Present Value Constant Growth Perpetual Annuity

This Present Value Perpetual Annuity Due equation computes the amount of money accumulated if you invest a number of periodic payments and continue this investment indefinitely.  This equation calculates the same series of periodic payments as the present value of the perpetual ordinary annuity except that the payments start immediately at the beginning of the initial period.

APPLICATIONS

Real estate and preferred stock are investments that results in values represented by the perpetuity and prices for the real estate or preferred stock can be established using this equation.

INPUTS

The inputs are as follows:

• A - the cash flow amount each period, the periodic payment, which starts t the beginning of the first period
• r - the interest rate entered as a percentage; in other words you enter 4.9 for a 4.9% interest rate

NOTES

To receiving money now is generally worth more than receiving the same amount in the future, primarily because you can invest it now at a compounding rate. for example, to receive $12,000 today is worth more than receiving $1,000 each month for a year.  You can invest the $12,000 today at the same interest rate as you might invest each $1000 as the payments are received and the $12,000 today would earn more interest.  So, receiving $12,000 today is worth more at the end of the year than receiving 12 payments of $1000 across the year. 

This equation then tells you how much money today is equal to the money earned at a specified interest rate if it were received in monthly payments for perpetuity.  This is the same as the present value of the perpetual ordinary annuity except it includes one more payment.

EXAMPLE

If the interest rate for a stock (shares) were estimated to be 11%, then the value of the perpetual annuity due per dollar of investment would be $10.09.  This would be the assumed dividend income per dollar of investment.