Week 7 Perpetuities

Week 7: Lecture

Perpetuities

A perpetuity is an annuity in which the stream of payments goes on forever. Perpetuities have present values just like regular annuities, but you can’t use the regular PV formula to calculate the PV of a perpetuity because n in the formula would be infinity.

The situation is not as tough as it appears, however. Consider the following example:

How much would you pay for $1,200 a year forever? Long term interest rates are 11%. (Recognize that this is a PV of an annuity problem.)

The formula to calculate the present value of a perpetuity is:

tvm_present_value_perpetuity_formula.jpg

 

Let’s use this formula to calculate the PV of $1,200 a year:

tvm_present_value_perpetuity_1200_a_year.jpg

 

So the PV of getting $1,200 a year forever, if your required rate of return is 11%, is $10,909.10. This means that if you invested $10,909.10 in an account paying 11% interest, you could withdraw $1,200 at the end of each year forever and the account would never run dry.