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

value today $5.32

Step-by-step explanation:

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

`(Dividends)/((1 + rate)^(time) ) = PV`

where:

rate = 0.12

Year 1

`(0.40)/((1 + .012)^(1) ) = PV`

Year 2

`(0.60)/((1 + .012)^(2) ) = PV`

Year 3

`(0.75)/((1 + .012)^(3) ) = PV`

Then, on Year 4 we apply the gordon model

`(divends)/(return-growth) = Intrinsic \: Value`

dividend = 0.75

return 12%

growth 3.5%

`(0.75)/(0.12-0.035) = Intrinsic \: Value`

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

`(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]`