Question

A stock is expected to pay a dividend of $0.75 at the end of the year. The required rate of return is r_s = 10.5%, and the expected constant growth rate is g = 3.5%. What is the stock's current price?

Select the correct answer.

a. $13.61

b. $10.71

c. $15.06

d. $12.16

e. $16.51

Answer 1

Solution:

As per the Gordon growth model the current price of a stock can be calculated using the following formula :

P₀ = D₁ / (rs – g )

Where,

P₀ = Current Price of the stock

D₁ = Dividend payment at the end of the year

rs = required rate of return

g = Expected constant growth rate

As per the information given in the question we have

D₁ = $ 0.75 ;    g = 3.5 % = 0.035   ; rs = 10.5 % = 0.105

P₀ = To find

Applying the above information in the formula we have

= 0.75 / ( 0.105 – 0.035 )

= 0.75 / 0.07

= 10.7143

= $ 10.71 ( when rounded off to two decimal places )

Thus the stock’s current price = $ 10.71

The solution is option b. $ 10.71