Question

Explain why the equation for PV of a perpetuity is so simple as = C/Rate, if is a constant stream of CF that lasts forever?

Answer 1

Perpetuity is a perpetual annuity, it is a series of equal infinite cash flows that occur at the end of each period and there is equal interval of time between the cash flows. Present value of a perpetuity equals the periodic cash flow divided by the interest rate.

Let’s say a government wants to set up an endowment that will off $1 million each year in scholarship for ever. This constitutes a perpetuity because the payment is fixed, there is equal duration between each payment, i.e. one year and there are infinite number of payments.

Let’s follow the endowment example above. Let the endowment value be PV, the annual scholarship withdrawals be PMT and i being the periodic interest rate. If we want the endowment to finance scholarships each year perpetually, the interest earned on PV in one year must equal PMT. This can be expressed mathematically as follows:

PMT = PV × i

Rearranging the above equation, we get the formula to find present value of a perpetuity:

PV of Perpetuity is equal to PMT divided by i.