Python for Finance

Chapter 5
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 is 14%. Then the present
value of the stock is $62.87:
>>>1.5/(1+0.14)+(2+78)/(1+0.14)**2
62.873191751308084
Along the same lines, we could estimate the cost of equity if both the present value
and futures values are given. If the current price is $30 and the expected selling price
at the end of one year is $35:
[ 171 ]