Growing Perpetuity Calculator

Formula

The formula to calculate the present value of a growing perpetuity is:

\[ \text{PV} = \frac{\text{D}}{\text{r} - \text{g}} \]

Where:

$\text{PV}$ is the present value of the growing perpetuity
$\text{D}$ is the amount of the first payment
$\text{r}$ is the discount rate
$\text{g}$ is the growth rate

What is a Growing Perpetuity?

A growing perpetuity is a series of periodic payments that grow at a proportionate rate and continue indefinitely. It is a type of perpetuity, which is an infinite series of payments. The concept is often used in finance to determine the present value of a company’s cash flows, dividends, or other financial metrics that are expected to grow at a constant rate over an indefinite period. The formula for calculating the present value of a growing perpetuity takes into account the initial payment, the growth rate, and the discount rate.

Example Calculation 1

Let's assume the following values:

Amount of First Payment (D) = $100
Discount Rate (r) = 0.08
Growth Rate (g) = 0.03

Using the formula:

\[ \text{PV} = \frac{100}{0.08 - 0.03} = \frac{100}{0.05} = 2000 \]

The Present Value of the Growing Perpetuity is $2000.

Example Calculation 2

Let's assume the following values:

Amount of First Payment (D) = $150
Discount Rate (r) = 0.10
Growth Rate (g) = 0.04

Using the formula:

\[ \text{PV} = \frac{150}{0.10 - 0.04} = \frac{150}{0.06} = 2500 \]

The Present Value of the Growing Perpetuity is $2500.