Question

The market price of a stock is $21.98 and it is expected to pay a dividend of $1.59 next year. The required rate of return is 11.86%. What is the expected growth rate of the dividend?

Answer format: Percentage Round to: 2 decimal places (Example: 9.24%, % sign required. Will accept decimal format rounded to 4 decimal places (ex: 0.0924))

Answer 1

Solution :

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

P = D₁ / ( K_e – g )

Where,

P= Price of the stock   ;   D₁ = Next year dividend payment

K_e = Required rate of return    ;   g = Expected growth rate

As per the information given in the question we have

P = $ 21.98     ;   D₁ = $ 1.59    ;    K_e = 11.86 % = 0.1186   ; g = to find

Applying the above values in the formula we have

21.98 = 1.59 / ( 0.1186 – g )

21.98 * (0.1186 – g ) = 1.59

( 0.1186 – g ) = 1.59 / 21.98

0.1186 – g = 0.072338                              

0.1186 - 0.072338 = g

g = 0.1186 - 0.072338

g = 0.046262

g = 4.6262 % ( when rounded off to four decimal places )

g = 4.63 % ( when rounded off to two decimal places )

Thus the expected growth rate of the dividend = 4.63 %