Question

City Movers announced that its next annual dividend will be $.40 a share. The following dividends will be $.60, and $.75 a share annually for the following two years, respectively. After that, dividends are projected to increase by 3.5 percent per year. How much is one share of this stock worth at a rate of return of 12 percent

Answer 1

Answer:

value today $5.32

Explanation:

For the first three years, we will calculate the present value using the expected rate of return

$\frac{Dividends}{(1 + rate)^{time} } = PV$

where:

rate = 0.12

Year 1

$\frac{0.40}{(1 + .012)^{1} } = PV$

Year 2

$\frac{0.60}{(1 + .012)^{2} } = PV$

Year 3

$\frac{0.75}{(1 + .012)^{3} } = PV$

Then, on Year 4 we apply the gordon model

$\frac{divends}{return-growth} = Intrinsic \: Value$

dividend = 0.75

return 12%

growth 3.5%

$\frac{0.75}{0.12-0.035} = Intrinsic \: Value$

Then we calculate the present value of this because it is 4 years into the future

$\frac{Gordon's \: Valuation}{(1 + .012)^{4} } = PV$

Finally, we add them all to get the value of the stock today

$\left[\begin{array}{ccc}Year&Cash \: Flow&PV\\1&0.4&0.36\\2&0.6&0.48\\3&0.75&0.53\\4&0.75&3.95\\Total&&5.32\\\end{array}\right]$