What a perpetuity is
A perpetuity is a cash-flow stream modelled as continuing indefinitely. Preferred shares and endowment distributions are common approximations; real securities still carry legal, credit, and operating risks.
Perpetuity Calculator
Calculate the present value of level or growing perpetual cash flows. A level perpetuity uses PV = C / r; a growing perpetuity uses PV = C1 / (r − g), where C1 is the first cash flow after the valuation date.
Calculate value
The payment one period after today.
Required return per selected payment period.
Use 0 for a level perpetuity; negative growth is allowed.
Changes display only, not the calculation.
Cash flow, r, and g must all use this same period.
For the ordinary Gordon Growth formula, enter the first cash flow after the valuation date (C1), not the latest cash flow.
Advanced options — timing and reverse solving
Required when reverse-solving for C, r, or g.
Enter cash flow from the final forecast year (Cn). The calculator grows it once to Cn+1 before applying the Gordon Growth formula.
FCFF, FCFE, dividend, or other matching cash flow.
A sustainable long-run rate.
Use WACC with FCFF or cost of equity with equity cash flow.
The final explicit forecast year.
Use 0 to show terminal value without discounting.
Editable terminal-value scenarios
Set the WACC and perpetual growth assumptions you want compared.
ScenarioWACC %Growth %
Conservative
Base
Optimistic
Results
Present value
$20,000.00
Cash flow per year
$1,000.00
Discount-growth spread (r − g)
5.00 pp
Value per 1 unit of cash flow
20.00×
Implied cash-flow yield
5.00%
Formula breakdown
PV = C / rPV = $1,000.00 / 0.0500 = $20,000.00
Sensitivity analysis
Nearby rate assumptions show how value changes.
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Perpetuity valuation guide
Time value of money
A future payment is worth less today because capital has an opportunity cost. Discounting every future payment and summing the series produces present value.
Level versus growing
A level perpetuity keeps C constant and uses PV = C / r. A growing perpetuity changes cash flow by g each period and uses PV = C1 / (r − g).
Ordinary versus due timing
Ordinary means the first payment arrives next period. Due means the first payment arrives today. For a level stream, the due value equals the ordinary value plus today's payment.
Perpetuity versus annuity
An annuity ends after a specified number of payments. A perpetuity has no final period, so its formula does not contain a payment count.
Choosing r and g
Match the discount rate to the cash flow's risk, currency, inflation basis, and period. Use a sustainable long-run g below r; a smaller r − g spread produces a much more sensitive valuation.
Frequency and units
Annual cash flow needs annual r and g; quarterly cash flow needs quarterly rates; monthly cash flow needs monthly rates. The selector labels results but does not convert rates automatically.
Real-world limitations
No business or security literally grows at one fixed rate forever. Test multiple assumptions, distinguish nominal from real inputs, and treat terminal value as an estimate rather than a quoted market price.
Worked examples
Level perpetuity
- Inputs: C = $1,000; r = 5%.
- Convert: 5% = 0.05.
- Substitute: PV = $1,000 / 0.05.
- Result: $20,000.
This is the value today of $1,000 paid every year from next year onward at a 5% required return.
Growing perpetuity
- Inputs: C1 = $1,000; r = 7%; g = 2%.
- Convert: r = 0.07; g = 0.02.
- Substitute: PV = $1,000 / (0.07 − 0.02).
- Result: $20,000.
The first $1,000 payment arrives next year and then grows 2% each year forever.
Preferred stock
- Inputs: annual dividend C = $2.50; required return r = 6.25%.
- Convert: 6.25% = 0.0625.
- Substitute: price = $2.50 / 0.0625.
- Result: $40.00 per share.
This is the indicated value if the dividend remains level and the required return is appropriate.
Endowment payout
- Inputs: fund PV = $1,000,000; target return r = 4.5%.
- Convert: 4.5% = 0.045.
- Rearrange: C = PV × r.
- Result: $45,000 per year.
Ignoring fees, inflation, and volatility, this is the level annual payout implied by the perpetuity model.
Gordon Growth terminal value
- Inputs: year-5 FCF = $50,000; WACC = 8%; g = 3%.
- Next cash flow: C6 = $50,000 × 1.03 = $51,500.
- Terminal value: TV5 = $51,500 / (0.08 − 0.03) = $1,030,000.
- Discount: PV = $1,030,000 / 1.085 = $701,000.69.
The terminal value sits at the end of year 5; discounting converts it to today's value.
Frequently asked questions
How is the present value of a perpetuity calculated?
For a level perpetuity, divide the next-period payment C by the discount rate r: PV = C / r. For a growing perpetuity, divide next-period cash flow C1 by the discount-growth spread: PV = C1 / (r − g). Enter rates as decimals in the formula, so 5% is 0.05.
Why must the discount rate r exceed the growth rate g?
The growing-perpetuity formula requires r > g so distant cash flows shrink in present-value terms and the infinite series converges. If r is equal to or below g, the formula does not produce a finite value.
Which cash flow belongs in the growing perpetuity formula?
Use C1, the first cash flow after the valuation date. If you only have the current or final forecast-period cash flow C0, calculate C1 = C0 × (1 + g) before applying PV = C1 / (r − g).
How is a perpetuity different from an annuity?
A perpetuity is modelled as continuing forever, while an annuity has a fixed number of payments. An annuity formula therefore includes the number of periods; a perpetuity formula does not.
Can a perpetuity have a negative growth rate?
Yes. A negative g models cash flows that decline by a constant percentage each period. The same growing-perpetuity formula applies as long as r > g and the assumptions remain economically meaningful.
How is the perpetuity formula used for terminal value?
At the end of forecast year n, grow that year's cash flow once to obtain Cn+1, then calculate terminal value TVn = Cn+1 / (r − g). To express it in today's money, discount TVn by (1 + r) raised to the number of years back to today.
What does perpetuity due mean?
A perpetuity due makes its first payment immediately rather than one period from now. A level perpetuity due is worth one payment more than an ordinary level perpetuity: PVdue = C0 + C0 / r.
Methodology, review, and sources
Methodology
The calculator applies the closed-form present-value equations shown on this page. Percent inputs are divided by 100, calculations retain JavaScript floating-point precision, and displayed monetary values round to two decimals. Terminal value grows the final forecast-year cash flow once, then optionally discounts the result.
Scope and disclaimer
Educational use only—not financial, investment, tax, or accounting advice. The model does not estimate risk, inflation, taxes, reinvestment needs, default probability, or whether a chosen growth rate is sustainable.
Sources
- OpenStax, Principles of Finance: Perpetuities — level and growing perpetuity formulas and preferred-stock applications.
- Aswath Damodaran, NYU Stern: Discounted Cash Flow Models — Gordon Growth timing uses the expected next-period cash flow.
- Aswath Damodaran, NYU Stern: Estimating Terminal Value — stable-growth terminal-value method and limitations.