Answer:
value today $5.32
Explanation:
For the first three years, we will calculate the present value using the expected rate of return
[tex]\frac{Dividends}{(1 + rate)^{time} } = PV[/tex]
where:
rate = 0.12
Year 1
[tex]\frac{0.40}{(1 + .012)^{1} } = PV[/tex]
Year 2
[tex]\frac{0.60}{(1 + .012)^{2} } = PV[/tex]
Year 3
[tex]\frac{0.75}{(1 + .012)^{3} } = PV[/tex]
Then, on Year 4 we apply the gordon model
[tex]\frac{divends}{return-growth} = Intrinsic \: Value[/tex]
dividend = 0.75
return 12%
growth 3.5%
[tex]\frac{0.75}{0.12-0.035} = Intrinsic \: Value[/tex]
Then we calculate the present value of this because it is 4 years into the future
[tex]\frac{Gordon's \: Valuation}{(1 + .012)^{4} } = PV[/tex]
Finally, we add them all to get the value of the stock today
[tex]\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][/tex]
