Generally, perpetuity means continuity forever, without maturity, for life. In Estate Management terminology, freehold means an estate forever, for life. That is a person having a freehold interest in a property is having an estate lasting him forever. It is forever because it can be inherited by the heirs of his body at his death or to anybody he may deem fit to receive it through his will that must have been made during his lifetime.
A life estate is an unencumbered one, that there is no obstacle or barrier to the constant and continuous enjoyment of the estate. It is owned in perpetuity. It does not revert back to any superior lessor or grantor in any form. It is however pertinent to understand for a particular term of years but they are viewed as freehold. For example, an old man of eighty years being granted a lease of fifty years on a plot of land may be said to hold it in perpetuity. Already the man ought to have died were it not for his strength. Definitely he cannot see the end of the given interest in land. But the fact that the estate was registered in his name and held his name even after death while being enjoyed by the heirs of his body, it can be formally said to be an estate in perpetuity to the old man. However the same estate created for a boy of say fifteen years, may be looked upon as a mere leasehold owing to the fact that the adolescent may grow to see the determination of the estate. Ross, Westerfield and Jaffe (1999) pointed to us another dimension of perpetuity. In their book, they defined perpetuity as a constant stream of cash flows without end. To prove the reality of perpetuities they forwarded the case of an unending cash flow stream: the British bonds called Consol. According to them, an investor purchasing a Consol is entitled to receive yearly interest from the British government forever.
How can the price of a consol be determined? They consider a consol that pays a coupon of C dollars each year and will do so forever. Simply applying the present value (PV) formula given us:
PV = c + c + c + ……..
i+r (i+r) 2 (i+r) 3
The dots at the end of the formula stand for the infinite string of terms that continues that formula. The present value of the consol is the present value of all its futures coupons. In other words, it is the amount of money that an investor has today would enable him to achieve the same pattern of expenditures that the consol and its coupon would.
Reference
Ross, A.S; Westerfield, R.W; Jaffe, J. (1991). Corporate finance. USA: Irion McGraw-Hill.
