No. of Recommendations: 3

Thanks for all of the great responses and discussion. Some of the
posts arrived at the same valuation that I have in mind, but we also
saw some considerable variation.
My answer is that all three companies have a per share value of $10.
While I described the three cases as shares in a company, they actually
represent putting $10 in a deposit account earning interest at 10% per
annum. If we use a discount rate of 10%, it is obvious that the value
of each is $10.
Company A represents the situation where interest is automatically
added to the principal.
Company B represents the situation where half of the interest is paid
out and the other half is added to the principal.
Company C represents the situation where all of the interest is paid out.
I think that DCF analysis theory is good, but I think the danger is
deciding what represents a cash flow. In the cases of B and C, where
people used dividends as cash flow, the correct answer was arrived at.
If we restrict cash flows to dividend payouts, how do we value company A.
*there is no price that is too high to pay for certain and unlimited
growth at the rate which you require. no matter how much you overpay,
on the long journey to eternity, the compounding will eventually
overwhelm your entrance price. try modeling the NPV of each cash flow,
and you'll see.
present value of $1 received in year 1? $1!
present value of $1.10 received in year 2? $1!
present value of $1.21 received in year 3? $1!
so you see the series diverges.
of course, it is a very bad idea to model risk-free growth for eternity
at rates above the risk-free (or risk-indifferent) rate. but if you
give me such a model, that's the only conclusion to reach.
in practice, what's usually done is to break the model into a two- or
three-part DCF valuation. the first period is high growth (above the
discount rate); in subsequent periods growth drops below the discount rate.
it's rare to see such a model that doesn't smack of false precision.*
The discussion above shows that if we use earnings as a measure of cash
flow, we get an incorrect answer (infinite value). The reason for this
is that we are valuing the retained earnings more than once - i.e.
valuing them when earned, but also valuing them based on the future
additional earnings generated by retaining the same earnings.
So...
What is the real return to the owner. It is a combination of Dividend
plus Growth. In the three simple examples, we can see that the Growth
part is the direct result of the retained earnings (interest). In our
simple examples, we can see that the return on our $10 investment =
dividend yield + growth rate in all cases.
I would propose then that we need to value dividends and retained
earnings separately. Valuing dividends is easy as they are "real".
Probably compare yield with something like the 10 year Aa Corporate
bond yield to get a valuation or perhaps compare with Aa Corporate bond
yield + 5% to get a bargain valuation.
For example. Current 10 year Aa Corporate bond yield is in the region of 4.5%
Lets say we have a Dividend per share of 0.50 per annum.
Then the full value of the dividend stream would be 0.50/0.045 = $11.11
The Bargain value of the dividend stream would be 0.50/(0.045 + 0.050) = $5.26
For the retained earnings part, we need to think like Warren
Buffet, "Do I get at least $1 of value for each $1 of retained
earnings?"
What do managements typically do with retained earnings? Some possible answers:
1. Invest in the company to increase profits.
2. Buy back shares to increase earnings on a per share basis
3. Reduce debt and interest expense.
I'm sure you could add to this list, and there are many arguments to be
made to say whether the decisions of management in relation to my money
that they have chosen to retain are good decisions or bad decisions,
but it really comes down to this.
"If retained earnings do not result in an increased EPS, they have
probably been wasted or stolen by management and will never benefit me."
Perhaps an example will help at this point. Lets look at Reliance
Steel & Aluminum. I will take the data provided at the link below at
face value. It should be split adjusted already.
http://moneycentral.msn.com/investor/invsub/results/statemnt.asp?Symbol=rs&lstStatement=10YearSummary
So what has been the real return to a buy and hold shareholder over the
last nine years. The EPS has not increased (it is about the same at
the end of the period as at the beginning) so 1 share now does not have
a greater value than 1 split adjusted share 9 years earlier (based on
earnings power) so the only real return to shareholders has been the
dividend stream. Over that nine year period, the dividend stream has
totalled $1.46, however the reported earnings per share over the same
period totalled $13.01. It would appear then that the $11.55 retained
earnings per share are worthless to the shareholder so I would suggest
that this company should be valued only based on its dividend stream.
Take another example (Thomas Industries):
http://moneycentral.msn.com/investor/invsub/results/statemnt.asp?Symbol=tii&lstStatement=10YearSummary
As summary of the results are:
Year EPS Div Ret EPS
2003 2.12 0.37 1.75
2002 2 0.33 1.67
2001 1.8 0.34 1.46
2000 1.91 0.3 1.61
1999 1.62 0.3 1.32
1998 1.5 0.3 1.2
1997 1.38 0.275 1.105
1996 1.09 0.267 0.823
1995 0.83 0.267 0.563
Lets compare 2002 with 1996. For each of these years, we will use the
average earnings centered on the year in question - i.e. Use average
EPS 2001 to 2003 for the 2002 number.
Earnings power (per share) in 2002 = $1.97
Earnings power (per share) in 1996 = $1.10
Over the 6 year period, EPS has increase by $0.87
Over the 6 years, 1996 through 2001, the total retained earnings per
share is $7.52.
It would appear then that this company has been able to generate an
11.6% return (0.87/7.52) on retained earnings so I would suggest that
these retained earnings are real unlike the situation with Reliance
Steel & Aluminum.
So what value do we put on the retained earnings.
A simple rule would be to use a multiplier equal to the rate of return
up to a maximum of 20 for a purchase price.
This is loosely based on the following logic.
10 year Aa Corporate bond yields typically vary between about 3.5 and
6.5. On a bargain basis, if we require a 5% premium, we would want a
yield of between 8.5% and 11.5%. This give us a multiplier of between
8.7 and 11.8. To simplify, we could go with a middle value of
requiring a 10% yield and a multiplier of 10. If retained earnings
produce a return above or below 10, we would factor the multiplier up
or down accordingly.
Using this logic, based on data up to the end of 2003, we might use a
3 year average for the earnings power of TII. This would give an
earnings power of $1.97. We could break this down into:
Dividend = $0.38. Bargain Value = 0.38/0.095 = $4
Retained = $1.59. Bargain Value = 1.59 * 11.6 = 18.44
Total bargain value = $4 + 18.44 = $22.44
If this method were used for the valuation of Comapnies A, B and C
requiring a yield of 10% (discount rate) and a miltiplier of 10, we
would calculate a value of $10 for each company.
I believe this approach provides a simple way to address the following concerns:
1. Owners Earnings versus reported earnings
2. Paying appropriately for growth and the return on invested capital
3. Dilution of value through stock option grants and poor aquisitions, etc
I believe a balance sheet analysis would still be needed to ensure the
liquidity and safety of the stock.
Comments please.
StevnFool