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Finance Calc Kit
Investments

Perpetuity Calculator

Calculate the present value of a standard or growing perpetuity stream with custom cash flow and discount rate.

Cash Flow Inputs

$
%

Present value

$20,000.00

Cash flow (C)

$1,000.00

Discount rate (r)

5.0%

How This Is Calculated

PV=Cr\mathrm{PV} = \frac{C}{r}

• Cash flow (C): $1,000.00 per period

• Discount rate (r): 5.0%

• Present value: $1,000.00 ÷ 0.0500 = $20,000.00

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What Is a Perpetuity?

A perpetuity is a stream of equal cash payments that continues forever. Because the payments never end, you cannot simply add them up. Instead, finance uses present value to express what that infinite stream is worth today at a required discount rate.

Perpetuities appear in dividend valuation, preferred stock pricing, endowment modeling, and terminal value in discounted cash flow analysis. If you are discounting a finite set of cash flows, start with the net present value calculator. For company valuation that ends with a Gordon Growth terminal value, use the discounted cash flow calculator or the intrinsic value calculator. For finite payment streams with ordinary, due, or growing schedules, the present value annuity calculator handles multiple compounding frequencies.

Standard Perpetuity Formula

When each payment C stays constant and the discount rate is r (as a decimal), present value collapses to a simple fraction:

PV=Cr\mathrm{PV} = \frac{C}{r}

The discount rate reflects your required return or opportunity cost. A higher rate lowers present value because future dollars are worth less to you today.

Growing Perpetuity Formula

A growing perpetuity increases each payment by a constant growth rate g. The Gordon Growth form is:

PV=Cr−g\mathrm{PV} = \frac{C}{r - g}

The growth rate must stay strictly below the discount rate. If g equals or exceeds r, the denominator is zero or negative and present value is undefined.

Worked Example

An investment pays $1,000 every year forever and you require a 5% return:

PV=$1,0000.05=$20,000\mathrm{PV} = \frac{\$1{,}000}{0.05} = \$20{,}000

You would pay up to $20,000 today to earn $1,000 per year at a 5% required return. If payments grew 2% annually instead, the denominator becomes 0.05 minus 0.02 and present value rises to about $33,333.

Practical Uses

  • Preferred stock: Fixed dividends with no maturity date are often modeled as perpetuities.
  • Endowments: Foundations estimate how much principal is needed to fund a fixed annual payout.
  • Terminal value: DCF models frequently cap explicit forecasts with a growing perpetuity terminal value.

Frequently asked questions

Why does present value stay finite if payments never stop?
Each future payment is discounted by a larger factor. The geometric discounting series converges when the discount rate is positive, so the infinite sum has a finite limit.
What happens if the growth rate equals the discount rate?
The denominator in the growing perpetuity formula becomes zero, which makes present value undefined. In practice, sustained growth at or above your required return is not economically stable over an infinite horizon.
Should I use annual or monthly cash flows?
Match the period of C, r, and g. If payments are monthly, express the discount rate and growth rate on a monthly basis. Mixing annual rates with monthly payments produces incorrect results.
How is a perpetuity different from an annuity?
An annuity ends after a fixed number of periods. A perpetuity has no final payment date. For finite schedules, use an annuity or loan payment calculator instead.
Can present value be negative?
Not with positive cash flows and a positive discount rate. Negative cash flows, such as ongoing maintenance costs, would produce a negative present value.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.