Present Value-Growing Perpetuity

The Present Value Growing perpetuity (PVG) is the cash flow after the first period divided by the difference between the discount rate and the growth rate.

• D = Dividend or Coupon at Period1
• r = Discount rate
• g = A constant growth rate

Note: r MUST not be equal to g otherwise you will have a zero and run into infinity.

EXAMPLE

You want to invest in a preferred share of stock in company X that promises to pay you a cash dividend of $25 at the end of the year, which will increase every year by 1%, forever, What would you be willing to pay?   The interest rate is fixed at 4.75%. 

Solution

PV = 25 / (0.0475 - 0.01) = $666.67