Answer
A perpetuity is a constant cash flow continuing indefinitely. Its present value is cash flow / r (for a level perpetuity) or, for a growing perpetuity, cash flow / (r - g). Perpetuity formulas are used for terminal values and valuing long-lived income streams in appraisal and valuation.
PV of 5,000/yr forever at 10% = 5,000 / 0.10 = 50,000.Real-world example A terminal value is estimated as a growing perpetuity of the final year's cash flow.