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What is a perpetuity and how is it valued?

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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.

Common follow-ups: What is the growing perpetuity formula? | Where is it used?