Perpetuity Calculations
perpetuityCalculate present value of a perpetuity for level, due, or growing payments. Solves infinite payment stream valuation for preferred stock, endowments, and rental income.
Instructions
Calculate present value of a perpetuity (infinite series of payments).
A perpetuity is an annuity that continues forever. Common in: - Preferred stock dividends - Endowment funds - Real estate with infinite rental income - UK Consol bonds (historically)
Formulas: Level Ordinary: PV = C / r Level Due: PV = C / r × (1 + r) Growing: PV = C / (r - g), where r > g
Examples:
LEVEL PERPETUITY: £1000 annual payment at 5% payment=1000, rate=0.05 Result: PV = £20,000
GROWING PERPETUITY: £1000 payment growing 3% annually at 8% discount payment=1000, rate=0.08, growth_rate=0.03 Result: PV = £20,000
PERPETUITY DUE: £1000 at period start at 5% payment=1000, rate=0.05, when='begin' Result: PV = £21,000
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| context | No | Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification. | |
| output_mode | No | Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details. | full |
| payment | Yes | Periodic payment amount (e.g., 1000) | |
| rate | Yes | Discount rate per period (e.g., 0.05) | |
| growth_rate | No | Payment growth rate (None or 0 for level, e.g., 0.03 for growing) | |
| when | No | Payment timing: 'end' or 'begin' | end |
Output Schema
| Name | Required | Description | Default |
|---|---|---|---|
| result | Yes |