startup-valuation

CAPM & Cost of Equity

valuation_capm

Read-onlyIdempotent

Calculate cost of capital and discount rates for startup DCF valuation using CAPM, startup-adjusted CAPM, portfolio beta, or WACC.

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; other parameters are method-dependent, so supply those named for the selected method and omit the rest (documented defaults apply where defined). Returns an object with value, method, inputs, assumptions, chapter, formula_number and calculation steps. Pure arithmetic: no I/O and no external calls, and numeric results are returned rounded to 2 decimals. No authentication, credentials, or rate limits apply. Supplying an unknown method, or leaving unset a parameter that the chosen method requires, 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.
`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.
`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').

Schema Changelog

Changes observed during successful MCP inspections.

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

A4.6/5.0

Behavior4/5

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

Annotations already declare readOnly, idempotent, non-destructive, closed-world, but the description adds substantial context the annotations cannot: pure arithmetic with no I/O or external calls, results rounded to 2 decimals, no auth/rate limits, and importantly that unknown methods or missing required params return an error rather than a value. That failure-mode disclosure is valuable beyond the structured hints.

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 routing, then a compact method-to-parameter map, then return/behavior notes. It is dense and mostly earns its length, though the requirement that only method is required is stated twice and could be tightened.

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 tool with an output schema, the description covers the method-dependent input contract, failure behavior, precision, and routing to related tools. Nothing needed to invoke 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 contributes cross-parameter semantics the schema does not: which parameters pair with each method, and the constraint that weights and betas must be equal length. This relational guidance genuinely reduces misuse risk.

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 and resource ('Estimate the cost of capital') and enumerates the four distinct methods (standard CAPM, startup-adjusted CAPM, portfolio beta, WACC), which cleanly separates it from the other valuation_* siblings. An agent can tell exactly what computation it performs 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?

Explicit routing: use it to derive the discount rate that feeds valuation_time_value and DCF models, and add valuation_international for cross-border rates. It also specifies when-supply-what per method and instructs to omit parameters not named for the selected method.

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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