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Perpetuity Present Value Calculator

Value a perpetuity from its payment and discount rate.

How it is calculated

A perpetuity is worth its yearly payment divided by the rate of return you require: PV = payment ÷ (rate ÷ 100). Payment is the amount received each period in dollars, and rate is the discount rate for that same period in percent (8 means 8%). The rate must match the payment frequency: an annual payment needs an annual rate, a monthly payment a monthly rate. The tool assumes the first payment arrives one period from now and that the payment stays the same forever, with no growth. The discount rate must be above zero, because at zero or below the value would be infinite or meaningless, so those inputs return no result. A payment of zero gives zero, and a negative payment gives a negative value, which you can use for a permanent cost. The rate is shown as a percentage next to the result.

Worked example

A fund pays $5,000 a year forever, and you require an 8% return. Convert the rate to a decimal: 8 ÷ 100 = 0.08. Present value: 5,000 ÷ 0.08 = $62,500.00. In other words, paying $62,500 today for this stream would earn exactly 8% a year. If you required 10% instead, the value would drop to 5,000 ÷ 0.10 = $50,000, showing how sensitive a perpetuity is to the discount rate you choose.

Try this example →

Common mistakes

  • Typing 0.08 for an 8% rate. The rate field is in percent, so 0.08 would give a value of about $6.25 million instead of $62,500.
  • Using an annual rate with monthly payments, or the reverse. Both must refer to the same period, or the value will be off by a factor of up to twelve.
  • Applying the formula to payments that grow each year. The tool assumes a flat payment; growing cash flows need a different formula and would be worth more.
  • Treating the result as precise. A small change in the discount rate moves the value a lot, so check a range of rates rather than one number.

About this calculator

A perpetuity is a stream of equal payments that continues forever, and its present value has one of the simplest formulas in finance: PV = Payment / Discount Rate. Because payments stretch infinitely into the future, the formula collapses the entire endless stream into a single number today, discounted by the rate of return an investor requires. The concept traces back to instruments like the UK's historical consols (perpetual government bonds) and is still used to value preferred stock, endowment funds, and any cash flow assumed to continue indefinitely at a constant level.

This calculator takes the periodic payment amount and the discount rate and returns the present value of that infinite payment stream. It's a useful building block for finance students and analysts modeling terminal value in a discounted cash flow analysis, where a company's cash flows beyond a forecast period are often approximated as a perpetuity.

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