Stock valuation

There are several ways to estimate the price of a stock. One method is called the dividend discount model. The logic is that the price of a stock today is simply the summation of the present value of all its future dividends. Let's use the simplest one period model to illustrate. We expect a $1 dividend at the end of one year and its selling price is expected to be $50. If the appropriate cost of equity is 12%, what is the price of stock today? The timeline and future cash flows are shown here:

The price of stock is simply the present values of those two future cash flows, $45.54:

>> (1+50)/(1+0.12)
>>>
     45.535714285714285
>>> import scipy as sp
>>>sp.pv(0.12,1,1+50)
     -45.53571428571432

Let's look at a two-period model. We expect two dividends of $1.5 and $2 at the end of the next 2 years. In addition, the selling price is expected to be $78. What is the price today?

Assume that for this stock, the appropriate discount rate...