Question

mr. li kai is the financial manager of addy caddy inc. the company has just paid a dividend of $1.56 per share on its stock. mr. li kai plan to keep the growth rate of dividends constant at 8 percent per year, indefinitely. what will the price of this stock be in 7 years if investors require a 15 percent rate of return.

Answer 1

Solution:

Calculation of Price of the stock in Year 7 :

As per the dividend growth model, the price of a stock in Year “n” can be calculated using the following formula :

P_n = [ D₀ * ( 1 + g ) ^{( n + 1 )} ] / ( K_e – g )

Where,

P_n = Price of the stock at time ‘ n ‘ ; D₀ = Dividend just paid ; n = no. of years ; K_e = Required Return    ;

g = growth rate ;

As per the information given in the question we have

D₀ = $ 1.56    ;    g = 8 % = 0.08   ; K_e = 15 % = 0.15   ;   n = 7 years ;

Applying the above information in the formula we have

= [ 1.56* ( 1 + 0.08 ) ^{( 7 + 1 )} ] / ( 0.15 – 0.08 )

= [ 1.56* ( 1.08 ) ^{( 8)} ] / ( 0.15 – 0.08 )

= [ 1.56* 1.850930 ] / 0.07

= 2.887451 / 0.07

= 41.249302

= $ 41.25 ( when rounded off to two decimal places )

Thus the price of the stock in Year 7 = $ 41.25

Note : The value of ( 1.08 ) ⁸ has been calculated using the excel function =POWER(Number,Power). Thus =POWER(1.08,8) = 1.850930