Present Value of Perpetuity Calculator

Introduction

A perpetuity is a stream of equal cash flows that never end, with the first cash flow occurring one period from now and not immediately. You can determine the value of such a series of infinite future cash flow using our Present Value of Perpetuity Calculator.

This payment type is called payment in arrears and is this standard practice in all loan payment calculations.

Present Value (PV) is the current value of future cash flows or stream of cash flows. These cash flows are discounted at an appropriate discount rate reflecting the investment’s expected return and risk profile.

How to use Present Value of Perpetuity Calculator?

Using the Present Value of Perpetuity Calculator, you can calculate the present value, discount rate, and cash flow value by inputting the other variables required for the calculation.

The variables in the Present Value of Perpetuity Calculator are:

Discount Rate
The rate at which the cash flows should be discounted. This could be interest rates or an appropriate rate reflecting the investment’s expected return and risk profile.

Cash Flow
The cash flow received in perpetuity.

Present Value of the Perpetuity
The perpetuity’s value at the current point in time.

What is Present Value?

The present value refers to discounting future cash flows using an appropriate rate of return reflecting the return and risk profile of the investments or cash flows to obtain its value in today’s terms.

Determining the appropriate discount rates to discount the cash flows is key to determining the value of the asset or investment.

One of the core principles in finance is that a sum of money is worth more now than the same sum of money at a future date due to its earning potential. This is called the Time Value of Money.

There are two primary reasons that support this theory:

1. Opportunity cost of capital: This is the investment opportunities that the investors forgo by choosing a particular course of action. The capital that the investor has could be invested into other projects and could possibly earn a higher return over time.

2. Inflation: The effects of inflation are also another risk to consider which actually erode the return on investment and thereby future cash flows lose their value.

Investors and financial planners need to find the present value of investments to understand the equivalence of cash flows at different dates or points in time. This will help them make their investment decisions accordingly.

How is the Present Value of Perpetuity Calculated?

The present value of a Perpetuity is calculated using the following formula.

Present Value Formula

Where,

PV → Present Value of Perpetuity
It is the value of the entire stream of cash flows.

r → Discount rate in % Per Annum
The rate at which the cash flows should be discounted. This could be interest rates or an appropriate rate reflecting the investment’s expected return and risk profile.

C → Cash flow received every period
The cash flow that is received in perpetuity every period.

Example

Let’s say an investor wants to earn $10,000 every year from now on forever by investing some amount. He knows that the investments will return about 8% per annum. What will be the amount that he will have to invest to get $10,000 in perpetuity?

So, if the investor invests $125,000 now, he will be able to earn $10,000 every year in perpetuity. Given that his investments earn 8% in perpetuity.

How is the Cash Flow in Perpetuity Calculated?

The cash flow in perpetuity can also be thought of as the return that the investment generates in that period. For example, if you deposit an amount P in a bank account that provides an interest rate of r per annum. Then every year we can withdraw the interest that the amount P earns. And in this case, the amount P remains untouched in the bank account.

The interest earned by amount P is given by the following formula