What Factors Affect the Present Value of a Perpetuity?

John Lister
John Lister
Man climbing a rope
Man climbing a rope

A perpetuity is a financial asset that will continue paying at an agreed rate forever. It is more of an economic model than a reality. The present value of a perpetuity can be calculated by a simple formula involving the payment to be made each year and a discount rate. The choice of a discount rate is somewhat subjective, meaning that calculating the present value of a perpetuity is not an objective process.

A perpetuity is a type of an annuity, a financial instrument by which one party pays a flat sum and the other party returns a fixed amount each year until the first party dies. When valuing the annuity, most analysts will in reality take account of the person's age, gender and health to work out the expected lifespan and then assume this is how long the payment will last. Viewing the annuity as a perpetuity is more of a mathematical concept that works on the basis that the payments will in fact last for an infinite period. This isn't necessarily a realistic view, but from a mathematical perspective it reflects the uncertainty. There are some genuine perpetuities such as British war bonds that cannot be redeemed for their face value but can be traded, and thus will theoretically continue paying out an annual amount to the current holder forever.

Financial analysts will often attempt to work out the present value of an asset that pays a fixed amount. For example, the analyst may attempt to put a value on a bond that will pay a certain amount for each of the next 10 years. This valuation may take account of the fact that the person must wait for the money, the risk that the payments won't be made as promised, and the return the person could have made by instead putting the money in a risk-free or extremely low-risk investment. Investors and analysts can compare this valuation to the market price of the asset to see if it is a worthwhile investment, on paper at least.

At first glance, it may appear impossible to calculate the present value of a perpetuity because one of the factors involved — the number of years of payment — is infinity. Carrying out a calculation involving infinity does not normally produce a usable result. In practice though, the rate at which the present value increases for each additional year of payment slows down every year and eventually becomes so low as to effectively be worthless.

The calculation of the present value of a perpetuity is thus a simple formula: the amount to be paid each year, divided by a discount rate. The discount rate is a percentage figure that is chosen subjectively. In the context of an annuity, it will normally take account of prevailing interest rates for other investments, along with an adjustment to take into account the risk that the payments won't be made as promised, for example if an annuity provider goes into liquidation. For example, if interest rates are low and the annuity provider is a national government, the discount rate will be lower, meaning the present value of the perpetuity is higher. This is because not only is it very likely the payments will continue as promised, but the payments will appear more rewarding compared to other investments.

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