Question

A stock with a beta of 0.6 just paid a dividend of $5.60 and is priced at $250.00. If the risk-free rate is 2% and the market risk premium is 6%, what is the expected growth rate for the stock? A. 3.36% OB. 4.46% C. 3.29% D. 2.119

Answer 1

Solution:

Calculation of Required Rate of Return:

As per Capital Asset Pricing Model, required return of a stock is calculated using the following formula:

R_S = R_F + [ β * ( R_M - R_F ) ]

Where

R_S = Required rate of return of stock ; R_F = Risk free rate of return ; β = Beta of the stock ;

( R_M – R_F ) = Market risk Premium

As per the information given in the question we have

β = 0.6    ;    R_F = 2 % = 0.02 ;   ( R_M - R_F ) = Market Risk Premium = 6 % = 0.06 ;

R_S = To find ;  

Applying the above information in the formula we have

= 2 % + [ 0.6 * 6 % ]

= 2% + 3.6 %

= 5.6 %

The required rate of return of the stock = 5.6 %

Calculation of growth rate:

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 = Price of the share;      D₀ = Recent dividend paid ; g = growth rate ;

k_e = Required rate of Return

As per the information given in the question we have ;

D₀ = $ 5.60 ;        k_e = 5.6 % ; P₀ = $ 250

g = To find ; Let growth rate be = x

Applying the above values in the formula we have

250 = [ 5.60 * ( 1 + x ) ] / ( 0.056 – x )

250 * ( 0.056 – x ) = [ 5.60 * ( 1 + x ) ]

14 – 250x = 5.60 + 5.60x

14 – 5.60 = 250x + 5.60x

8.40 = 255.60x

255.60x = 8.40

x = 8.40 / 255.60

x = 0.032864

x = 3.2864 %

x = 3.29 %

Thus the growth rate = 3.29 %

The solution is Option C. 3.29 %