Question

PLEASE SHOW THE FORMULAS EMBEDDED INTO EACH CELL SO THAT I CSN MIMICK THE FORMULAS MYSELF

3. (10 pts.) Mathematically show whether the stock price of company A, which features a required rate of return five times the value of it's expected growth rate, is necessarily lower than the stock price of company B, which features a required rate of return three time the value of it's expected growth rate.

Answer 1

Po =   D1
Ke-G

Where,
P0 = . Fair Value of Stock
D1 = Expected Dividend

Ke = Required Rate of return

G = Growth Rate.

Lets take Example :

Company A: required rate of return five times the value of it's expected growth rate :
Expected Dividend = $10 ; Required rate of return = 10% ; Growth Rate = 2%

Now calculate the P0 with above formula = $10
0.10-0.02

P0 = $125

Lets take Example 2.  

Company B : Required rate of return three time the value of it's expected growth rate.
: Expected Dividend = $10 ; Required rate of return = 6% ; Growth Rate = 2%

Now calculate the p0 in same manner only values changed :

So, P0 = $10
0.06-0.02

P0 = $250

In view of the above we can conclude that Higher the Required rate of return lower will be the fair value of stock.
We can find the same in our example where Company A : required rate is higher so, its fair value of Stock price is lower compare to Company B. Because company b have lower required rate of return.