What Is the Present Value of a Perpetuity Formula and What Are Perpetuities?

First of all, what is the ordinary meaning of "perpetuity?" It simply means "forever." So in finance, what do we mean by this same concept? Well, imagine I gave you a piece of paper or certificate, and that paper promised that I would pay you a fixed amount every year, forever. That piece of paper is called a "perpetuity." Simple! How is it different from, say, a promissory note? It isn't. We can say it's a special type of promissory note which lasts forever, with regular payments every year (or every month or other time period).

Now the question is... if I tried to sell you this piece of paper, how much would you be willing to pay for it? If I said... buy this piece of paper for only $100, and I'll give you $2 for the rest of your life, forever. Would you buy it? It sounds like a great deal, doesn't it? After all, you just pay once, and then you'll get money from me forever!

But think about it another way too... Let's say the bank's interest is 5% per year. If you put the same $100 in the bank and left it there forever, how much would you get every year, forever? You'll get $5 per year! ($5 is 5% of $100). Much more than the $2 per year you would get from me if you buy my piece of paper above for $100! So, are you still willing to pay me $100 to get $2 per year forever? Or, would you rather use the same $100 to deposit in the bank, and get a much higher $5 per year instead?

Of course, you'll prefer to put your money in the bank! However, you might still be willing to buy my piece of paper or perpetuity if I lower the price. How much should I lower it to make it worth your money? $80? $60? $40? Naturally, we can't simply use our feelings to guess the right price. So how do we find the exact amount? For this, we use the Present Value of a Perpetuity Formula. With this, you will find that the "fair value" in this case is $40. The simplest formula, which assumes consistent annual cash flows, looks like this:

Present Value of a Perpetuity = (Yearly Cashflow)/(bank interest rate per year)

*Fair value = $40 means that if you pay any more than that, you're getting a sour deal... you'll be in a better situation putting your money in the bank.

What is the logic behind this "fair value"? We go back to the IRR concept. At the fair value of $40, the IRR of our perpetuity is exactly the same as the interest rate of your bank deposit. Meaning: $40 earning $2/year will have an IRR of 5%. A bank deposit of $100 earning $5 per year will also have an IRR of 5%; thus making the returns the same or "fair."

David Michael is the creator of MBAbullshit.com, a fun and free online tutorial website for lots of MBA courses and business school topics. Go to http://mbabullshit.com/blog/2011/12/17/present-value-of-a-perpetuity-formula-in-6-minutes-2 for a super easy quick video on Present Value of a Perpetuity Formula in 6 Minutes

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Selling Structured Settlement Payments: Part 2 - Understanding the Present Value of Future Payments

As called for in a structured settlement, individuals are designated to receive future payments. The payments are issued via an annuity purchased from a large, relatively safe insurance company. Recipients of structured settlement payments sometimes decide that there is an important need to receive settlement funds before the scheduled payment dates. This can be done pursuant to an assignment process that is regulated by the law. At some point in that process, the seller must agree to a price.

What then is a reasonable price for money scheduled to be paid in the future? How does the "market" determine that price? An informed seller can feel protected if they understand two things: 1) The method used to determine the Present Value of a future payment, and 2) The absolute need to confirm that the competitive marketplace has played a role in determining that Present Value.

The Present Value is based on a mathematical discounting process taking into account the amount of time between now and when future money is due. A payment is therefore "discounted" from its future full value back to its Present Value using a discount rate plus the passage of time. A financial calculator, easily found online, will determine the Present Value of any future dollar amount. The calculation requires input of the future value (the amount(s) scheduled to be paid under the settlement), the date that you are scheduled to receive the payment(s) being sold, and the discount rate (interest rate) being charged. Anyone with a mortgage payment, or a car payment, already understands the concept (whether they know it or not). The Present Value of a series of car payments was the price paid for the car (minus any down payment). It is a given that the total of the car payments is more than the amount financed, due to an interest charge. In the same way, the future settlement/annuity payments will be more than a seller receives today due to the discount/interest charge used by the purchaser to create the Present Value. The Present Value is the price received for the future payments.

It is very important for the seller to make sure that the market, made up of all interested purchasers, provide the lowest possible interest charge. Competition takes care of that, as it does for the sale of anything. Summary: Sellers of structured settlement payments can feel comfortable that the sales process is regulated by the law, but the individual seller is fully responsible for forcing the market to work in his or her favor.

Shannon Harvey writes for Annuity Transfers a buyer of structured settlement payments. If you are looking to sell your structured annuity payments visit Annuity Transfers.

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Selling Structured Settlement Payments: Part 3 - Finding Value in the Legal Process

Structured settlement payments are received from an annuity that was created as part of a legal compromise. A plaintiff, having filed a lawsuit, and a defendant, responding to the claim, ultimately agree to settle the case and avoid further litigation. The settlement releases the defendant from future liability, and the release is exchanged for monetary compensation. An annuity is purchased from an insurance company and payments are made to the plaintiff, who is thereafter referred to as the "payee". Structured settlement payees, originally satisfied with the terms of the settlement, sometimes decide that waiting for future annuity payments is not in their best interest. The payee makes a decision to sell the rights to receive future payments. In legal terms, a structured settlement payee decides to "transfer" future payments at a contractually agreed upon price. In order to do so effectively, sellers must understand what is required legally when selling structured settlement payments and how the legal framework for selling payments actually protects them.

Forty-seven states have specific laws that regulate the sale of structured settlement payment rights. The laws vary slightly from state to state, but all require that a court approve the transaction. The relevant state law requires that a particular court and a particular judge determine that the reason for selling, and the terms of the sale, collectively represent the best interests of the seller.

Sellers should realize exactly what that means to the process and the deal. A seller of structured settlement payments should always request nothing less than what the market will bear. The seller may remind the purchaser that the better the terms of the deal, the more likely the judge is to approve the deal. This does not mean that these types of "transfers" exist outside the bounds of normal supply and demand. All purchasers are restricted by the underlying transaction costs, and the risk inherent in purchasing a future payment. It is understood that a purchaser pays for something today, but must wait until some future date to receive payment. Unlike the purchase of a car or a house, this transaction is scrutinized by a third-party, and is not approved in court unless it represents a real "win-win" situation. Purchasers cannot assume that courts will approve all structured settlement transactions, just as sellers should not assume that all offers to purchase payments are constrained by the legal process.

No one involved in the structured settlement transfer process should assume anything. Sellers use the requirement for court approval to their advantage, while accepting the reality that no sale is possible without a fair price. The market would not exist and will not exist in the future unless the purchaser is willing to take on some level of risk — but all risk comes at some cost.

Shannon Harvey writes for Annuity Transfers a buyer of structured settlement payments. If you are looking to sell your structured annuity payments visit Annuity Transfers.

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