Answer:
Intrinsic value: 53.41 dollars
Explanation:
First, we use the CAPM model to know the value of the stock
risk free 0.085
premium market =(market rate - risk free) = 0.045
beta(non diversifiable risk) 1.3
Ke 0.14350
Now we need to know the present value of the future dividends:
D0 = 2.8
D1 = D0 x (1+g) = 2.8 * 1.23 = 3.444
D2 3.444 x 1.23 = 4.2361200
The next dividends, which are at perpetuity will we solve using the dividned grow model:
![\frac{divends}{return-growth} = Intrinsic \: Value](https://tex.z-dn.net/?f=%5Cfrac%7Bdivends%7D%7Breturn-growth%7D%20%3D%20Intrinsic%20%5C%3A%20Value)
In this case dividends will be:
4.23612 x 1.07 = 4.5326484
return will be how return given by CAPM and g = 7%
plug this into the Dividend grow model.
![\frac{4.5326484}{0.1435 - 0.07} = Intrinsic \: Value](https://tex.z-dn.net/?f=%5Cfrac%7B4.5326484%7D%7B0.1435%20-%200.07%7D%20%3D%20Intrinsic%20%5C%3A%20Value)
value of the dividends at perpetity: 61.6686857
FInally is important to note this values are calculate in their current year. We must bring them to present day using the present value of a lump sum:
![\frac{Principal}{(1 + rate)^{time} } = PV](https://tex.z-dn.net/?f=%5Cfrac%7BPrincipal%7D%7B%281%20%2B%20rate%29%5E%7Btime%7D%20%7D%20%3D%20PV)
![\frac{3.444}{(1 + 0.1435)^{1} } = PV](https://tex.z-dn.net/?f=%5Cfrac%7B3.444%7D%7B%281%20%2B%200.1435%29%5E%7B1%7D%20%7D%20%3D%20PV)
3.011805859
![\frac{4.23612}{(1 + 0.1435)^{2} } = PV](https://tex.z-dn.net/?f=%5Cfrac%7B4.23612%7D%7B%281%20%2B%200.1435%29%5E%7B2%7D%20%7D%20%3D%20PV)
3.239633762
![\frac{61.6686857}{(1 + 0.1435)^{2}} = PV](https://tex.z-dn.net/?f=%5Cfrac%7B61.6686857%7D%7B%281%20%2B%200.1435%29%5E%7B2%7D%7D%20%3D%20PV)
47.16201531
We add them and get the value of the stock:
53.413455