Perpetuities and Growth Perpetuities

Perpetuities are annuity payments that never end. There are two types of perpetuities, which are normal perpetuities or consols and growth perpetuities.

What is a perpetuity?

A perpetuity is an annuity payment that never ends.  In other words, the darn thing keeps paying out forever.  However, the payout never changes either.

What is formula for a perpetuity?

The Formula for a perpetuity is dividend one divided by rate.

Dividend or payment / Rate

Sample Problem for a Perpetuity:

Your great great grandmother is retiring at the end of this year. She would like to ensure that her son receive annual payments of $10,000 a year forever and ever, starting when she retires next year. If she can earn 8.0 percent annually, how much does your grandmother need to invest to create the desired payments to her son?

PV = 10,000 / .08

PV = 125,000

What is a growing perpetuity?

A growing perpetuity is an annuity payment that never ends either.  Except the damn thing keeps growing and growing and growing… at the designated growth rate.

What is formula for a growing perpetuity?

The formula for a growing perpetuity is dividend 1 or the next dividend paid divided by the difference between the expected return and expected growth rate.

Present Value of Perpetuity = Dividend 1 / (Rate – Growth)

Sample growing perpetuity problem:

A person is evaluating a growing perpetuity investment option from a large financial services firm in the US.  The investment guarantees an initial payment of $10,000 at the end of this year and following payments that will increase at a rate of 5 percent annually.  If you use a 10 percent discount rate for investments such as this, what is the present value of the growing perpetuity?

PV = 11,000 / (.1 – .05)

PV = 11,000 / .05

PV =220,000

About Finance Homework Help…

Finance Homework Help is supplied by Paul Borosky, Doctoral Candidate, MBA. and owner of Tutor4FinanceFinance Homework Help, TutorWithPaul and Quality Business Plan.  Our driving reason for this information is that finance is tough.  Without proper assistance good people will struggle with the class through no fault of their own.  From this, please enjoy the information and hopefully you will find it beneficial.  Don’t forget, if you need more help, just contact us!!

Call or Text Paul Now!

321-948-9588

Email: Paulb@Tutor4Finance.com

Help is available 7 days a week! From 7AM to Midnight EST.

Need help with a finance assignment? Contact us below!