Answer:
Intrinsic value: 53.41 dollars
Explanation:
First, we use the CAPM model to know the value of the stock
[tex]Ke= r_f + \beta (r_m-r_f)[/tex] Â
risk free 0.085
premium market =(market rate - risk free) = 0.045
beta(non diversifiable risk) 1.3
[tex]Ke= 0.085 + 1.3 (0.045)[/tex] Â
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:
[tex]\frac{divends}{return-growth} = Intrinsic \: Value[/tex]
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.
[tex]\frac{4.5326484}{0.1435 - 0.07} = Intrinsic \: Value[/tex]
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:
[tex]\frac{Principal}{(1 + rate)^{time} } = PV[/tex]
[tex]\frac{3.444}{(1 + 0.1435)^{1} } = PV[/tex]
3.011805859
[tex]\frac{4.23612}{(1 + 0.1435)^{2} } = PV[/tex]
3.239633762
[tex]\frac{61.6686857}{(1 + 0.1435)^{2}} = PV[/tex]
47.16201531
We add them and get the value of the stock:
53.413455
