Learning outcomes. After completing this video you should be able to distinguish between a perpetuity and a growing perpetuity. Calculate the stock price using the Gordon Growth Model. >> Perpetuities and stock valuation. In this video, we will see what perpetuities are and how they relate to stock valuation. We have talked about annuities, which have a fixed number of periodic payments. What if the cash flows occur periodically but never end? You wonder what type of cash flows behave like this. A company pays dividends every year to its shareholders. And is expected to do so forever. You can think of this stream of dividends as a perpetuity. The present value of perpetuity, PVP, is the payment, PMP divided by R. Where PMT is the periodic payment of the perpetuity, and R is the interest rate. The interest rate, R is frequently referred to as a discount rate. And so I'm going to switch to saying discount rate instead of interest rate from now on. Let's look at a simple example. A stock pays a dividend of $2 every year forever. The discount rate is 10% per year. How much must the stock be worth today? The question asks use, what the present value of this perpetuity is. We know PMT is equal to two. And R is equal to 10%. Plugging in the values, the stock price equals two divided by 0.1. Which equal $20. Given the $2 stream of cash flows every year forever and a discount rate of 10%, the stock price should be $20 today. But is it reasonable to assume that a company pays the same dividend every year forever? Companies tend to grow in size over time, and hence are more likely to increase dividends over time. Let's denote the growth rate in payments by g. We now have what is called a growing perpetuity. With the first payment of the growing perpetuity being PMT. The present value of a growing perpetuity is given by PMT divided by R- g. When applied to calculating stock prices, this formula is commonly referred to as the Gordon Growth Model. Let's apply the Gordon Growth Model to an example. A stock pays a dividend of $2 every year forever. And it's expected to increase at 5% a year forever. The discount rate is 10% per year. How much must the stock be worth today? The question asked us what the present value of this growing perpetuity is. We know PMT is equal to two, R is 10%, and g is 5%. Plugging in the values, the stock price equals 2 divided by 0.1- 0.05, which equals $40. Given the $2 stream of dividends every year forever, growing at a rate of 5% a year, again forever, and a discount rate of 10% the stock price should be $40 today. Next time, we will start talking about expected returns and risks, and how to measure that.