By Sunil K. Parameswaran
A level annuity is a series of identical money flow payments created at equally spaced intervals of time. There are quite a few such examples in genuine life. Salaries and rent till they are revised. Interest on fixed deposits and coupon payments from fixed price bonds. Instalments paid on loans such as housing loans, automobile loans, educational loans and individual loans are also examples of annuities.
Annuity payout
An N period annuity tends to make its initially payment right after one period, and its final payment right after N periods. On the other hand, an N period annuity due will make the initially payment straight away, that is, at time zero, and its final payment right after
N-1 periods. Examples of annuity dues consist of premiums on life and common insurance coverage policies. As you will be conscious, if an insurance coverage policy is taken, the initially year’s premium is payable upfront and not right after one year. There are also expanding annuities, exactly where the payments improve at a price that is generally assumed to be continual, year right after year.
The present worth of an annuity due is equal to that of an identical annuity, multiplied by a element of (1+r), considering the fact that each and every money flow is discounted for one period much less. If the future worth of an N period annuity and an identical N period annuity due are computed at time N, the latter will have a future worth that is higher by a element of (1+r) considering the fact that each and every money flow is compounded for one period additional. Thus, the future worth of an annuity due at N-1, will be equal to that of the annuity at time N.
Future worth
A perpetuity is an annuity that pays forever. This sounds like a wonderful deal, but money flows beyond a point contribute insignificantly to the worth of such a money flow stream. If a perpetuity promises to spend Rs 10,000 per year, and the investor desires a price of return of 8% per annum, he will spend 10,000/.08 = 1,25,000, in spite of the reality that the payments will in no way cease.
The future worth of a perpetuity of course can not be computed considering the fact that the payments will in no way quit. The present worth of a perpetuity due is the present worth of the perpetuity plus the initial money flow at time zero. In this case it will be 1,25,000 + 10,000 = 1,35,000.
Coupon paying bonds have a connected statistic named the duration, which captures their interest price sensitivity. For plain vanilla bonds the duration is also a measure of the productive time to maturity of the money flows. Duration can be computed for each annuities and perpetuities. Despite the reality that the money flow stream is endless, the duration of a perpetuity is (1+r)/r, exactly where r is the periodic interest price.
The duration of a perpetuity due is 1/r, which is reduced than that of the corresponding perpetuity. The explanation is that whilst the initially money flow of a perpetuity due is received straight away, and therefore the weight corresponding to its initially money flow is multiplied by zero whilst computing the typical time to maturity, it will have a larger price tag than the corresponding perpetuity due to the added money flow at the outset. Consequently, the weights attached to each and every money flow are reduced than in the case of an equivalent perpetuity, and therefore the duration is reduced.
The writer is CEO, Tarheel Consultancy Services