Question

Woidtke Manufacturing's stock currently sells for $26 a share. The stock just paid a dividend of $2.75 a share (i.e., D0 = $2.75), and the dividend is expected to grow forever at a constant rate of 9% a year. What stock price is expected 1 year from now? Round your answer to the nearest cent. What is the estimated required rate of return on Woidtke's stock? Do not round intermediate calculations. Round the answer to three decimal places. (Assume the market is in equilibrium with the required return equal to the expected return.)

Answer 1

Solution :

Calculation of estimated required rate of return on Woidtke'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 = $ 2.75 ;       g = 9 % = 0.09 ;    P₀ =$ 26 ; k_e = To find   ;

Applying the above values in the formula we have

$ 26 = [ 2.75 * ( 1 + 0.09 ) ] / (k_e – 0.09 )

$ 26 = (2.75 * 1.09) / (k_e – 0.09)

$ 26 = $ 2.9975 / (k_e – 0.09)

(k_e – 0.09) = $ 2.9975 / $ 26

(k_e – 0.09) = 0.115288

k_e = 0.09 + 0.115288 = 0.205288

k_e = 20.5288 %

k_e = 20.529 % ( when rounded off to three decimal places )

The estimated required rate of return on Woidtke's stock = 20.529 %

Calculation of Expected price of stock one year from now:

The Expected price of a share one year from now is calculated using the following formula:

P₁ = D₁ * [ ( 1 + g ) ] / ( k_e – g )

Where

P₁ = Price of the share one year from now;      D₁ = Expected Dividend of Year 1     ; g = growth rate ;

k_e = Required rate of return

As per the information given in the question we have ;

g = 9 % = 0.09 ;    k_e = 20.529 %    ;

D₁ = D₀ * ( 1 + g) = $ 2.75 * ( 1 + 0.09) = $ 2.9975 ;       

P₁ = To find

Applying the above values in the formula we have

= [ 2.9975 * ( 1 + 0.09 ) ] / ( 0.20529 – 0.09)

= ( 2.9975 * 1.09 ) / ( 0.20529 – 0.09 )

= 3.267275 / 0.11529

= 28.3396

= 28.34 ( when rounded off to the nearest cent )

The Expected price of stock one year from now = $ 28.34