Question

3. The Johnson Company will pay an annual dividend of $2.05 next year. The company has increased its dividend by 3.5% a year for the past twenty years and expects to continue doing so. What will a share of this stock be worth 4 years from now if the required return is 14%

Answer 1

A share of this stock be worth$ 21.88 four years from now

Step-by-step explanation:

Amount of annual dividend that will be paid the next year = $ 2.05

increase in dividend by 3.5% =
`(100+3.5)/(100)` = increase by a factor of 1.035

Since there is a 14% return, overall increase in dividend =
`(1.035)/(0.14 - 0.035)` = 9.857

Note:

0.035 was obtained from
`(3.5)/(100)`= 0.035 (dividend increase)

0.14 was obtained from
`(1.4)/(100)` = 0.14 (percentage return required)

over the next 20 years his new value of dividend will be

New value of dividend = $2.05 + 9.857 = 11.907

Converting to a percentage,

`(100+11.907)/(100)`= 1.1907

Net dividend increase =

Dividend returns minus increase in dividend for 20 years is given as

14% - 3.5% = 10.5%

From the above, the

Worth of a share of his stock 4 years from now can be computed by

(dividend X Percentage increase in 20 years)/ net percent dividend increase + (increase in 4 years/ net dividend increase) X 100

`((2.05 (1.1907)) )/(10.5)` +
`((2.2729))/(10.5)` × 100 =$21.88

∴ A share of this stock be worth$ 21.88 four years from now