Perpetuity

What is Perpetuity?

A perpetuity is an investment which regularly pays a certain amount of money indefinitely, sometimes referred to as a perpetual annuity. There are very few of these actually in existence as annuities are far more common. Despite the fact that the cash is paid forever, it is still possible to create a net present value of the money because each payment is only a fraction of the previous payment (due to the time value of money calculation), i.e. payments a long way into the future are worth close to zero in present value. The formula for calculating the present value of a perpetuity is as follows:

  • PV = C / R

Where C is the value of each payment and r is the discount rate. r is calculated by taking the current risk-free rate such as US Treasuries, savings accounts etc. and dividing by the interest rate paid on the perpetuity. Assume the following characteristics:

  • Perpetuity with a face value of $100 is purchased
  • The perpetuity pays a $4 periodic payment which is a yield of 4%
  • US Treasuries are currently yielding 2%
  • The discount rate on the perpetuity is 2% / 4% = 0.5
  • Therefore each dollar you have is worth 2x as much in a perpetuity than in a Treasury bond, making the value of the perpetuity $200

Perpetuities are actually used in financial theory to estimate a present value of a dividend paying company and this is called the dividend discount model. The idea is that a company now is worth the sum of all its future dividend payments and for this you need to know the current value of the dividend as well as the dividend growth rate (both of these are usually set out by management in the annual reports).

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