Company Z-prime is like Z in all respects save one: Its growth will
stop after year 4. In year 5 and afterward, it will pay out all
earnings as dividends. What is Z-prime?s stock price? Assume next
year?s EPS is $15.

Hi there,

I believe your question pertains to the Dividend Discount Model, which
can be easily found if you Google it.

The Value of a Stock = DPS1 / ( r - g)

where DPS1 = Expected Dividends one year from now

r = Required rate of return
  = Risk-free rate + (Market risk premium) * Beta

The rate on t-bills can be used to determine the risk-free rate. The
market risk premium is the expected return of the market in excess of
the risk-free rate. Beta can be thought of as the sensitivity of the
stock compared with the market.

g = Annual Growth rate in dividends forever

So since company growth = 0, dividend growth = 0, g = 0

Your question seems to be lacking some details. Like, which year are
we at now? Year 0, I presume. What's the company's earnings growth
rate? What's the discount rate? Only then can we find out what the EPS
will be when they stop growing and start giving out dividends (that
will be at the end of Year 5).

What you then do is calculate the expected EPS at the end of Year 5.
And since all earnings are distributed as dividends, that will be your
"DPS1". You then calculate "r", the required rate of return. Divide
DPS1 by r and you've got an figure.

But of course, that would be the value of the stock at the end of Year
4, so you will have to discount that figure using the discount rate,
for 4 years, in order to find the present value of the stock. And
THAT, my friend, should be the theoretical price of the stock.

Hello again, I'm sorry I read your question again and realized that I
worked only on the assumption that the company distributed the
earnings it made from year 5 onwards.

If, and only if, the company also distributes the retained earnings
from Years 1 through 4, then you will have do some simple arithmetic
to account for the value of the extra dividend.

Just add up all the EPS for Years 1 through 4 (making sure you account
for earnings growth in the period), then to find their present value,
discount that figure for 5 years using your discount rate. Why 5
years? Because all those retained earnings will only be given out 5
years from now.

Best of luck in your studies.
Cheerio!