# Perpetuities

A * perpetuity * is an asset that provides a never ending periodic fixed amount of cash flow.

Endowments and trust funds and long lived assets like oil wells or gas fields can be regarded as a perpetuity.

The value of a perpetuity can be calculated as

P = F_{ 1 }/ (1 + i)^{ 1 }+ F_{ 2 }/ (1 + i)^{ 2 }+ F_{ 3 }/ (1 + i)^{ 3 }+ ...... + F_{ n }/ (1 + i)^{ n }

= F / i (1)

where

P = present value

F = F_{ 1 }= F_{ 2 }.. F_{ n }= the fixed amount of cash flow per period

i = discount rate of return (per time period)

### Example - The Value of a Company and Net Income

A company is able to deliver a net income every year of * 100 * . Assuming that this is a perpetuity - a never ending income - the value of this cash flow (and the value of the company) with a discount rate of * 10% (i = 0.10) * can be calculated to

* P = (100) / 0.10 *

* = 1000 *

### Growing Perpetuity

If a cash flow grows in a constant rate the value of the perpetuity can be expressed as

P = F / (i - g) (2)

where

g = growth rate of cash flow (per time period)

### Example - The Value of a Growth Company and Net Income

A growth company is able to deliver a net income first year of * 200 * with a net income growth rate the next years of * 3% (g = 0.03) * . Assuming that this is a perpetuity - a never ending income - the value of this cash flow (and the value of the company) with a discount rate of * 10% (i = 0.10) * can be calculated to

* P = (100) / (0.10 - 0.03) *

* = 1429 *

### Perpetuity Value Calculator

## Related Topics

### • Economics

Engineering economics - cash flow diagrams, present value, discount rates, internal rates of return - IRR, income taxes, inflation.