Question

Green Company's common stock is currently selling for $53.04 per share. Last year, the company paid dividends of $1.59 per share. The projected growth at a rate of dividends for this stock is 6.53 percent. Which rate of return does the investor expect to receive on this stock if it is purchased today?

Answer 1

Solution:

Calculation of Rate of return on Green Company’s common stock:

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

P₀ = [ D₀ * ( 1 + g ) ] / ( k_e – g )

Where

P₀ = Current Price of the share;      D₀ = Dividend paid last year ;     

g = growth rate ;    k_e = Rate of return

As per the information given in the question we have ;

D₀ = $ 1.59 ;       g = 6.53 % = 0.0653 ;    P₀ =$ 53.04   ;   k_e = To find   ;

Applying the above values in the formula we have

$ 53.04 = [ 1.59 * ( 1 + 0.0653 ) ] / ( k_e – 0.0653 )

$ 53.04 = ( 1.59 * 1.0653) / ( k_e – 0.0653)

$ 53.04 = $ 1.693827 / ( k_e – 0.0653 )

(k_e – 0.0653) = $ 1.693827 / $ 53.04

(k_e – 0.0653) = 0.031935

k_e = 0.0653 + 0.031935 = 0.097235

k_e = 9.7235 %

k_e = 9.72 % ( when rounded off to three decimal places )

Thus the rate of return the investor expects to receive on this stock if it is purchased today = 9.72 %