startup-valuation

CAPM & Cost of Equity

valuation_capm

Read-onlyIdempotent

Estimate cost of capital and discount rates via CAPM, startup-adjusted CAPM, portfolio beta, or WACC to feed DCF valuations and time-value models.

Instructions

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.

Input Schema

TableJSON Schema

Name	Required	Description
`beta`	No	Systematic risk beta (market = 1.0).
`betas`	No	Asset betas aligned with weights; typically 0.5–3.0 (market = 1.0).
`method`	Yes	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`	No	Portfolio or factor weights, each in [0,1] and summing to 1 (same order as the paired value list).
`tax_rate`	No	Effective tax rate as a decimal in [0,1].
`debt_value`	No	Market value of debt, in currency units.
`cost_of_debt`	No	Pre-tax cost of debt Rd as a decimal.
`equity_value`	No	Value of equity offered, currency units.
`size_premium`	No	Small-cap / size premium as a decimal.
`market_return`	No	Expected market return as a decimal (e.g. 0.10 for 10%).
`cost_of_equity`	No	After-tax cost of equity Re as a decimal.
`risk_free_rate`	No	Risk-free rate as a decimal (e.g. 0.04 for 4%).
`liquidity_premium`	No	Illiquidity premium as a decimal.
`market_risk_premium`	No	Market risk premium as a decimal (e.g. 0.06).

Output Schema

TableJSON Schema

Name	Required	Description
`error`	No	Error message when the call fails.
`steps`	No	Intermediate steps for traceability.
`value`	Yes	Computed valuation or metric.
`inputs`	No	Echo of the normalised inputs used.
`method`	No	Formula / method name that produced the result.
`chapter`	No	Source textbook chapter.
`assumptions`	No	Modelling assumptions applied.
`formula_number`	No	Source textbook formula number (e.g. '3.1').
`defaults_applied`	No	Optional parameters that were not supplied, so their documented defaults were used.

Schema Changelog

Changes observed during successful MCP inspections.

Changed3 schema fields changedv2.1.1Oct 2, 2026

changedInput schema / properties / betas / description

Previous value: -"Asset betas aligned with weights."New value: +"Asset betas aligned with weights; typically 0.5–3.0 (market = 1.0)."

changedInput schema / properties / tax_rate / description

Previous value: -"Effective tax rate as a decimal."New value: +"Effective tax rate as a decimal in [0,1]."

addedOutput schema / properties / defaults_applied

Added value: +{
+  "description": "Optional parameters that were not supplied, so their documented defaults were used.",
+  "items": {
+    "type": "string"
+  },
+  "type": "array"
+}

Changed7 schema fields changedv0.1.5Sep 30, 2026

addedInput schema / properties / cost_of_debt

Added value: +{
+  "anyOf": [
+    {
+      "type": "number"
+    },
+    {
+      "type": "null"
+    }
+  ],
+  "default": null,
+  "description": "Pre-tax cost of debt Rd as a decimal."
+}

addedInput schema / properties / cost_of_equity

Added value: +{
+  "anyOf": [
+    {
+      "type": "number"
+    },
+    {
+      "type": "null"
+    }
+  ],
+  "default": null,
+  "description": "After-tax cost of equity Re as a decimal."
+}

addedInput schema / properties / debt_value

Added value: +{
+  "anyOf": [
+    {
+      "type": "number"
+    },
+    {
+      "type": "null"
+    }
+  ],
+  "default": null,
+  "description": "Market value of debt, in currency units."
+}

addedInput schema / properties / equity_value

Added value: +{
+  "anyOf": [
+    {
+      "type": "number"
+    },
+    {
+      "type": "null"
+    }
+  ],
+  "default": null,
+  "description": "Value of equity offered, currency units."
+}

changedInput schema / properties / method / description

Previous value: -"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."New value: +"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)."

changedInput schema / properties / method / enum

Previous value: -[
-  "capm",
-  "startup_capm",
-  "portfolio_beta"
-]New value: +[
+  "capm",
+  "startup_capm",
+  "portfolio_beta",
+  "wacc"
+]

addedInput schema / properties / tax_rate

Added value: +{
+  "anyOf": [
+    {
+      "type": "number"
+    },
+    {
+      "type": "null"
+    }
+  ],
+  "default": null,
+  "description": "Effective tax rate as a decimal."
+}

First observedv0.1.0Sep 30, 2026

TDQS

A4.8/5.0

Behavior5/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare read-only, idempotent, non-destructive, non-open-world behavior, and the description adds real context on top: pure arithmetic with no I/O or external calls, no auth or rate limits, rounding to 2 decimals, and that an unknown method or missing method-required parameter returns an error instead of a value. That is meaningful disclosure of failure modes and side-effect profile.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loaded with purpose, then usage, then method-dependent parameter mapping, then behavior — a sensible order with almost no filler. It is dense and slightly repetitive on units/weights already stated in the schema, so not quite maximal.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a 14-parameter, method-dependent tool, the description covers method selection, required-vs-optional inputs per method, cross-parameter constraints, input units, error behavior, and integration with sibling valuation tools. An output schema exists, so the brief return summary is redundant but harmless; nothing needed to call it correctly is missing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, so the baseline is 3, but the description adds non-schema constraints: the per-method parameter mapping (capm = risk_free_rate + beta + market_return, etc.) and the cross-parameter rule that weights and betas must be equal length. Some unit guidance (fractions, [0,1] sums) duplicates the schema, keeping this below a 5.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb ('Estimate the cost of capital') and enumerates exactly which computations it covers: standard CAPM, startup-adjusted CAPM with size/illiquidity premiums, portfolio beta, and WACC. It explicitly routes the agent away from itself toward valuation_time_value and valuation_international, so it is distinguishable from siblings without opening the schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines5/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Gives explicit when-to-use ('derive the discount rate that feeds valuation_time_value and DCF models') and a conditional alternative ('for cross-border rates add valuation_international'). It further specifies which parameters each method requires and that only 'method' is mandatory, which is actionable routing guidance.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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