Question

Columbus Manufacturing's stock currently sells for $ 24.32 a share. The stock just paid a dividend of $2 a share (i.e.,D0=2). The dividend is expected to grow at a constant rate of 3 % a year. What is the required rate of return on the company's stock? Express your answer in percentage, and round it to two decimal places, i.e., 13.54, for example for 0.1354)

Answer 1

Solution :

Calculation of required rate of return on the company's 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 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 ;

D₀ = $ 2 ;       g = 3 % = 0.03 ;    k_e = To find   ; P₀ = $ 24.32

Applying the above values in the formula we have

24.32 = [ 2 * ( 1 + 0.03 ) ] / (k_e – 0.03 )

24.32 = ( 2 * 1.03) / (k_e – 0.03)

24.32 = 2.06 / (k_e – 0.03)

(k_e – 0.03) = 2.06 / 24.32

(k_e – 0.03) = 0.084704

k_e = 0.03 + 0.084704 = 0.114704

k_e = 11.4704 %

k_e = 11.47 % ( when rounded off to two decimal places )

The required rate of return of the company’s stock = 11.47 %