Question

Why can't the future value of a perpetual stream of cash flows be found?

Answer 1

A perpetual stream of cash flow continues indefinitely in future and has no end. In order to compute future value of any cash flow we should know the end date of the cash flow so that it can be incorporated in the appropriate formula. But in case of a perpetual stream of cash flow we do not know the end date and so computing the future value is not possible.

I can explain the above theory numerically also. Consider an annual cash flow of $1,000 will occur for next 10 years and the appropriate rate is 5%. Thus future value of this cash flow = 1,000* [(1+r)^n – 1/r]

= 1,000*[((1.05^10) – 1)/0.05]

= 1,000*12.57789

= $12,577.89

But suppose that the cash flow of $1,000 continues forever and not for 10 years. In this case the value of “n” (i.e. number of years) cannot be determined. In the formula provided above we can see that “n” is one of the variables on the basis of which future value is computed. In the absence of a value of “n” it will not be possible to compute future value.