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

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Request for Question Clarification by omnivorous-ga on 19 Sep 2005 17:06 PDT

Jaemarie --

We can't tell from the information provided: you have no idea what the
market rate-of-return is.  We also have no idea how it grows in years
1-4.

Best regards,

Omnivorous-GA

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Clarification of Question by jaemarie-ga on 19 Sep 2005 20:16 PDT

Company Z,s earnings and dividends per share are expected to grow
indefinitely by 5% per year.  If next year's dividend is $10 and the
market capitalization rate is 8 percent, what is the current stock
price?  Company Z-prime is like Z in all aspects 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.  Hope this clarifies the question.

Jaemarie ?

Here are the important assumptions about Z-Prime:

?	Year 1 dividend = $10
?	Year 2 dividend = $10.50
?	Year 3 dividend = $11.025
?	Year 4 dividend = $11.576
?	Year 5 and onwards: $17.36

Ks or discount rate = 8%

This provides the following discount factors for NPV:

Year1: 1/1.08 = .9259
Year2:  1/(1.08)^2 = .8573
Year3:  1/(1.08)^3 = .7938
Year4   1/(1.08)^4 = .7350
Year5:  1/(1.08)^5 = .6806

So it become easy to track NPV of the cash flows for years 1-4 by
multiplying each by their NPV factor:

Year1: $9.26
Year2: $9.00
Year3: $8.75
Year4: $8.51

But what?s the value of the never-ending series of dividend payments
from year 5 to eternity?


CONSTANT GROWTH MODEL
==========================

Also called the Dividend Valuation Model, this allows an investor to
calculate a value based on returns to the investor.   Here, the 
dividends represent cash flows ? something that?s not always true in
the real world.

The general model for stock pricing is below.  We?ll use period 5
(year 5) but you can use i as year one or any other starting point if
you?re an analyst trying to figure out how to value a company --

Pi = Di / (Ks - g)

Pi = price in period i
Di = dividends in period i
Ks = required rate of return (in decimals)
g = dividend growth rate (in decimals)
i = period, usually expressed in years 

So the value at the end of year 5 is:

P = $17.36 / (0.08 ? 0.05) = $17.36 / 0.03 = $578.67

However, that?s the value in year 5 ? not today.  We have to discount
it back to year 0 (that?s how ?today? is often described in financial
problems ? so it?s:

$578.67 * Year5 NPV factor = $393.84

TOTAL VALUE OF Z-PRIME = $9.26 + $9.00 + $8.75 + $8.51 + $393.84 = $429.36



Google search strategy:
?constant growth model? dividends


Best regards,

Omnivorous-GA

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Clarification of Answer by omnivorous-ga on 19 Sep 2005 22:04 PDT

Jaemarie --

I no sooner than finished the calculations when I realized that I'd
over-estimated the Year5 onwards.  There's no growth in the firm,
which substantially reduces the value of the now-constant dividends. 
Here's how the Constant Growth Model should evaluate it:

The value at the end of year 5 is:

P = $17.36 / (0.08 ? 0.00) = $17.36 / 0.08 = $217.00

However, that?s the value in year 5 ? not today.  We have to discount
it back to year 0 (that?s how ?today? is often described in financial
problems ? so it?s:

$217 * Year5 NPV factor = $147.69

TOTAL VALUE OF Z-PRIME = $9.26 + $9.00 + $8.75 + $8.51 + $147.69 = $183.21


My apologies for the confusion.

Best regards,

Omnivorous-GA

As I was looking at the answers, how did you calculated Z-Prime's 5
year onward dividend to be at $17.36?

I also could not figure out the $17.36

How could you use the EPS of $15 to find this answer?  
Or is there somehow a simpler way to calculate the NPV of yrs 1-4 as a
growth stock and then add that to the NPV of Yr 5 as a
dividend/nongrowth stock for the price?