Question

stock currently sells for $35.25 per share. The dividend is projected to increase at a constant rate of 4.75% per year. The required rate of return on the stock, rs, is 11.50%. What is the stock's expected price 5 years from now?

Answer 1

Answer:

The stock price 5 years from now will be 44.46

Explanation:

The stock price will increase like  compound interest at the same rate as the dividends.

$Stock(1+ g)^{time} = Amount$

Stock 35.25

time 5

dividend grow rate 0.0475

$35.25 (1+ 0.0475)^{5} = Amount$

Amount 44.45588696

The stock price 5 years from now will be 44.46

Reasoning:

In five years, if we calcualte the gordon dividend growth model:

$\frac{divends_{year5}}{return-growth} = Intrinsic \: Value$

and year 5 dividends would be:

$Dividend\: (1+ g)^{5} = Divends_{year5}$

$\frac{Dividend\: (1+ g)^{5}}{return-growth} = Intrinsic \: Value$

we can arrange the formula like this:

$\frac{Dividend}{return-growth} \times (1+ g)^{5}= Intrinsic \: Value$

The first part is the current stock price so our formula is confirmed.

$Market Value Today \times (1+ g)^{5}= Intrinsic \: Value$