present value, discounted cash flow with a Gordon terminal value, constant-rate compound growth of revenue or cash flow, and the implied compound annual growth rate (CAGR). Method selects the formula. Use to convert future cash to today's value, to value a full forecast with a terminal value (dcf), to project a revenue or cash-flow series forward, or to derive the growth rate implied by two values; get the discount rate from valuation_capm or valuation_international. Parameters apply per method: present_value needs future_value + rate + periods; npv needs cash_flows + rate; annuity needs payment + rate + periods; dcf needs cash_flows + rate (optional: terminal_growth); compound_growth needs starting_value + growth_rate + periods; cagr needs starting_value + ending_value + periods. growth_rate must be greater than -1, cagr requires starting_value > 0 and periods > 0, and dcf requires rate greater than terminal_growth. Not for option values (use valuation_advanced) or for expected values over outcomes (use valuation_probability). Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.

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Argument	Type	Description
rate	number	Per-period discount rate as a decimal (0.10 = 10%).
method*	string	Formula to apply. Options: present_value = PV = C / (1+r)^t.; npv = NPV = Σ Cₜ / (1+r)^t.; annuity = PV = P·[1-(1+r)^-n]/r.; compound_growth = V_n = V_0 (1+g)^n.; cagr = CAGR = (V_n / V_0)^(1/n) - 1.; dcf = DCF = Σ Cₜ/(1+r)^t + [C_n(1+g)/(r−g)]/(1+r)^n.

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Startup Valuation MCP Server

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