Any help including web sites, formulas, etc. to aid in solving
question is welcomed.

Mr. Smith decided to trade his company's shares in the public market
but is worried about what he should sell his shares for.  Based on the
following investment information and growth and a 15% rate of return,
advise Mr. Smith on what he should sell his company's shares for in
the two different scenarios:

								
								
								
			2000	2001	2002	2003	2004	
Book value start of year$62.70 	$66.10 	69	73.9	76.5	
Earnings		$9.70 	9.5	11.8	11	11.2	
Dividends		$6.30 	6.6	6.9	7.4	7.7	
Retained earnings	$3.40 	2.9	4.9	2.6	3.5	
Book value end of year	$66.10 	69	73.9	76.5	80	


			RAPID GROWTH SCENARIO					
			   2005	 2006	2007	2008	2009	2010
Book value strat of year    80    92	105.8	121.7	139.9	146.9
Earnings		    12	13.8	15.9	18.3	21	22
Dividends		     0	 0	0	0	14	14.7
Retained earnings	    12	13.8	15.9	18.3	7	7.4
Book value end of year	    92	105.8	121.7	140	146.9	154.3


			CONSTANT GROWTH SCENARIO					
			2005	2006	2007	2008	2009	2010
Book value start of year 80	84	88.2	92.6	97.2	102.1
Earnings		 12	12.6	13.2	13.9	14.6	15.3
Dividends		 8	8.4	8.8	9.3	9.7	10.2
Retained earnings	 4	4.2	4.4	4.6	4.9	5.1
Book value end of year	 84	88.2	92.6	97.2	102.1	107.2

Hi boobee,

A share's value is equal to the discounted stream of free cash flow
per share, not to the discounted stream of each future earnings per
share.  (Principles of Corporate Finance, fourth edition, Brealey and
Myers, McGraw-Hill, 1991, page 60)

Using a discounted cash flow approach, I came up with a price of
$62.86 for the rapid growth scenario and a price of $62.81 for the
constant growth scenario.  Let me explain my assumptions.  I assumed
that the shares would be sold in 1999, so that investors would receive
dividends from 2000 until 2010 in both scenarios (the company's
financial results begin to diverge starting with 2005).  I also
assumed that the long-term dividend growth rate of the company in both
scenarios after 2009 would be 5%.  I obtained this by dividing the
year 2010 dividend by the year 2009 dividend for the rapid growth
scenario and by examining the growth rate in the dividend over the
period 2005 through 2010 for the constant growth scenario.

Since no information was provided regarding industry price-to-earnings
ratios or price-to-book ratios, I adopted a discounted cash flow model
with the following structure for the calculation:

Present Value (business) = Present Value (free cash flow) + Present
Value (horizon value) where

Present Value (free cash flow) = Sigma (t=1 to 10) DIV(t)/(1+r)^t and

Present Value (horizon value) = 1/(1+r)^ 10[DIV(11)/(r-g)].

t is the time period  (2000 = 1, 2010 = 11).

r is the rate of return (0.15).

g is the long-term dividend growth rate (0.05).

DIV(t) is the dividend in time period t.  The dividends are the same
as free cash flow per share since they are the cash that is not
reinvested in the business.

The Present Value (horizon value) can be calculated using other
methods involving a price-to-earnings ratio or a price-to-book ratio. 
In the absence of this information, a constant growth formula is the
only alternative.  The purpose for calculating the present value
(horizon value) is to assign a valuation to the future cash flows
beyond 2010.

Note that the valuations are almost identical.  While the rapid growth
scenario pays a higher dividend in the constant growth scenario, the
fact that it is significantly further out in the future and requires
four years of no dividends to achieve offsets its higher value. 
Furthermore, the rapid growth scenario does not appear to lead to
higher long-term dividend growth rate than the constant growth
scenario.  If it did, then the company would be valued more highly in
that scenario.

I hope you find the above helpful.  Please feel free to keep the
finance questions coming.

Wonko

---

Clarification of Answer by wonko-ga on 28 Jun 2003 23:12 PDT

Thank you for your rating.  I wanted to add another possible method
for calculating g since the data to do so was included in your
problem.  The dividend growth rate, g, can be calculated by
multiplying the plowback ratio by the return on equity.  The plowback
ratio = 1-DIV(t)/EPS(t).  The ROE = EPS(t)/starting book value per
share(t).  Calculating g using this method over the last couple of
years in the time series for both scenarios still yields a result of
approximately 5% for g for both.

Wonko

Thanks -- and expect to hear from me regularly over the next two weeks.