Question

The Three Amigos just paid an annual dividend of $.60 per share but plans to double that amount each year for three years. After that, the firm expects to maintain a constant dividend. What is the value of this stock today if the required return is 15 percent?

Answer 1

Answer:

Ans. The value of this stock today is $27.05

Explanation:

Hi, we have to bring to present value all future dividends of the relevant period of time (that is all 3 year dividends), the horizon period (I mean, from year 4 and beyond) we need to use another formula, which we will also bring to present value.

For the first 3 years, the formula is as follows.

$PresentValue=\frac{Dividend}{(1+r)^{n} }$

Where r is the discount rate (in our case, 0.15 or 15%), n is the year where the dividend takes place.

For the horizon value, since there is no growth rate from there, the formula is:

$HorizonValue=\frac{Dividend}{r}$

We have to bring it to present value (this formula provides the value in year 3 of all future dividends from year 4 and beyond), so the complete formula is:

$PV(H)=\frac{Dividend}{r} *\frac{1}{(1+r)^{3} }$

Now, the whole calculation should look like this:

$PresentValue=\frac{1.20}{(1+0.15)^{1} }+\frac{2.40}{(1+0.15)^{2} }+\frac{4.80}{(1+0.15)^{3} }+\frac{4.80}{0.15} *\frac{1}{(1+0.15)^{3} }$

$PresentValue=1.0435+1.8147+3.1561+21.0405=27.05$

So, the value of this stock today if the required return is 15 percent is $27.05

Best of luck