FinanceTime Value of MoneyA-Level
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Perpetuity Present Value Calculator

PV of infinite equal payments.

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Present Value

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Overview

The perpetuity present value formula calculates the current value of a stream of identical cash flows that continue indefinitely. This mathematical model assumes the first payment is received one period from today and that the discount rate remains constant over time.

Symbols

Variables

PV = Present Value, C = Cash Flow, r = Interest Rate

Present Value
$
Cash Flow
$
Interest Rate

Apply it well

When To Use

When to use: Apply this formula when evaluating financial instruments with no maturity date, such as British Consols or perpetual preferred stock. It is also used in corporate finance to estimate the terminal value of a firm that has reached a stable, mature growth phase.

Why it matters: This formula simplifies the complex task of valuing infinite future payments into a single, manageable figure. It serves as a foundational tool for investors to determine if a permanent income stream is priced fairly relative to its risk-adjusted return.

Avoid these traps

Common Mistakes

  • Applying to finite streams.
  • Using growth rate incorrectly.

One free problem

Practice Problem

A philanthropist wishes to establish a permanent university scholarship that pays out 15,000 dollars every year. If the annual interest rate is 6%, how much must the donor contribute today to fully fund this endowment?

Cash Flow15000 $
Interest Rate0.06

Solve for:

Hint: Divide the annual payment by the decimal interest rate.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Brealey, Richard A., Myers, Stewart C., and Allen, Franklin. Principles of Corporate Finance. McGraw-Hill Education.
  2. Ross, Stephen A., Westerfield, Randolph W., and Jordan, Bradford D. Fundamentals of Corporate Finance. McGraw-Hill Education.
  3. Wikipedia: Perpetuity (finance)
  4. Perpetuity (finance) Wikipedia article
  5. Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  6. Wikipedia article 'Perpetuity' (finance)
  7. Standard curriculum — A-Level Accounting / Finance