Which rate is most appropriate for valuing Prairie Home Stores?  
Explain why. 
I will use the rate of 15% because this was used in the past and seems
to work. Even though the article says different I believe that Prairie
Homes has a better handle on their own direction.


The basic valuation equation is:
					  Value = Div / (r-g).

You?ve already decided what to use for ?r? (either the 11% or 15%
above).  Next, you need to determine what to use for ?g?.  Recall from
the text (page 99) that the formula for a ?sustainable growth rate?
is:
			Sustainable growth rate = plowback ratio X return on equity

The 15% return on equity quoted above is useful for computing the
growth rate of dividends.  But we?ll also need a plowback ratio.  (See
the text?s glossary if you can?t recall what a plowback ratio is.) 
Starting in 2005, in the Constant Growth Scenario, 2/3 of earnings
will be paid out as dividends, and 1/3 will be reinvested.

The plowback ratio is therefore what?
1/3


Therefore, the sustainable growth rate as of 2005 is:

			return on equity ? plowback ratio =  5%              =  

We?ll get to the Rapid Growth Scenario valuation in a moment.  Let?s
do the Constant Growth Scenario valuation first.




Valuation based on past growth scenario 

	The firm has been growing at 5% per year.  Dividends are proportional
to book value and also have grown at 5% annually.  Dividends paid in
the most recent year, 2004, were $7.7 million and they are projected
to be $8 million next year, in 2005.

	The value of the firm is therefore

	Value2005   = Div2005 / (r-g) =  $80,000,000           

The value per share is the value you just computed divided by the
number of shares outstanding (400,000).
The value per share is therefore:
$200 per share
			

Valuation based on rapid growth scenario 

In this scenario shareholders will have to give up dividend payments
until 2009 to achieve this rapid growth.  We can?t really use our
valuation formula without dividends, so we can?t compute a value until
2009 or 2010.  Let?s compute the value in 2010 and then discount that
value back to 2005 to make it comparable to our other scenario
valuation.

	Using the 2010 dividend, the value of the firm in 2010 will be 

	Value2010  =   Div2010 / (r-g)   = 

The value of the firm as of the year 2005 is the present value of this
amount plus the present value of the dividend to be paid in 2009,
which is projected to be $14 million.

	Value2005  = (Value2010  +   Div2009 ) / ( 1+ r)5

	(note that we are discounting the 2010 value back 5 years to 2005)

	After including the 2009 dividend and discounting back to 2005, the
value of the firm in 2010 will be:

	Value2005  =


The value per share is the value you just computed divided by the
number of shares outstanding (400,000).
The value per share is therefore:


Conclusion.
Given your valuation of each scenario, which plan is preferable