Answer:
the intrinsic value of the stock is 42.97
If the stock is priced at 40 dollars it would be a good idea to purchase the share as will provide a better yield than the cost of capital of 9.6%
Explanation:
First, we solve for the cost of equity using the CAPM:
[tex]Ke= r_f + \beta (r_m-r_f)[/tex]
risk free = 0.03
market rate = 0.09
premium market = (market rate - risk free) = 0.055
beta(non diversifiable risk) = 1.2
[tex]Ke= 0.03 + 1.2 (0.055)[/tex]
Ke = 0.09600
Now we solve for the intrinsic price using the gordon model
with multi-stage growth:
First, we calcualte the future dividends
grow rate Dividends
0 1.25
1 0.25 1.5625
2 0.25 1.953125
3 0.25 2.44140625
4 0.25 3.051757813
4 0.03 3.143310547
Now in the last year, we calcualte using the gordon model or constant grow:
[tex]\frac{3.143310547}{0.096-0.03} = Intrinsic \: Value[/tex]
32.7128182
Now we calculate and add together the present value of each of this future cash flow to determnate the intrinsic value ofthe share:
[tex]\frac{Principal}{(1 + rate)^{time} } = PV[/tex]
Present Value
1 1.5625 / (1+0.096)^1 = 1.425638686
2 1.953125 / (1+0.096)^2 = 1.625956531
and so on, giving the following values:
3 1.854421226
4 2.114987712
present value of the future dividends at 3% 22.67126448
Finally we add them and get:
42.97160726
