# Perpetuity Calculator & Formula

Simply put, perpetuity is a flow of payments which continues indefinitely. Some people also call this a perpetual annuity. Investors can purchase a perpetuity in order to receive this cash flow which would never end. However, the investor never gets back the initial principal amount. A perpetuity provides a fixed payment which means that the payments made in the future would have a reduced present value of a perpetuity the farther away they occur. This also means that eventually, these payments will approach zero. To calculate the perpetuity value, you can use this perpetuity calculator or do it manually by using a perpetuity formula.

## How to use the perpetuity calculator?

This perpetual annuity calculator is a convenient tool for those who want to find out perpetuity value. Follow these steps to use the calculator and get the value you need:

• There are three values you can acquire from this perpetuity calculator. The Present Value, the Annual Interest Rate, and the Payment.
• To get the Present Value, input the payment amount which is a monetary value and the annual interest rate in percentage. In doing this, the calculator will automatically generate the Present Value.
• To get the Annual Interest Rate, input the payment and the present value which are both monetary values. In doing this, the calculator will automatically generate the Annual Interest Rate.
• To get the Payment, input the present value amount which is a monetary value and the annual interest rate in percentage. In doing this, the calculator will automatically generate the Payment.

## How to calculate perpetuity?

In the world of finance, a perpetuity refers to a situation where an investor receives a steady amount of payments continuously. When used in valuation analysis, you can use the perpetuity to find your company’s present value of the projected cash flow in the future as well as the terminal value of your company. You can calculate this value using this growing perpetuity formula:

PV = C / R

Where:

PV refers to the Present value

C refers to the Amount of continuous cash payment

R refers to the Interest yield or rate

## What is the perpetuity formula? When you try to determine the perpetuity formula, there are 3 different formulas to consider. Mainly, you can find out the value of the perpetuity using the Present Value as this will give you the amount of the payments you’ll receive. You can also use the Present Value formula to calculate the Interest Rate and the amount of the regular Payments. You can use this perpetuity calculator to get these values or compute them manually using these formulas:

Present Value = pmt / r

Payment = PV * r

Interest Rate = pmt / PV

where:

PV refers to the Present value of the perpetuity

Pmt refers to the Payment amount

R refers to the Annual interest rate

## How do you calculate effective annual rate?

The Effective Annual Rate or EAR refers to the interest rate that’s adjusted for compounding over a specific period of time. In other words, it’s the interest rate which an investor can either pay or earn in one year after taking compounding into consideration. Some people refer to the EAR as the effective rate, the annual percentage yield, the annual equivalent rate or the effective interest rate. Calculate the EAR using this formula:

EAR = ( 1 + i / n )n – 1

Where:

i refers to the stated annual interest rate

n refers to the number of compounding periods

The EAR is an essential tool which allows you to evaluate the true return on your investment or the true interest rate on your loan. Because of compounding, there can be a significant difference in the effective interest rate and the stated annual interest rate.

You need the effective interest rate to figure out the best possible loan amount or when you need to determine which investment would provide you with the highest return rate. When you consider compounding, the stated annual interest rate would always be significantly lower than the effective annual interest rate.

## What is the formula for terminal value?

There are three main methods for calculating the terminal value, and it usually depends on where it’s used. These methods are:

#### Perpetuity Growth Method

The most preferred method for calculating the terminal value is the perpetual growth method. This is especially preferred by academics because there’s a mathematical theory behind it. With this method, you assume that your company’s growth will continue and your return on capital will be significantly higher than your cost of capital. In other words, this method would assume that your company will keep on generating continuous cash flow for an indefinite time. To calculate the terminal value for this method, use this formula:

TV  =  (FCFn x (1 + g))  /  (WACC – g)

where:

TV refers to the terminal value

FCF refers to the free cash flow

g refers to the perpetual growth rate of FCF

WACC refers to the weighted average cost of capital

#### No Growth Perpetuity Method

This method assumes that you would have a growth rate of zero. It implies that your return on investments would only be as much as your cost of capital. You can use this method when you have very high competition, and your chance to earn more returns may move to zero. Use this formula:

PV = C / R

where:

PV refers to the Present value

C refers to the amount of continuous cash payment

r refers to the Interest yield or rate

#### Exit Multiple Method

This method assumes that the basis for a market multiple is a fair approach to giving a value to a business. In other words, this method assumes that you can assign a value to your business or company based on observed comparable trading multiples for businesses similar to yours.

This method is a lot more common among professionals in the industry. This is because they would like to compare the value of their business to something in the market that’s observable. For this method, you can calculate the terminal value using this formula:

TV  =  Financial metric * trading multiple