Question

jk stock currently sells for $50 a share. the stock has just paid a dividend of $2 a share. the dividend is expected to grow at a constant rate of 6% per year. what is the stock price that would be expected in one year from now? what is the required rate of return on jks stock?.

Answer 1

Solution :

Calculation of Required rate of return of stock :

As per the Gordon growth Model price of a stock is calculated using the following formula:

P₀ = D₀ * [ ( 1 + g ) ] / ( k_e – g )

Where

P₀ = Current Price of the stock ;      D₀ = Dividend paid in Year 0 i.e., Recent dividend paid ; g = growth rate ;

k_e = Required Rate of return

As per the information given in the question we have ;

P₀ = $ 50 ;   D₀ = $ 2 ;       g = 6 % = 0.06 ;    k_e = To find

Applying the above values in the formula we have

50 = 2 * [ ( 1 + 0.06 ) ] / ( k_e – 0.06)

50 = 2 * [ ( 1.06 ) ] / ( k_e – 0.06)

50 * ( k_e – 0.06) = 2 * 1.06

50 * ( k_e – 0.06) = 2.12

( k_e – 0.06) = 2.12 / 50

( k_e – 0.06) = 0.0424

k_e = 0.06 + 0.0424 = 0.1024

k_e = 10.24 %

Thus the required rate of return on jks stock = 10.24 %

Calculation of the stock price of jks, that would be expected in one year from now :

As per the Gordon growth Model price of a stock, one year hence, is calculated using the following formula:

P₁ =[ D₁ * ( 1 + g ) ] / ( k_e – g )

Where

P₁ = Price of the stock one year from now ;      g = growth rate ;    D₁ = D₀ * ( 1 + g ) ;

k_e = Required Rate of return

As per the information given in the question we have ;

g = 6 % = 0.06 ;    k_e = 10.24 % = 0.1024 ;       

D₀ = $ 2 ;      D₁ = D₀ * ( 1 + g ) = $ 2* ( 1 + 0.06 ) = $ 2.12

P₀ = To find ;  

Applying the above values in the formula we have

= [ 2.12 * ( 1 + 0.06 ) ] / ( 0.1024 – 0.06)

= [ 2.12 * ( 1.06 ) ] / ( 0.1024 – 0.06)

= [ 2.12 * ( 1.06 ) ] / 0.0424

= 2.2472 / 0.0424

= $ 53

Thus the price of jks stock one year from now = $ 53