Perpetuity Calculator

What the perpetuity calculator does

The perpetuity calculator finds the present value of a cash flow that pays the same amount forever, or grows at a steady rate each year. Money arriving in the distant future is worth less than money in hand now, so even an infinite series of payments has a finite value once each future amount is discounted back to the present.

Preferred shares that pay a fixed dividend, certain government consols, endowments, and the terminal value in a company valuation all behave like an endless income stream, and the calculator values them from three figures.

How a perpetuity works

A perpetuity is an annuity with no final date. A payment of one thousand due next year is worth less than one thousand today, and one due in fifty years is worth far less. Further into the future, each payment shrinks in present-value terms until the additions become negligible, and the sum converges on a finite number.

The discount rate, the return you could earn elsewhere on money of similar risk, largely sets that number. A high rate penalises future payments heavily and lowers the value today; a low rate leaves more of the future value intact. Small changes in the assumed rate can move the result substantially.

The formula

Present value = Payment ÷ (r − g)

The payment is the amount received each year, r is the discount rate as a decimal, and g is the growth rate of the payment. With no growth, the formula is the payment divided by the discount rate: a fixed annual payment of one thousand discounted at five percent is worth twenty thousand today, because one thousand divided by 0.05 is twenty thousand.

A payment of one thousand that grows two percent a year, discounted at five percent, is worth one thousand divided by 0.03, about thirty-three thousand. Growth raises the value because each payment is larger than the last, but only while the discount rate stays above the growth rate.

When the value is undefined

If growth equals or exceeds the discount rate, the payments expand at least as fast as discounting shrinks them, and the series never converges; the value would be infinite or negative. The calculator returns zero in that case, which signals that the inputs do not describe a sustainable stream, not a valuation of nothing.

A growth rate close to or above the discount rate usually means an assumption is unrealistic. No income stream can outpace the market's required return forever, so analysts keep long-run growth below the discount rate, often anchored to expected inflation or the growth of the wider economy.

Common uses

Many preferred shares promise a fixed dividend indefinitely, a level perpetuity. Dividing the annual dividend by the required return gives a fair price: a preferred share paying five a year with a required return of eight percent is worth about sixty-two and a half.

In a discounted cash flow model, analysts project a company's cash flows for a few years and then assume the business settles into steady growth forever. That growing tail is a growing perpetuity, and it often makes up most of the valuation, so the discount and growth assumptions have a large effect on the final figure.

If a fund must pay out a set amount every year without running down its capital, the capital needed to endow it is the present value of a perpetuity. The calculator shows how much is required to support a chosen annual payout at a given expected return.

Choosing your inputs

The discount rate reflects your view of risk and opportunity cost and moves the answer more than the payment does. Try a range of rates to see how sensitive the value is. For a growing stream, keep the growth rate conservative and below the discount rate; aggressive growth assumptions can inflate a valuation until it is no longer useful.

About This Perpetuity Calculator

Use this perpetuity calculator to get an instant estimate based on the figures you enter. Adjust the inputs above to match your situation, or browse all our calculators to plan your next step.