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Present value of perpetuity calculator
Free present value of perpetuity calculator for level and growing perpetuity (Gordon growth model) cash flows. Use the present value of perpetuity formula (PV = C ÷ r) or Gordon model live — enter payment, discount rate, and growth rate for PV, formula breakdown, discount-rate sensitivity, and CSV/PDF export. Advanced options solve for payment or rate; monthly frequency available. No sign-up.
What is a perpetuity?
A perpetuity is a stream of equal cash payments that continues forever — dividends on preferred stock, perpetual bond coupons, or fixed rental income with no end date. Unlike a finite annuity, there is no final payment, yet the present value of perpetuity is finite because each distant payment is discounted more heavily.
That follows the time value of money: money today can earn a return, so a $100 payment received in 50 years contributes almost nothing to present value even though the payment stream never stops. Infinite payments can still sum to a bounded PV — which is what this perpetuity calculator computes.
Results are illustrative for planning and education, not investment advice.
Level perpetuity
Fixed payment each period — PV = Payment ÷ Discount rate.
Growing perpetuity
Gordon model — payments grow at a constant rate g < r.
Sensitivity table
See how PV moves when discount rate changes ±1%.
CSV/PDF export
Download inputs and headline PV for Excel or reports.
Related tools: present value calculator, NPV calculator, WACC calculator, intrinsic value calculator, and future value calculator.
Present value of perpetuity formula
When payments stay constant each period, the present value of perpetuity formula is:
Level perpetuity
PV = C ÷ r where C is the periodic payment and r is the discount rate (as a decimal).
Worked example: A bond pays $10 per year forever at a 5% discount rate → PV = $10 ÷ 0.05 = $200. At 8%, the same $10 stream is worth $125 today.
Growing perpetuity formula (Gordon growth model calculator)
A growing perpetuity pays C₁ in the first period and grows by a constant rate g each period. The growing perpetuity formula is:
Gordon growth model
PV = C₁ ÷ (r − g) where r is the discount rate and g is the growth rate (both as decimals). r must be greater than g.
Worked example: $10 first-year payment, 8% discount, 2% growth → PV = $10 ÷ (0.08 − 0.02) = $166.67. This is the same math used for simplified DCF terminal value when cash flows grow steadily.
Perpetuity vs annuity vs NPV
An annuity has a fixed number of payments. A perpetuity has infinite payments but uses the same time-value-of-money logic. Use our present value calculator when you know the number of periods (leases, pensions with a term, vendor contracts).
NPV sums discounted project cash flows and subtracts an initial investment — use the NPV calculator for uneven yearly project streams. This perpetuity tool does not replace full project NPV; it answers “what is an infinite equal payment worth today?”
For corporate valuation terminal value, pair perpetuity math with a consistent WACC from our WACC calculator or a full intrinsic value calculator DCF.
Perpetuity due vs ordinary perpetuity
An ordinary perpetuity pays at the end of each period (typical bond coupon timing). A perpetuity due pays at the beginning of each period — you receive cash sooner, so present value is higher.
Perpetuity due formula
PVdue = (C ÷ r) × (1 + r) in decimal rate form — equivalent to receiving the first payment immediately plus an ordinary perpetuity. Example: $10 per year at 5% → ordinary PV $200; perpetuity due PV $210.
This calculator models ordinary timing (end of period), matching most textbook and bond examples. For finite streams with beginning-of-period payments, use Annuity due timing on our present value calculator.
Excel formula and real-world examples
Level perpetuity in Excel: if payment is in A1 and rate is in B1 (as a decimal), =A1/B1 gives present value. For a rate entered as 5%, use =A1/(B1/100). Google Sheets uses the same syntax.
Growing perpetuity in Excel: =A1/((B1-C1)/100) when B1 is discount % and C1 is growth %. Export CSV from this calculator to paste inputs into your model.
Real-world examples:
- Preferred stock — fixed dividend forever; use level perpetuity with your required return as discount rate.
- UK consols / perpetual bonds — fixed coupon with no maturity; same PV = C ÷ r logic (historical consols were redeemed; coupons can be suspended).
- Real estate — stable net rent modeled as infinite can be valued as perpetuity, though leases often have terms — use present value calculator when a lease ends.
- DCF terminal value — after an explicit forecast, Gordon terminal value is a growing perpetuity; pair with WACC and intrinsic value calculator for full equity value.
Always align the discount rate with cash-flow risk (cost of equity vs WACC) and whether flows are pre- or post-tax.
How to use this perpetuity calculator
Choose perpetuity type
Level perpetuity for fixed payments, or growing perpetuity for Gordon growth.
Enter payment and discount rate
Type periodic payment (dividend, rent, coupon) and annual discount rate as a percent.
Add growth rate if needed
For growing mode, enter growth % — it must stay below the discount rate.
Review PV and export
Read present value, sensitivity table, and export CSV or PDF. Use advanced options to solve for payment or discount rate.
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Frequently asked questions about this perpetuity calculator
How do you calculate perpetuity?
For a level perpetuity, divide the periodic payment by the discount rate: PV = C ÷ r (use r as a decimal). For a growing perpetuity: PV = C₁ ÷ (r − g) with r > g. Enter payment, discount rate, and optional growth in this calculator for live PV and a sensitivity table.
How do you calculate the present value of a perpetuity?
For a level perpetuity, divide the periodic payment by the discount rate: PV = C ÷ r. Example: $10 per year at 5% → $10 ÷ 0.05 = $200.
What is the present value of a perpetuity?
The present value of a perpetuity is today’s worth of an infinite stream of equal periodic payments, discounted at your required return. It is finite because distant payments contribute very little under the time value of money — even though the payment count never ends.
What is the formula for a growing perpetuity?
PV = C₁ ÷ (r − g) where C₁ is the first payment, r is the discount rate, and g is the constant growth rate. The growth rate must be less than the discount rate.
What is a $100 perpetuity?
A $100 perpetuity pays $100 every period forever with no final principal repayment — like a perpetual coupon or preferred dividend. Its present value depends only on your discount rate: at 10%, PV = $100 ÷ 0.10 = $1,000 today.
What is a $100 perpetuity worth at 10%?
A level perpetuity paying $100 per year at a 10% discount rate has present value $1,000 ($100 ÷ 0.10).
Why must the growth rate be less than the discount rate?
If g ≥ r, the denominator (r − g) is zero or negative, so present value would be infinite or undefined — which violates the economic assumption that distant growing payments still lose value over time.
What is the difference between a perpetuity and an annuity?
An annuity ends after a set number of periods. A perpetuity never ends. Use our present value calculator for finite annuities and lump sums.
What is the future value of a $100 perpetuity with a 10% return?
A standard perpetuity has no finite future value — the payment stream never ends, so you cannot sum to a final lump sum. Analysts use present value instead. If you mean “what is $100 per year worth today at a 10% discount rate,” that is $1,000 PV — not future value.
What is the Excel formula for perpetuity?
Level: =A1/B1 when B1 is the rate as a decimal, or =A1/(B1/100) if B1 is a percent. Growing: =A1/((B1-C1)/100) with discount and growth in percent cells.
What is perpetuity due?
Perpetuity due pays at the beginning of each period (vs end for an ordinary perpetuity). Present value is higher: PVdue = (C ÷ r) × (1 + r). Example: $10 at 5% → $210 due vs $200 ordinary. See the perpetuity due section above; this calculator uses ordinary (end-of-period) timing.
What is the Gordon growth model calculator?
A Gordon growth model calculator values a growing perpetuity: PV = C₁ ÷ (r − g). Switch to Growing perpetuity mode or load the Gordon example preset ($10, 8% discount, 2% growth → $166.67). Used for DCF terminal value when cash flows grow at a constant rate forever.
What is the future value of a perpetuity?
A standard perpetuity has no finite future value — payments continue forever. In practice, analysts focus on present value. For finite horizons, use future value calculator or present value calculator.
How is perpetuity used in DCF terminal value?
Terminal value often assumes cash flows grow at g forever: TV = FCFF₁ ÷ (WACC − g). Estimate WACC with our WACC calculator and full equity value with the intrinsic value calculator.
Can you calculate a monthly perpetuity?
Yes — open Advanced options and set Payment frequency to Monthly. The engine converts the annual discount and growth rates to monthly period rates for the payment per month.
Example: $1 monthly payment with 12% annual discount (1% per month) → PV ≈ $100 ($1 ÷ 0.01). For finite monthly annuities, use the present value calculator with monthly compounding.
Is this perpetuity calculator free?
Yes. Level and growing perpetuity modes, solve-for options, sensitivity table, and CSV/PDF export are free with no sign-up.