Perpetuity
A stream of equal cash flows that continues forever. PV-perpetuity = C / r, where C is the constant payment and r is the discount rate. Derivation: take the PV-annuity formula and let n → ∞; the (1+r)⁻ⁿ term drives to zero, leaving C/r. Worked example: an endowment paying $40,000/year forever, earning 5% on its investments, requires PV = $40,000 / 0.05 = $800,000 to fund. The British Treasury issued perpetuity bonds called "consols" from 1751 to 2015. The math forgives the "forever" assumption because distant cash flows contribute almost nothing to PV at any positive discount rate (50 years out at 5% captures 91% of the perpetuity value; 100 years captures 99%).
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Related terms
Adjusted Cost Basis · Annuity · Capital Gains Distribution · Capitalized Interest · Cost Basis · Dividend Discount Model (DDM)
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