Jefferson's recently paid an annual dividend of $6 per share. The dividend is expected to decrease by 3% each year. How much should you pay for this stock today if your required return is 14% (in $ dollars)? $_ 

Solution :

The current value of a stock can be calculated using the following formula:

P₀ = [ D₀ * ( 1 + g ) ] / ( r – g )

Where

P₀ = Current value of the stock ;   D₀ = Recent annual dividend paid ; g = growth rate of dividend ;

k_e = Required return   ;

As per the information given in the question we have ;

D₀ = $ 6 ;       g = - 3 % = - 0.03 ;    r = 14 % = 0.14    ;

Applying the above values in the formula we have the value of the stock today as

= [ $ 6 * ( 1 - 0.03 ) ] / ( 0.14 - ( - 0.03 ) )

= ( $ 6 * 0.97 ) / 0.17

= $ 5.82 / 0.17

= $ 34.235294 per share

Thus the amount that should be paid for the stock today

= $ 34.24 per share ( when rounded off to two decimal places )

= $ 34 ( when rounded off to the nearest dollar )