Question

Jia's Fashions recently paid a $2.34 annual dividend. The company is projecting that its dividends will grow by 20 percent next year, 12 percent annually for the two years after that, and then at 6 percent annually thereafter. Based on this information, how much should Jia's Fashions common stock sell for today if her required return is 10.5%?

Select one:

a. $60.80

b. $54.90

c. $69.22

d. $59.16

Answer 1

Solution :

The current price of a share of a company is calculated as follows :

The Current price of a share = Present value of dividends + Present value of share at year ‘ n ‘

Thus the current price of the share with respect to the details given in the question is calculated using the formula

= [ D₁ * ( 1 / ( 1 + r)¹ ) ] + [ D₂ * ( 1 / ( 1 + r)² ) ] + [ D₃ * ( 1 / ( 1 + r)³) ] +   [ P₃ * ( 1 / ( 1 + r)³ ) ]

Calculation of Dividend per share Years 1 to 3 :

As per the information given in the question we have

D₀ = $ 2.34 ; g₁ = 20 %   ; g₂ = 12 %   ; g₃ = 12 % ;

Thus the Dividend per year can be calculated as follows :

D₁ = D₀ * ( 1 + g₁ ) = $ 2.34 * ( 1 + 0.20 ) = $ 2.34 * 1.20 = $ 2.808000

D₂ = D₁ * ( 1 + g₂ ) = $ 2.808000 * ( 1 + 0.12 ) = $ 2.808000 * 1.12= $ 3.144960

D₃ = D₂ * ( 1 + g₃ ) = $ 3.144960 * ( 1 + 0.12 ) = $ 3.144960 * 1.12 = $ 3.522355

Thus we have D₁ = $ 2.808000 ; D₂ = $3.144960   ; D₃ = $ 3.522355    ;

Calculation of price of share at year 3:

Price of the share at year 3 where the firm expects a constant growth rate of 6 %

The formula for calculating the price of the share at year 3

P₃ = [ D₃ * ( 1 + g ) ] / ( K_e – g )

We know that

D₃ = $ 3.522355 ; g = 6 % = 0.06   ; K_e = 10.5 % = 0.105 ;

P₃ = [ $ 3.522355 * ( 1 + 0.06 ) ] / ( 0.105 - 0.06 )

= ( $ 3.522355 * 1.06 ) / ( 0.105 - 0.06 )

= ( $ 3.522355 * 1.06 ) / 0.045

= $ 3.733697 / 0.045

= $ 82.971034

Thus the price of the share at year 3 = $ 82.971034

Calculation of price of share today :

Thus the current price of the share = [ D₁ * ( 1 / ( 1 + r) ) ] + [ D₂ * ( 1 / ( 1 + r)² ) ] + [ D₃ * ( 1 / ( 1 + r)³) ] + [ P₃* ( 1 / ( 1 + r)³ ) ]

Applying the available information in the formula we have the price of the share as follows :

= [ $ 2.808000 * ( 1 / 1.105 ) ¹] + [ $ 3.144960 * ( 1 / 1.105 )² ] + [ $ 3.522355 * ( 1 / 1.105 )³ ] + [ 82.971034 * ( 1 / 1.105 )³ ]

= [ $ 2.808000 * 0.904977 ] + [ $ 3.144960 * 0.818984 ] + [ $ 3.522355 * 0.741162 ] + [ $ 82.971034 * 0.741162 ]

= $ 2.541175 + $ 2.575672 + $ 2.610636 + $ 61.494985

= $ 69.222468

= $ 69.22 ( when rounded off to two decimal places )

Thus Jia's Fashions common stock sells today for $ 69.22 , if the required rate of return is 10.5 %

The solution is option c. $ 69.22