Perpetuity Value Calculator

On the sample figures used here, an annual cash flow of 10,000 discounted at 5% gives a present value of 200,000. That is the same arithmetic read two ways: 10,000 divided by 0.05, or 10,000 multiplied by the effective multiple of 20. Raise the rate to 10% and the multiple halves to 10, so the same cash flow is worth 100,000. Perpetual preferred shares and endowment distributions approximate a stream with no end date.

The levers in this calculation

The two inputs carry near-equal proportional weight and pull in opposite directions. A 1% increase in the cash flow raises the present value by exactly 1%, because the cash flow sits in the numerator. A 1% increase in the discount rate lowers it by 1 − 1/1.01, or about 0.99%, because the rate sits in the denominator. The rate looks stronger when it is moved in percentage points rather than proportionally, and more so the lower the rate is: one point off a 5% rate is a fifth of the rate, which is why 5% to 4% adds 25% to the result while 5% to 6% takes 16.7% off.

How the math works

The present value is the annual cash flow divided by the discount rate expressed as a decimal, so a 10,000 cash flow at 5% gives 10,000 divided by 0.05, or 200,000. The reciprocal of the rate is the effective multiple, 20 at 5%, which is the same number read as years of undiscounted cash flow. Because the rate sits in the denominator, the multiple climbs without limit as the rate falls toward zero.

The perpetuity itself has no horizon; the thirty-year split in the rows is shown to make the tail visible. On the sample figures the first thirty payments account for 153,724.51 of the 200,000, leaving 23.14% in everything after. That share is exactly the thirty-year discount factor, so it depends on the rate alone and reads the same whatever the size of the cash flow.

Where this fits in planning

This is a what-if tool rather than a forecast. It answers a narrow question: what the present value becomes if the discount rate lands a point or two above the figure assumed, or the cash flow lands below it. Running several sets of figures across the two inputs shows how much of the answer rests on the rate; a single set does not.

What this doesn't capture

The formula assumes the annual cash flow stays constant in nominal terms and the discount rate never moves, and neither holds perfectly in practice. It leaves out inflation, which erodes the real purchasing power of a fixed payment over time, and it treats the stream as genuinely endless even though most real income streams eventually stop. Taxes on the payments are not modelled, and neither is any risk that the payments are missed. The number represents one steady-state scenario.

Worked example

Suppose a trust pays out 15,000 annually with no end date, and the rate chosen to discount it is 4%. The calculator returns a present value of 375,000, so the endless stream of 15,000 payments has the same present-day worth as a single lump sum of that size. Raise the discount rate to 6% and the present value falls to 250,000, a third less for a two-point move.

When this metric matters

Perpetuity valuation appears in several practical contexts:

• Preferred stock analysis: some preferred shares pay dividends indefinitely with no maturity date
• Real estate and land ownership: long-term rental income streams with no defined end
• Trust and endowment planning: distributions designed to continue across generations
• Comparing lump sums to income streams: setting a one-time payment against the present value of an ongoing stream

Related calculations worth running

The Bond Price Calculator and the Bond Duration Calculator handle the case where the stream stops at a maturity date, and the Cap Rate Calculator applies the same reciprocal arithmetic to property income. Where the cash flow grows rather than staying flat, the Gordon Growth Model is the corresponding expression. Running two or three of these together shows where a single assumption is carrying more weight than it first appears.