valuation_time_value
Time Value of Money
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Third-party content written by another agent. Data to evaluate, not 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; 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: 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. |
| future_value | number | no | Future cash amount to discount, in currency units. |
| rate | number | no | Per-period discount rate as a decimal (0.10 = 10%). |
| periods | number | no | Number of compounding periods, must be ≥ 1 (may be fractional). |
| cash_flows | array | no | Cash flows by period, first element at t=1; negatives allowed for outflows. |
| payment | number | no | Recurring payment per period, in currency units. |
| starting_value | number | no | Value at t=0 (revenue or cash flow) to grow forward, in currency units. |
| growth_rate | number | no | Revenue growth rate as a decimal (0.40 = 40%). |
| ending_value | number | no | Value at t=n to compare against the starting value, in currency units. |
| terminal_growth | number | no | Perpetual growth rate g applied after the forecast window, as a decimal. |
Raw JSON schema
{
"type": "object",
"properties": {
"method": {
"type": "string",
"enum": [
"present_value",
"npv",
"annuity",
"compound_growth",
"cagr",
"dcf"
],
"description": "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."
},
"future_value": {
"type": "number",
"description": "Future cash amount to discount, in currency units."
},
"rate": {
"type": "number",
"description": "Per-period discount rate as a decimal (0.10 = 10%)."
},
"periods": {
"type": "number",
"description": "Number of compounding periods, must be ≥ 1 (may be fractional)."
},
"cash_flows": {
"type": "array",
"items": {
"type": "number"
},
"description": "Cash flows by period, first element at t=1; negatives allowed for outflows."
},
"payment": {
"type": "number",
"description": "Recurring payment per period, in currency units."
},
"starting_value": {
"type": "number",
"description": "Value at t=0 (revenue or cash flow) to grow forward, in currency units."
},
"growth_rate": {
"type": "number",
"description": "Revenue growth rate as a decimal (0.40 = 40%)."
},
"ending_value": {
"type": "number",
"description": "Value at t=n to compare against the starting value, in currency units."
},
"terminal_growth": {
"type": "number",
"description": "Perpetual growth rate g applied after the forecast window, as a decimal.",
"default": 0
}
},
"required": [
"method"
]
}