Question

A company currently pays a dividend of $2.8 per share (D0 = $2.8). It is estimated that the company's dividend will grow at a rate of 23% per year for the next 2 years, and then at a constant rate of 7% thereafter. The company's stock has a beta of 1.3, the risk-free rate is 8.5%, and the market risk premium is 4.5%. What is your estimate of the stock's current price? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Intrinsic value: 53.41 dollars

Step-by-step explanation:

First, we use the CAPM model to know the value of the stock

`Ke= r_f + \beta (r_m-r_f)`

risk free 0.085

premium market =(market rate - risk free) = 0.045

beta(non diversifiable risk) 1.3

`Ke= 0.085 + 1.3 (0.045)`

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:

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

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.

`(4.5326484)/(0.1435 - 0.07) = Intrinsic \: Value`

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:

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

`(3.444)/((1 + 0.1435)^(1) ) = PV`

3.011805859

`(4.23612)/((1 + 0.1435)^(2) ) = PV`

3.239633762

`(61.6686857)/((1 + 0.1435)^(2)) = PV`

47.16201531

We add them and get the value of the stock:

53.413455