**PV of perpetuity = D ÷ r**

PV = present value

D = Dividend or coupon per period

r = discount rate

Perpetuity is a sort of annuity that gets an infinite number of periodic defrayments. An annuity is a money instrument which pays occasional payments consistently. Similarly, perpetuity equation also takes in to account the present value of future payments as it is the case with any annuity.

Typically, perpetuity formula is utilized for ROI calculation in preferred stocks. Preferred stocks typically get their profits before any dividends paid to regular stocks. Moreover, the earnings are typically fixed future cash flow can be determined by utilizing the perpetuity formula.

The estimation of perpetuity may change after some time despite the fact that the payment remains same as before. This happens as the discount rate utilized for calculation may change. On the off chances that lower the discounted rate utilized at the denominator of the equation the higher will the final value.

It ought to be noticed that the equation above assumes that the payments per period never show signs of change.

### Perpetuity value formula illustration

Mr. Kyne is offered a stock which pays a value of $80 per year and will show perpetuity (continue for infinite period of time). Let’s assume a discount rate of 4% so with above formula we can calculate PV of perpetuity as following

PV of perpetuity = $80 ÷ 0.04

PV of perpetuity = $2,000

So, after calculation of given scenario we can say that this perpetuity will receive $2,000 in revenue.

#### Alternative to PV of Perpetuity formula

Basically, perpetuity formula is derived from present value of future cash flows formula and it is a simplified version. Present value of perpetuity expression can also be presented as;

**PV of perpetuity = ^{∞}∑_{n=1} [D ÷ (1 + r)^{n }]**

The above equation of showing this equation is;

PV of perpetuity = [D ÷ (1 + r) ] + [D ÷ (1 + r)^{2} ] + … + [D ÷ (1 + r)^{n} ]

This above equation can be simplified further to give the formula available at the top of the page.