valuation_capm
CAPM & Cost of Equity
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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
| Property | Type | Required | Description |
|---|---|---|---|
| method | string | 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). |
| risk_free_rate | number | no | Risk-free rate as a decimal (e.g. 0.04 for 4%). |
| beta | number | no | Systematic risk beta (market = 1.0). |
| market_return | number | no | Expected market return as a decimal (e.g. 0.10 for 10%). |
| market_risk_premium | number | no | Market risk premium as a decimal (e.g. 0.06). |
| size_premium | number | no | Small-cap / size premium as a decimal. |
| liquidity_premium | number | no | Illiquidity premium as a decimal. |
| weights | array | no | Portfolio or factor weights, each in [0,1] and summing to 1 (same order as the paired value list). |
| betas | array | no | Asset betas aligned with weights; typically 0.5–3.0 (market = 1.0). |
| equity_value | number | no | Value of equity offered, currency units. |
| debt_value | number | no | Market value of debt, in currency units. |
| cost_of_equity | number | no | After-tax cost of equity Re as a decimal. |
| cost_of_debt | number | no | Pre-tax cost of debt Rd as a decimal. |
| tax_rate | number | no | Effective tax rate as a decimal in [0,1]. |
Raw JSON schema
{
"type": "object",
"properties": {
"method": {
"type": "string",
"enum": [
"capm",
"startup_capm",
"portfolio_beta",
"wacc"
],
"description": "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)."
},
"risk_free_rate": {
"type": "number",
"description": "Risk-free rate as a decimal (e.g. 0.04 for 4%)."
},
"beta": {
"type": "number",
"description": "Systematic risk beta (market = 1.0)."
},
"market_return": {
"type": "number",
"description": "Expected market return as a decimal (e.g. 0.10 for 10%)."
},
"market_risk_premium": {
"type": "number",
"description": "Market risk premium as a decimal (e.g. 0.06)."
},
"size_premium": {
"type": "number",
"description": "Small-cap / size premium as a decimal.",
"default": 0
},
"liquidity_premium": {
"type": "number",
"description": "Illiquidity premium as a decimal.",
"default": 0
},
"weights": {
"type": "array",
"items": {
"type": "number"
},
"description": "Portfolio or factor weights, each in [0,1] and summing to 1 (same order as the paired value list)."
},
"betas": {
"type": "array",
"items": {
"type": "number"
},
"description": "Asset betas aligned with weights; typically 0.5–3.0 (market = 1.0)."
},
"equity_value": {
"type": "number",
"description": "Value of equity offered, currency units."
},
"debt_value": {
"type": "number",
"description": "Market value of debt, in currency units."
},
"cost_of_equity": {
"type": "number",
"description": "After-tax cost of equity Re as a decimal."
},
"cost_of_debt": {
"type": "number",
"description": "Pre-tax cost of debt Rd as a decimal."
},
"tax_rate": {
"type": "number",
"description": "Effective tax rate as a decimal in [0,1].",
"default": 0.3
}
},
"required": [
"method"
]
}