Perpetuity Calculator

How to use the Perpetuity Calculator

1. 1Enter the payment, the discount rate and the growth rate.
2. 2Pick the units or options from the menus if the perpetuity value tool offers them.
3. 3Read the perpetuity value in the large result box.
4. 4Look at the extra rows for related figures.
5. 5Press Copy result to keep the answer.

When you need the perpetuity value

Finance students use it for preferred shares and the Gordon growth model. Investors use it as a quick way to price endless income, and property buyers use it to value ground rents.

The result is very sensitive to the rate: halving the rate doubles the value. The growth rate must be lower than the discount rate, or the sum would be infinite and the formula does not apply.

How the perpetuity value is worked out

Present value = payment ÷ rate. With growth, present value = first payment ÷ (rate − growth). A perpetuity due is worth (1 + rate) times as much as an ordinary perpetuity. A payment of 1,000 a year at 5% is worth 1,000 ÷ 0.05 = 20,000. If the payment grows at 2% a year, the value is 1,000 ÷ (0.05 − 0.02) = 33,333.33.

Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.

• Growth and due options
• Shows the income yield
• Clear error if growth is too high

Mistakes to avoid with perpetuity value

Use the rate for the same period as the payment: a monthly payment needs a monthly rate. And do not use a growth rate above the discount rate, since the formula then gives meaningless negative values.

On phone and computer

On a phone, type into the boxes one after another and read the perpetuity value underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the perpetuity value move. The perpetuity calculator works the same on both.

Checking your perpetuity value by hand

A good habit is to test the perpetuity calculator with a case you already know. A payment of 1,000 a year at 5% is worth 1,000 ÷ 0.05 = 20,000. If the payment grows at 2% a year, the value is 1,000 ÷ (0.05 − 0.02) = 33,333.33.

If your own figures give a surprising answer, repeat the working yourself: Present value = payment ÷ rate. With growth, present value = first payment ÷ (rate − growth). A perpetuity due is worth (1 + rate) times as much as an ordinary perpetuity. Small differences usually come from rounding, from mixing units, or from a typing slip in one of the inputs. A perpetuity depends on a discount rate, so see how it fits other value tools. Use the Present Value and NPV Calculator for sums that end, the Compound Interest Calculator to see growth, and the WACC Calculator to pick a rate for a company.

Features

• Rate and payment periods must match
• Growth must stay below the rate
• Value is very sensitive to the rate
• Clear messages when the perpetuity value inputs make no sense
• Copy the result with one tap
• Private: nothing is uploaded

Frequently asked questions