startup-valuation

Time Value of Money

valuation_time_value

Read-onlyIdempotent

Discount future cash flows to today's value, compute NPV, annuity or DCF with terminal value, project compound growth, or derive implied CAGR.

Instructions

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; 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
`rate`	No	Per-period discount rate as a decimal (0.10 = 10%).
`method`	Yes	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.
`payment`	No	Recurring payment per period, in currency units.
`periods`	No	Number of compounding periods (may be fractional).
`cash_flows`	No	Cash flows by period, first element at t=1; negatives allowed for outflows.
`growth_rate`	No	Revenue growth rate as a decimal (0.40 = 40%).
`ending_value`	No	Value at t=n to compare against the starting value, in currency units.
`future_value`	No	Future cash amount to discount, in currency units.
`starting_value`	No	Value at t=0 (revenue or cash flow) to grow forward, in currency units.
`terminal_growth`	No	Perpetual growth rate g applied after the forecast window, as a decimal.

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.

Changed3 schema fields changedv0.1.5Sep 30, 2026

changedInput schema / properties / method / description

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

changedInput schema / properties / method / enum

Previous value: -[
-  "present_value",
-  "npv",
-  "annuity",
-  "compound_growth",
-  "cagr"
-]New value: +[
+  "present_value",
+  "npv",
+  "annuity",
+  "compound_growth",
+  "cagr",
+  "dcf"
+]

addedInput schema / properties / terminal_growth

Added value: +{
+  "anyOf": [
+    {
+      "type": "number"
+    },
+    {
+      "type": "null"
+    }
+  ],
+  "default": null,
+  "description": "Perpetual growth rate g applied after the forecast window, as a decimal."
+}

Changed5 schema fields changedv0.1.4Sep 30, 2026

addedInput schema / properties / ending_value

Added value: +{
+  "anyOf": [
+    {
+      "type": "number"
+    },
+    {
+      "type": "null"
+    }
+  ],
+  "default": null,
+  "description": "Value at t=n to compare against the starting value, in currency units."
+}

addedInput schema / properties / growth_rate

Added value: +{
+  "anyOf": [
+    {
+      "type": "number"
+    },
+    {
+      "type": "null"
+    }
+  ],
+  "default": null,
+  "description": "Revenue growth rate as a decimal (0.40 = 40%)."
+}

changedInput schema / properties / method / description

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

changedInput schema / properties / method / enum

Previous value: -[
-  "present_value",
-  "npv",
-  "annuity"
-]New value: +[
+  "present_value",
+  "npv",
+  "annuity",
+  "compound_growth",
+  "cagr"
+]

addedInput schema / properties / starting_value

Added value: +{
+  "anyOf": [
+    {
+      "type": "number"
+    },
+    {
+      "type": "null"
+    }
+  ],
+  "default": null,
+  "description": "Value at t=0 (revenue or cash flow) to grow forward, in currency units."
+}

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 readOnly/idempotent/non-destructive, but the description goes further: it discloses that it is pure arithmetic with no I/O or external calls, that results are rounded to 2 decimals, that no auth/credentials/rate limits apply, and that unknown methods or missing method-required params return an error rather than a value. This is behavioral context well beyond the annotation set.

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?

The paragraph is long but dense and front-loaded: purpose first, then method semantics, then per-method parameters, then constraints, exclusions, and return/error behavior. Nearly every sentence carries distinct information, though it could be split for readability.

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 10-parameter multi-method calculator, the description covers purpose, per-method param requirements, constraints, exclusions, error behavior, and result rounding; with an output schema present it need not detail the return shape, and it still sketches it. Nothing an agent needs to invoke 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 real value the schema lacks: a method-to-parameter mapping (which params each method needs) and validation constraints (growth_rate > -1, cagr needs starting_value > 0 and periods > 0, dcf needs rate > terminal_growth). It also explains that only method is required and the rest should be omitted per method.

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?

Names specific verbs (discount, compound, forecast) and the resource (value over time), then enumerates the six concrete formulas it computes. An agent can distinguish it from valuation_capm, valuation_advanced, and valuation_probability purely from the description.

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?

Explicitly states the four main use cases (convert future cash to present, value a forecast with terminal value, project a series forward, derive implied growth) and routes elsewhere for out-of-scope work ('Not for option values (use valuation_advanced)', 'expected values over outcomes (use valuation_probability)'), plus names valuation_capm as the source of the discount rate.

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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