Perpetuity Calculator
Value a stream of payments that continues forever, either level or growing at a steady rate.
Perpetuity Calculator
Present Value
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Value ÷ First Payment
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First Payment ÷ Value
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Every Payment
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Share of present value from the first payments
Sensitivity: Present Value vs. Discount Rate and Growth
| Discount rate |
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Assumptions & method
- Level perpetuity: PV = C ÷ r, with the first payment C one period from now (ordinary). Growing perpetuity: PV = C₁ ÷ (r − g), where C₁ is the first payment and later payments grow by g each period.
- Payments at the start of each period (perpetuity due) are worth (1 + r) times the ordinary value, because every payment arrives one period earlier. For a growing due perpetuity, the first payment is made now.
- The formula needs r greater than g and r greater than 0. If growth is equal to or above the discount rate, the sum does not converge and the calculator shows a message instead of a value.
- The rate and growth are per payment period and constant forever. Use an annual rate with annual payments, or a periodic rate matching the payment interval.
- The sensitivity table varies the discount rate and growth in 1-point steps around your inputs. Cells with growth at or above the rate show n/a. Your base case is highlighted.
Results are estimates based on the figures you enter. They are not guarantees and not financial advice.
What is a perpetuity?
A perpetuity is a stream of payments with no end date. Examples include preference shares paying a fixed dividend and some endowment-style payouts. Even though the payments never stop, their present value is finite because each distant payment is discounted heavily. A level perpetuity is worth the payment divided by the rate. If payments grow at a steady rate, the Gordon growth formula divides the first payment by the gap between the discount rate and growth, so a small gap produces a very large value. That sensitivity is the reason the table shows how the value moves when either assumption changes by a point or two. The bars show how much of the value comes from the first few payments, which is a useful reality check on how long you really wait.