Different Asset Classes in which Pension Funds can Invest
Pension funds have a very large amount of money at their disposal. However, that does not mean that the management of these funds can deploy this money as per their will. Pension funds are highly regulated and the asset classes in which they can invest in are limited. Over the years, the limitations have been […]
History of the Forex Market: The Gold Standard
The word “money” has not always meant what it means today. Today when we use the word “money” we refer to “currency”. Both, money as well as currency used to mean very different things until about a couple of centuries ago. Prior to the monetary system that we have today, the world was on a […]
Dividend Discount Model: Share Repurchase Programs
In corporate finance we studied that companies had an option when it came to compensating their equity shareholders. They could both pay these shareholders cash dividends from the earnings of the current year or alternatively they could conduct a share repurchase program and buy back some shares from the same proceeds. The monetary effect would […]
The Bias Blind Spot
We are now aware of the fact that investment markets are not driven by mathematical decisions alone. They are heavily influenced by the emotional quotient of investors. In fact, a large number of successful investors attribute their success to their ability to manage their emotions. This is done by understanding the different types of behavioral […]
Longevity Risk and Pension Funds
Advances in medical science have increased the life span of individuals. It is now common for people to live for ten to twenty years longer than their previous generation. This seems like a good development from a humanist point of view. However, from a pension fund’s point of view, a longer life span has several […]
We have seen that a perpetuity represents an infinite stream of future cash flows. However, we have also seen that as time passes the value of these cash flows constantly diminishes. $100 may be able to buy us quite a few goods today, but in 50 years time $100 will not be nearly as valuable as it is today. It is for this reason that receiving infinite payments is not enough. The payments must also keep growing at a certain rate. This will ensure that they are not considerable behind inflation. This is the idea behind a growing perpetuity. The same has been explained in detail in this article:
As already stated, a growing perpetuity involves payments that do not remain fixed. Instead these payments keep on growing at the same constant rate of growth. So, if the rate of growth of the payments is 7%, each payment will be 7% more than the payment received before it.
The present value of a growing perpetuity can be derived from a complex mathematical calculation. This is because a growing perpetuity is also an infinite series which has a finite sum. For our purposes, we can just remember the formula required for our calculation.
Present Value (Growing Perpetuity) = D / (R - G)
Where:
D = Expected cash flow in period 1
R = Expected rate of return
G = Rate of growth of perpetuity payments
However, we need to understand that for this formula to hold true, G must always be greater than R. If G is less than R or equal to R, the formula does not hold true. This is because, the stream of payments will cease to be an infinitely decreasing series of numbers that have a finite sum.
Examples:
Growing perpetuities are found in a variety of places in our daily lives. Some of them have been mentioned below:
The growing perpetuity, thus assumes that we will lose a small amount of the real value of money every year. Just like the perpetuity, a growing perpetuity can only be summed up because the series is infinitely decreasing. The growing perpetuity assumes that we will lose the real value of money at a slower rate as compared to an ordinary perpetuity.
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