Question

Business Solutions is expected to pay its first annual dividend of $.84 per share in Year 3. Starting in Year 6, the company plans to increase the dividend by 2 percent per year. What is the value of this stock today, Year 0, at a required return of 14.4 percent?

Answer 1

Answer:

Ans. the value of the stock today is $6.31

Explanation:

Hi, we need to bring to present value all the cash flows of this stock, that is bringing to present value the cash flows from year 1 through 6 and the horizon value which is the value in year 6 of the cash flows from 6 and beyond.

The formula to use for the dividends from year 1 - 6 is:

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

Where:

r = is the discount rate

n = number of consecutive dividends

And the present value of the horizon value is:

$PV(Horizon)=\frac{Dividend*(1+g)}{(r-g)} *\frac{1}{(1+r)^{n} }$

So everything together is:

$Price=\frac{Dividend((1+r)^{n}-1) }{r(1+r)^{n} }+\frac{Dividend*(1+g)}{(r-g)} *\frac{1}{(1+r)^{n} }$

Now, the numbers

$Price=\frac{0.84((1+0.144)^{6}-1) }{0.144(1+0.144)^{6} }+\frac{0.84*(1+0.02)}{(0.144-0.02)} *\frac{1}{(1+0.144)^{6} }=3.23+3.08=6.31$

So based on the future cash flows of this share, its fair price is $6.31

Best of luck.