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Author: StevnFool Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 1933  
Subject: DCF Analysis Date: 12/7/2004 12:46 PM
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Hi,

I know some people here use DCF analysis. I tend to be wary of the DCF analysis. I have three hypothetical companies for which I have valuations. I would like people to value 1 share of each company using their variation of DCF analysis. What I am looking for is intrinsic value, not bargain value or anything else. I want you to take all the numbers at face value - i.e. no need to adjust real earnings to owners earnings or anything. In a few days, I will advise what I believe 1 share of each company is worth and I will provide my rationale.

In all cases, please use a 10% discount rate for calculation.

In year 1, all three companies are expected to earn $1 per share.

Company A pays no dividend, but each year EPS will increase by 10% - i.e. Year 2 EPS will be $1.10. Year 3 EPS will be $1.21. It is expected that this rate of EPS growth will continue forever.

Company B pays out 50% of its earnings as a dividend, but each year EPS will increase by 5% - i.e. Year 2 EPS will be $1.05. Year 3 EPS will be $1.1025. It is expected that this rate of EPS growth and dividend payout ratio will continue forever.

Company C pays out all of its earnings as a dividend, but it is expected that its EPS and dividend will remain at $1 forever.

Lets see your valuations.

StevnFool
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Author: madmarv Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1779 of 1933
Subject: Re: DCF Analysis Date: 12/8/2004 1:58 AM
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A: The IV cannot be calculated because the discount rate is equal to the growth rate.
B: $20
C: $10

The above is calculated from the Gordon Growth Model using EPS as free cash flow.

Marv

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Author: trepanne Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1780 of 1933
Subject: Re: DCF Analysis Date: 12/8/2004 2:26 AM
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i concur with madmarv's valuations, noting the following assumptions:
1) "EPS" is fully-loaded FCF... i.e. companies A&B doesn't need to invest anything for expansion beyond what they've expensed in each perid, so their retained earnings are just piling up as hard cash in the bank. this is likely to be a poor assumption; great potential for double counting that plagues many naive DCF models.
2) the valuation is performed by a control buyer who can direct the allocation of corporate capital, so that the distinction between earnings & dividends aren't meaningful.

to be more conservative, from a passive investor's point of view, we could redo the valuation using the dividend discount model P0 = D1 / [r - g]:

a) NMF
b) $0.50/ (10% - 5%) = $10
c) $0.50/ 10% = $5

this method needs the following assumptions:
1) distribution of dividends won't decrease the growth rate, i.e., again, "EPS" is fully loaded. note, however, that valuing only distributions avoids any problems of double-counting.
2) liquidation value of company assets is zero

don't need to do DCF models to value securities, but it's helpful to develop the tools. all investment is a time-value-of-money game; you might as well try to improve your facility with applied compounding if it's not going to cause you to fall into grossly imprudent valuations. this lets you expand your range.

from the horse's mouth:

Indeed, the formula for valuing all assets that are purchased for financial gain has been unchanged since it was first laid out by a very smart man in about 600 B.C. (though he wasn’t smart enough to know it was 600 B.C.).

The oracle was Aesop and his enduring, though somewhat incomplete, investment insight was "a bird in the hand is worth two in the bush." To flesh out this principle, you must answer only three questions. How certain are you that there are indeed birds in the bush? When will they emerge and how many will there be? What is the risk-free interest rate (which we consider to be the yield on long-term U.S. bonds)? If you can answer these three questions, you will know the maximum value of the bush - and the maximum number of the birds you now possess that should be offered for it. And, of course, don’t literally think birds. Think dollars.

Aesop’s investment axiom, thus expanded and converted into dollars, is immutable. It applies to outlays for farms, oil royalties, bonds, stocks, lottery tickets, and manufacturing plants. And neither the advent of the steam engine, the harnessing of electricity nor the creation of the automobile changed the formula one iota - nor will the Internet. Just insert the correct numbers, and you can rank the attractiveness of all possible uses of capital throughout the universe.

Common yardsticks such as dividend yield, the ratio of price to earnings or to book value, and even growth rates have nothing to do with valuation except to the extent they provide clues to the amount and timing of cash flows into and from the business.


http://www.berkshirehathaway.com/2000ar/2000letter.html

trp

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Author: jkm929 Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1781 of 1933
Subject: Re: DCF Analysis Date: 12/8/2004 12:03 PM
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Company B: .50/(.10 - .05) = .50/.05 = 10

Company C: 1.00/.10 = 10

Company A: 10, because no dividend and earnings growing forever at 10% is the equivalent of a dividend paying stock that yields 10% forever with no change in the dividend forever and no growth in earnings forever.

jkm929

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Author: yoda83 One star, 50 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1783 of 1933
Subject: Re: DCF Analysis Date: 12/8/2004 1:34 PM
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Company A: n/a (see marv's comment)


Company B: Po = D1/(R-g)

= $0.50*(1.05)^1/(.10-.05)

Po = $10.40 - $10.60, depending on how you round the dividend.


Company C: Po = D/R

= $1.00/.10

Po = $10.00


If you you use the $1.00 EPS instead of just dividends paid,

Company A: n/a
Company B: $21.00
Company C: $10.00

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Author: yoda83 One star, 50 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1784 of 1933
Subject: Re: DCF Analysis Date: 12/8/2004 1:58 PM
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just took another look at stevenfool's post. if there is a "Year 0", then my numbers are off. im assuming Year 1 is the initial year.

...regarding company A, my gut tells me its value should be $10.00, but i know basic textbooks say "n/a". are there any methods for dealing with this situation of equal discount and growth rates?

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Author: trepanne Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1785 of 1933
Subject: Re: DCF Analysis Date: 12/8/2004 2:22 PM
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yoda,

reading your post i just noticed my own error. i misread stevnfool's setup; if company C is paying a $1/sh constant dividend, and we're capitalizing it at 10%, then of course the valuation per DDM is $10/sh (not $5 as i wrote... too late at night obviously).

if there is a "Year 0", then my numbers are off. im assuming Year 1 is the initial year.

you are not alone here. by convention, the gregorian calendar also starts in the year 1, which means that the millenial transition should have been celebrated "in arrears" (i.e. 1/1/2001 rather than 1/1/2000). DAMN these inflated valuations.

are there any methods for dealing with this situation of equal discount and growth rates?

no, and i think that there cannot be. 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.

another way to do it is to curtail the growth... model supranormal growth for 5 years, and then capitalize the final period's earnings with some terminal multiple (make it low).

trp

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Author: yoda83 One star, 50 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1787 of 1933
Subject: Re: DCF Analysis Date: 12/8/2004 3:30 PM
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trp, you're right. i guess in that gut feeling i was referring to, i was implicitly including a return of the "$10" at some point down the line.


..."false precision"? models smacking?

yeah, i completely agree.

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Author: iceberg0 Two stars, 250 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1790 of 1933
Subject: Re: DCF Analysis Date: 12/8/2004 11:19 PM
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Stevn -

In a few days, I will advise what I believe 1 share of each company is worth and I will provide my rationale.

I can't wait. (Nor can I wait for audited math so reader beware…)

Your market value problem as stated does not have enough information for a thorough analysis so headmaster B.Graham will assign a speculative rating to your security. For instance, you do not provide a beginning capital amount so an adequate return cannot be promised. Too, all kinds of cost of capital sirens are going off in my head.

Some might argue the market value of Company A is $0.00 because no cash will ever come out of it (to Stevn or a future owner) and the thing will just go supernova or black-hole some day (that's why the math blows up, too). Your A Co. has no inventory, no PP&E, no debt, no beginning equity, pays no taxes, makes no capex, has no selling expenses, no ESOs, no inflation/deflation in the $ – it just somehow drains $1 * 1.1**infinity out of whatever economy and keeps it. It seems A Co. will have some sort of (huge & growing) storage cost.

B Co. though is not so speculative and one little change will get an investment grade rating from the headmaster. For your one share it will pay out cash every year forever.

Suppose the change is that it has $10 of your USD cash starting capital and converts that to inventory on the first day of a beginning annual period. It sells that inventory in the economy over a year for net income of $11 (after-tax & selling expenses thus your $1 EPS or pre-dividend FCF). It then pays you $0.50 and reinvests $0.50 in incremental inventory so to grow sales in the next annual period.

At the beginning of the second period it can then buy $10.50 worth of inventory, rinse and repeat. (Interesting that B Co. has $10.50 of cash and you have $0.50 cash for a moment but that pile is a FV today & can be discounted back 1 annual period at 10%.)

In this case, the return on your capital is 10% since you are 100% control owner of B Co. Let's further say your alternative use of your $10 beginning capital in the B Co. economy has essentially 10% economic return elsewhere thus your cost of capital is 10%. As trp correctly wrote the B Co. beginning market value is $10 (by DDM) and B Co. grows in market value (after div.) every year (remember the $10.50 cash at end of first period above?). At the end of period two, B Co.'s market value is $11.03. (10*1.05*1.05) plus Stevn has $1.02 in cash ($0.50 + (1.05/2 = $0.52) – your conservative accountants round down the $0.005).

You can try and issue a press release saying something like “B Co. is aggressively identifying opportunities to grow our business and leveraging our core competencies to build shareholder value.” You might get a few brokerage upgrades and (if B Co. is already public) get the secondary market bidding the price a little higher but the NPV net of div. today doesn't change. It is still $10/shr by DDM.

A great BIG Note: Stevn has not gained any economic business value (or net worth in this economy) here today because he started B Co. with his 10 bucks and that is all the market value is today even though it promises to grow! Wow. (Of course, now you can grant ESOs and issue press releases, register & have an IPO and maybe even sell that share to Mr. Market (on one of his manic days) for $100 – what a wonderful thing B Co.'s business can be in a capitalistic society.)

So why did Marv write the B Co. business is worth $20 for that share? He's adding both income streams (as if they were both retained in the business) – but one is retained to increase B Co. market value and one paid out to the owner Stevn who presumably can earn 10% p.a. growing 5% elsewhere in the economy on that cash (taxes not considered).

In this economy NPV Market value B Co. plus dividend = .5/(.1-.05) + .5/(.1-.05) = $20 ( -$10 from Stevn for startup so his net worth is unchanged upon selling out this average business today for fair value.)

The market value of B Co. increases only enough to provide a 10 percent return (including dividend), which compensates Stevn for his capital costs but no more in this economy. The same is true for all subsequent periods for B Co.






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Author: yoda83 One star, 50 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1791 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 12:55 AM
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iceberg, nice write-up.

one thing: since we're just valuing a share, we dont need the cost of capital or beginning capital for these companies.

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Author: jkm929 Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1792 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 1:34 AM
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Some might argue the market value of Company A is $0.00 because no cash will ever come out of it (to Stevn or a future owner) and the thing will just go supernova or black-hole some day (that's why the math blows up, too). Your A Co. has no inventory, no PP&E, no debt, no beginning equity, pays no taxes, makes no capex, has no selling expenses, no ESOs, no inflation/deflation in the $ – it just somehow drains $1 * 1.1**infinity out of whatever economy and keeps it.

StevnFool says three things about Company A: (1) it doesn't pay a dividend; (2) it earns $1 a share; and (3) its earnings per share will grow 10% a year forever. We don't know if the 10% growth rate in earnings per share is due to the company successfully reinvesting all its earnings in a business with a 10% marginal return on equity or if it reinvests none of its earnings in its business but instead uses all of its earnings to buy back its stock at a 10% earnings yield. Company A could also reinvest part of its earnings in the business and use the remainder to reduce shares outstanding.

An investor seeking growth of capital could buy stock in Company A, do nothing and watch his investment appreciate 10% a year. Or he could buy stock in Company C, reinvest all the dividends in Company C stock and likewise watch his investment grow 10% a year.

The investor seeking cash flow could invest in Company A and sell off 10% of his shares every year. He could, alternatively, invest in Company C, do nothing and get a dividend yield of 10% a year.

Companies A, B, and C are all equivalent investments if purchased at $10 a share.

jkm929

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Author: trepanne Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1793 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 3:19 AM
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Companies A, B, and C are all equivalent investments if purchased at $10 a share.

yes, i believe that was intended to be the point of this exercise. if so, however, i believe that it's flawed if it neglects to account for the capital reinvestment needs of a growing business.

stevnfool gave us EARNINGS to work with, but then asked us to apply a CASHFLOW based valuation. there is a disconnect.

because of the capex, GAAP earnings usually outstrip cashflow during expansion; the inverse is also true.

if company A has got some kind of fantastic business where their earnings and their cashflows are equal, and they can grow at 10% without net additions to capital... then they should be able to pay out all their earnings as dividends every year, AND STILL grow profits at 10% compounded.

clearly, that business is worth a hell of a lot more than company C.

in fact, if your discount rate is 10%, i'd venture to say it's worth infinitely more...

trp

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Author: madmarv Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1794 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 3:57 AM
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Your market value problem as stated does not have enough information for a thorough analysis so headmaster B.Graham will assign a speculative rating to your security. For instance, you do not provide a beginning capital amount so an adequate return cannot be promised. Too, all kinds of cost of capital sirens are going off in my head.

Why are you jumping on his throat? Stevn specifically asked that you take his numbers at face value. It is clear that he is interested in discussing valuation methodology separately from all other aspects of security analysis.

So why did Marv write the B Co. business is worth $20 for that share? He's adding both income streams (as if they were both retained in the business) – but one is retained to increase B Co. market value and one paid out to the owner Stevn who presumably can earn 10% p.a. growing 5% elsewhere in the economy on that cash (taxes not considered).

No, I said that I assumed EPS = FCF. Under this assumption, the dividend is irrelavent to the analysis and the IV is calculated as $1 / (10% - 5%) = $20.

A great BIG Note: Stevn has not gained any economic business value (or net worth in this economy) here today because he started B Co. with his 10 bucks and that is all the market value is today even though it promises to grow!

You're not looking at the economics correctly. If you go through the DCF calcs, you will see that the discounted value of the dividend stream grows year by year. For example, assuming dividends = FCF, the PV at present (Year 0) is $0.50 / (10% - 5%) = $10. In Year 5, the then current dividend is $0.61 and the discounted sum of future (Year 6+) dividends are is $0.64 / (10% - 5%) = $12.76. Note that the $12.76 is in Year 5's $, which is a 5% CAGR over the Year 0 value. At Year 10, the value is $0.78 / (10% - 5%) = $16.29, and so on. The only way the IV (in Year 0's $) could be something other than $10 is if the cash flow stream itself were to change. For example, changing the assumed growth rate from 5% to 7%. It would increase the IV, but do not confuse this with value creation. The value of the company increases each year because of the earnings retained.

Marv

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Author: StevnFool Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1795 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 12:47 PM
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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


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Author: yoda83 One star, 50 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1796 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 3:42 PM
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im all for trying to understand the drivers behind earnings. really i am. but for this exercise, you gave us enough to value the shares of Company B and C. If you use eps as a proxy for future cash flows (which in theory, they are), then B and C are not equal.

remember, you gave constant growth rates (10% for A; 5% for B; 0% for C), and the beginning eps amount for all three companies. so we know what mgmt is going to do w/ their retained earnings. mgmt is going to grow them at (10, 5, or 0%). you also stated a discount rate of 10% for each investment. this is my required rate of return. this already takes issues such as Aa bond yields into account.

so i "know" mgmt is going to consistently grow eps at X% a year, regardless of their competence or character. and i "know" yields on alternative investments available to me, and for whatever reason, i've decided a 10% discount rate is appropriate for this particular share im trying to value. i also know eps for the following year (i guess i did interpret this incorrectly in my first post).

Given:
a constant growth rate, g
a required rate of return, R
and an eps amount for next year, D1

we can calculate the current per share value of B and C, P0

P0 = D1/(R-g)

using eps, the only difference between the value of B and C is their respective rates of growth, g. C doesnt have any and B's is 5%. an assumption i've made (and i think others made) is that the 0% or for 5% growth represents the highest return for comparable risk in the investment universe. so i cant take my dividends and earn a higher rate w/ another investment. otherwise, i would withdraw all of my funds from our company and sink them into these better alternatives.

like i said, im all for thinking and digging. and since your post got this kind of discussion going, i appreciate the thread. but for purposes of valuing these companies (specifically, B and C), you gave us all the info we needed. after that, it's plug and chug.




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Author: trepanne Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1797 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 4:24 PM
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stevnfool,

this is fun stuff (and a welcome distraction from some analysis i want to shirk).

i would like to nail to the door a manifesto entitled NO MAGIC BULLETS IN EQUITY VALUATION. i'd like to take an extremist stance against the reduction of stock analysis to routine mechanistic formulae. as i understand it, the job is to understand and judge corporate financial disclosures, not to drum up a better mathematical mousetrap.

multiple valuation methods, each of them with its own validity, may shine more light on the subject.

for example, when financial firms are paid to perform valuations, they will often use tripartite methodologies. they'll compute valuation from a DCF calculation, and they'll look at the earnings multiple of publicly-traded comparables, and they'll look at the buyout values of comparables on the private markets.

i would recommend that you acquire and study a copy of marty whitman's book, "value investing: a balanced approach". this book has been much more valuable to me than phil fisher's book (also, i have to admit, i really enjoy whitman's bitchy slams against ben graham - kill your idols).

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.


use a balance sheet approach, not an income statement valuation. the problem vanishes utterly. $10 in cash is worth $10. bang.

or, if it was factory plant generating the earnings instead of current assets, we can say the PP&E is worth $10 net. in this case, the problem resolves to one of evaluating the carrying value of assets & stated depreciation, which may be easier than trying to determine the present value of some contingent dividend payout that may or may not happen 20 years from now.

remember: assets are defined as things which will result in future cashflows (or earnings).

I would propose then that we need to value dividends and retained
earnings separately.


may i suggest that you don't value shareholder equity directly from its balance sheet accounts?

instead, value the assets, and subtract the liabilities. that is what i do - that is what "security analysis" taught me to do; there are some excellent chapters in adjusting stated book value to get at an estimate of liquidation value. i do this a lot; almost every day in fact.

if you are trying to study management's utilization of retained earnings, you might find it more useful to study things like ROE over time, dupont formula, gross/operating/net profitability, and growth rates in these lines on the income statement.

if you're wanting to keep it simple, and just look at one thing, may i suggest looking at ROA and ROE.

trp

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Author: yoda83 One star, 50 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1798 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 5:08 PM
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trp,

do you prefer "Value Investing" or "Agressive Conservative Investor"? i've only read "Aggressive" so far.

as far as whitman's slams on graham: the first few times were novel (and shocking), but after awhile it gets kind of stale. i read a transcript from a recent whitman conference on marginofsafety.com where he made another negative comment about graham. i didnt let it affect my reading of his comments, but i just thought it was kind of sad that whitman still feels it's necessary to take shots at ben. im not sure what the whole story is between the two (im not even sure if there is a story), but given everything whitman's accomplished and the insights he has to offer, he doesnt need to keep taking swings.

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Author: StevnFool Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1799 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 5:29 PM
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If you use eps as a proxy for future cash flows (which in theory, they are)

I guess the whole point of the exercise was that I was showing that EPS is a very poor proxy for future cash flows.

Given:
a constant growth rate, g
a required rate of return, R
and an eps amount for next year, D1

we can calculate the current per share value of B and C, P0

P0 = D1/(R-g)

using eps, the only difference between the value of B and C is their respective rates of growth, g. C doesnt have any and B's is 5%.


This just proves it.

B and C are both $10 deposits earning 10% interest. They are both obviously worth $10, but with your calculation, you value B at $20 (incorrect) because half of the interest is retained automatically which results in growth of interest whereas you value C at $10 (correct) because the interest is paid out.

StevnFool

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Author: StevnFool Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1800 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 5:52 PM
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i'd like to take an extremist stance against the reduction of stock analysis to routine mechanistic formulae.

Maybe I've spent too long on the MI board, but I would view a lot of Graham's ideas (unlike Fisher's) as using simple mathematical formulae.

as i understand it, the job is to understand and judge corporate financial disclosures, not to drum up a better mathematical mousetrap.

As Woodstove recently said, each person needs to adapt their methodology to something they are comfortable with. I do not intend to boil my analysis of a company completely down to one formula, but it helps to have a model in ones head that can take account of issues like owners earnings, dilution, utility of retained earnings, etc into account.

multiple valuation methods, each of them with its own validity, may shine more light on the subject.

I agree. This is one thing I like about these message boards. One person can post their valuation of a stock and another can tear it apart from a different perspective.

i would recommend that you acquire and study a copy of marty whitman's book, "value investing: a balanced approach". this book has been much more valuable to me than phil fisher's book (also, i have to admit, i really enjoy whitman's bitchy slams against ben graham - kill your idols).

Sometimes I wonder if too much reading may be as bad as too little. Perhaps if one mixes too many different perspectives, one may actually get a worse result.

For example. Graham's NET-NET or cigar butt methodology is a good way to make money from stock's, but the criteria used for selecting cigar butt stocks are of little benefit when selecting long term buy and hold stocks, yet I have seen people trying to combine Graham's ideas for cigar butts into their selection criteria for their long term holdings. For the most part cigar butt stocks are badly run, but still undervalued which will probably increase in price within a couple of years, but the majority of them would be very poor long term candidates.

use a balance sheet approach, not an income statement valuation. the problem vanishes utterly. $10 in cash is worth $10. bang.

It hard to trust a balance sheet too - particularly the non current asset section.

may i suggest that you don't value shareholder equity directly from its balance sheet accounts?

I think you mis-understood what I meant. I did not mean to value the retained earnings as they appear on the balance sheet. I meant that if a company reports an EPS of $1 and pays a dividend of $0.40. I would not simply value the company using a multiple of $1. I would divide the $1 EPS up into the dividend ($0.40) and the retained part ($0.60) and try to figure out a multiple (P/E) for each part and then add the two together to get a total valuation. I presented an example in the post you were replying to.

StevnFool

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Author: yoda83 One star, 50 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1801 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 5:58 PM
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stevn,

i agree that eps can be a poor practical proxy for future cash flows. but w/ the info we have, they're the best proxy we've got.

B and C are both $10 deposits earning 10% interest. They are both obviously worth $10, but with your calculation, you value B at $20 (incorrect) because half of the interest is retained automatically which results in growth of interest whereas you value C at $10 (correct) because the interest is paid out.

companies B and C are only equal under DDM. however, using eps, B is correctly worth $20 (and C is still worth $10). IIRC, in your original post, you called for a DCF, not a DDM.

again, there are many factors to consider when using DCF, but given your parameters, there is only one way to use DCF and calculate the value of these shares - so far as i know. im not the finance guru. if there is a way to find these share values w/ ONLY the info (D1, R, g) you supplied, then i admit right now, im not familiar w/ it.

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Author: yoda83 One star, 50 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1802 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 6:04 PM
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speaking of net-nets, i think i saw one in valueline, G-III Apparel Group (GIII). it doesnt have a message board. does anyone follow this company? im sure times are tough for them right now, but i was just wondering if anyone had a take.

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Author: StevnFool Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1803 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 8:08 PM
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speaking of net-nets, i think i saw one in valueline, G-III Apparel Group (GIII). it doesnt have a message board. does anyone follow this company? im sure times are tough for them right now, but i was just wondering if anyone had a take.

I just took a quick look.

From balance sheet at
http://finance.yahoo.com/q/bs?s=GIII

Current Assets = 99,706,000
Total Liabilities = 47,295,000

NET-NET Value = 52,411,000

From http://finance.yahoo.com/q/ks?s=GIII

Shares out = 7.18 million.

NET-NET per share then = $7.3

Buy at less than 2/3rd NET-NET Value

Buy price = $4.87

Current Price = $6.22

It needs to drop a bit more. Then there are a few more things to check. They have just reported on a more recent quarter so you would need to check if that changes the numbers when a balance sheet statement is available.

Then you need to check all news items since the end of the quarter that you based your calculation on to see if anything has materially changed(e.g. big dividend payout would have a big effect).

Then you should maybe go back a year earlier and calculate the NET-NET value to see if it is stable or dropping rapidly.

Generally these companies could take over a year to become valued more fairly. If the NET-NET value per share is dropping a big percentage per year, you might pass on it.

StevnFool


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Author: trepanne Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1804 of 1933
Subject: Re: DCF Analysis Date: 12/9/2004 11:08 PM
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I did not mean to value the retained earnings as they appear on the balance sheet. I meant that if a company reports an EPS of $1 and pays a dividend of $0.40. I would not simply value the company using a multiple of $1. I would divide the $1 EPS up into the dividend ($0.40) and the retained part ($0.60) and try to figure out a multiple (P/E) for each part and then add the two together to get a total valuation.

right... you're slapping a multiple on the retained earnings; directly capitalizing this account.

i think it's a fine idea to separate out the dividends from the retained earnings & value them separately.

the problem is, what is an appropriate generic valuation for $1 of retained earnings... really?

take it a step further. the accounts on the right-hand side of the balance sheet funds the assets on the left-hand side. when you examine what management is actually doing with the retained earnings, then you'll get an idea what the retained earnings are actually worth inside the business.

there are companies who increase value by retaining their earnings. there are companies who destroy value by retaining their earnings. you want to be able to tell the difference, because it can make a big difference.

would you capitalize the retained earnings of all companies equivalently?

hence my suggestion: if you're really determined to look for a simple way to slap a multiple on retained earnings, why don't you look at the ROE (say, averaged over 5 years or so)?

trp


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Author: yoda83 One star, 50 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1805 of 1933
Subject: Re: DCF Analysis Date: 12/10/2004 12:08 AM
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stevn,

"Current Assets = 99,706,000
Total Liabilities = 47,295,000

NET-NET Value = 52,411,000

NET-NET per share then = $7.3

Current Price = $6.22"


i think this is all that is necessary for a net-net. i know a purchase of 2/3 is mentioned in "Intelligent Investor", but i dont believe that's necessary for net-net status. however, i see that inventory comprises most of G-III current assets (which isnt surprising), and there's been kind of a build-up there. so depending on the value you place on the inventory, the "net-net" designation may be bust.

btw, i've only read the zweig version, so if the net-net definition has been altered from the earlier editions, i wouldnt know.


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Author: trepanne Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1806 of 1933
Subject: Re: DCF Analysis Date: 12/10/2004 12:27 AM
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yoda,

do you prefer "Value Investing" or "Agressive Conservative Investor"?

i have only read "value investing". i imagine it's all much of a muchness, though. he keeps recycling his material.

given everything whitman's accomplished and the insights he has to offer, he doesnt need to keep taking swings.

no, no, this is the best part! to me, it's very interesting to hear whitman elucidate his reasons for considering that graham wasn't a REAL value investor.

i've found that usually, great theorists tend to clash acrimoniously. i've learned to enjoy it.

a particularly enjoyable and lengthy exchange occurred over the course of many books between steven jay gould (america's greatest popularist of evolution) and richard dawkins (a leading light of the neo-darwinism). great stuff.

trp

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Author: StevnFool Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1807 of 1933
Subject: Re: DCF Analysis Date: 12/10/2004 8:36 AM
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i think this is all that is necessary for a net-net. i know a purchase of 2/3 is mentioned in "Intelligent Investor", but i dont believe that's necessary for net-net status. however, i see that inventory comprises most of G-III current assets (which isnt surprising), and there's been kind of a build-up there. so depending on the value you place on the inventory, the "net-net" designation may be bust.

I would recommend the 2/3 margin of safety for Net-Net's, but it is up to you. Although I admit that I have bought 1 or 2 at 80 - 85% of NET-NET, but if the NET-NET value is dropping or misrepresents the true liquidation value, it doesn't leave much margin of safety. I have gone back to requiring 2/3 which is why I can't find any to buy right now.

In relation to inventory, that is a good point. If you look at the chapter called "Significance of the Current Asset Value" in the Balance Sheet section of SA (1940 Ed), it deals with liquidation value. It gives % values for various categories of Assets. From memory it is something like:

Cash and Equivalents: 100%
Receivables: 80%
Inventory: 60%
Non-Current Assets such as plant, property and equipment 15%.

Obviously if you know more about the specific company, you may wish to adjust these numbers up or down.

Then somewhere (I couldn't find it this morning but it is either in the 1940 Ed of SA or else in II) Graham puts forward his thesis that in most cases Net-Net value as I have calculated it gives a good enough approximation for liquidation value. The logic is that the non-current asset which are valued at zero in the Net-Net calculation will make up for any shortfall in the value of the current assets.

My view however is that if a large % of the Current assets are either inventory or receivables and there are very few non-current assets, it may be wise to value it by both methods and use the lower one.

I also thought of one other thing to watch out for on NET-NET stock and that is share structure. Be very wary if there are preferred shares and either pass on the company or make sure you find out the status of the preferred. It may be that upon liquidation that they will take all of the value. Also watch out for different classes of shares.

StevnFool


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Author: StevnFool Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1808 of 1933
Subject: Re: DCF Analysis Date: 12/10/2004 8:53 AM
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the problem is, what is an appropriate generic valuation for $1 of retained earnings... really?

Have another read through my post 1795 and hoefully you will see the answer.

The multiple I select for the retained part of the EPS is selected based upon how I expect the retained earnings to convert into future increases in EPS.

I know in real life, it may take more than 1 year to convert retained earnings into increased EPS (you will note in my example in post 1795, I looked at the change over a 6 year period), but if we ignore this for the purposes of explanation and assume that like in a cash deposit account that retained earnings can be converted into increased earnings (interest) in 1 year, then if a company in 2004 retains $1 of reported earnings, I would look for an increase in EPS in 2005.

If the 2005 EPS is $0.50 greater than the EPS in 2004, then I would calculate that the $1 retained earnings has returned 50%. If my discount rate is 10%, then the $1 retained earnings is worth $5 of dividend as it returns 5 times as much value. On the other hand, if earnings don't increase, the $1 retained earnings has zero value.

I know this is simplistic and the increase in earnings may not be a direct result of the retained earnings, but do I care. If the company keeps some of my money and somhow increase their earnings the next year, they are obviously worth more.

In real life and in my example in post 1795, you need to look at the earnings growth and retained earnings over a longer time span (6 years in my example) and I think you need a ceiling on the multiple to use (I suggested 20) to avoid the dangers of growth stocks that Graham has warned us so much about.

I think my model does actually take into account the things that you have suggested.

StevnFool


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Author: trepanne Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1809 of 1933
Subject: Re: DCF Analysis Date: 12/10/2004 5:20 PM
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stevenfool,

Have another read through my post 1795 and hoefully you will see the answer.

this communication stuff can be difficult...

i believe i now understand your method of capitalizing the retained earnings. yes, we are talking about similar things.

your method is idiosyncratic, and isn't what i do... but that's not necessarily wrong. it has the advantage of being readily computable from standard reports of financial summaries.

in my own analysis, i go to some trouble to identify the drivers of earnings.

let me give you a few examples to chew over.

1) MO - they distribute about half their earnings. if we strip out the food business & concentrate on tobacco, this business does not need much reinvestment in order to grow. earnings growth comes from price hikes and cost reductions. basically, every dollar MO management retains represents about 15-20 cents worth of value incinerated; they keep pissing it away by overpaying for acquisitions, for example. however, this dynamic seems like it would be invisible to your test.

2) MCIP (a stock i hold). have a look at that and tell me how it does by this method. there are about three problems i can see - they just emerged from bankruptcy with "fresh start" accounting, their cash flows greatly exceed their GAAP earnings, and the major driver of their bottom line is cost reductions.

3) REITs. they don't retain earnings. why would anybody ever be so stupid as to pay a premium to NAV for a REIT, then?

just some posers, if you have the inclination.

trp

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Author: StevnFool Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1810 of 1933
Subject: Re: DCF Analysis Date: 12/10/2004 7:08 PM
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just some posers, if you have the inclination.

trp


If I have time next week, I might look. My next post gives the full methodology.

StevnFool

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Author: iceberg0 Two stars, 250 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1812 of 1933
Subject: Re: DCF Analysis Date: 12/11/2004 1:10 AM
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Marv –

Whoops, I didn't mean to appear to be jumping, just showing my interest in the subject maybe – I was writing kinda' fast. Like getting back to the fundamental blocking/tackling in football and risks/rewards of dribble driving at the basketball buzzer. Your reply got me going back to the security analysis textbook which is always a good thing.

Here's how I see the financials on Stevn's B Co. in a world economy of 10% cost of capital and the other business assumptions I made (no debt, etc). B Co. buys inventory for beginning capital funded by Stevn of $10 and then sells to cash during the year for net cash income of $1 that grows capital at 5%. It then repeats forever, no competition enters the picture. I think that fairly represents his model in #1778. A constantly growing annuity.

Time 0 1 2 3 … 5 … 10

EPS $1.00 $1.05 $1.10 … $1.22 … $1.55
Div 0.50 0.52 0.55 … .61 … .77
Retain.Earngs 0.50 0.52 0.55 … .61 … .77


Capital $10 10.50 11.02 11.57 … 12.76 … 16.29
Mrkt.Value $10 10.50 11.02 11.57 … 12.76 … 16.29
Return on Capital 10% 10% 10% 10% 10%
Cost of Capital 10% 10% 10% 10% 10%

So, right, B Co. is worth today $10/shr. Calculated from .5/(.1-.05). Cash value increases each period. Our numbers agree within rounding error. When you equate FCF to EPS to Retained earnings the picture changes for B Co.. But I still don't get this very well:

…the IV is calculated as $1 / (10% - 5%) = $20.

This is now Stevn's A Co. I see why Stevn writes that A Co. is worth $10 today and I was reminded after reading this thread:

(yoda - I had to add the beginning capital to see it for myself) –

Time 0 1 2 3 … 5 … 10

EPS $1.00 $1.10 $1.21 …$1.46 … $2.36
Retain.Earngs $1.00 $1.10 $1.21 …$1.46 … $2.36

Capital $10 11.00 12.10 13.31 … 16.11 … 25.94
Mrkt. Value $10 11.00 12.10 13.31 … 16.11 … 25.94
Return on Capital 10% 10% 10% 10% 10%
Cost of Capital 10% 10% 10% 10% 10%

This growth just eventually explodes in Stevn's economy and thus arguably never actually pays anything: 1/(.1-.1). Of course, one can trade out earlier in a secondary market and realize some economic gain. In the real world, of course, competition enters the scene here and/or resources dwindle and growth slows so some analysts get out their two and three stage (or more) DCF spreadsheets.

I've never been any good at estimating these growth stages though I've tried. I've given up on every stage except the first one. I just try to get to some owner earnings estimate and assume loooong term growth near or slightly above the world economy and discount by the 10 year treasury plus a decent equity premium that looks consistent with the recent 10 year market lows of the equity price.

Thanks to the other folks here, too – fun reading. Now some challenges.

If anyone is interested in killing more time over this (or shirking duty in trp's case), think about what happens if B Co. management finds it can allow invested capital to grow 5% while new investments were still producing a 20% return on capital in Stevn's economy instead of only 10%. FCF is equal to the cash dividend management can pay to shareholders while maintaining the desired level of operations (in B Co.'s case, 5% capital growth). What would happen to market value in that case? Hint: things get juicy as Marv implied. Wow.

Then if you still have not lost enough sleep, what if the cost of capital goes down to say 8%? More wow.

Again, my math comes with an across the board warranty period. Drive it across the board and the warranty period is over.


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Author: StevnFool Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 1819 of 1933
Subject: Re: DCF Analysis Date: 12/13/2004 8:36 AM
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1) MO - they distribute about half their earnings. if we strip out the food business & concentrate on tobacco, this business does not need much reinvestment in order to grow. earnings growth comes from price hikes and cost reductions. basically, every dollar MO management retains represents about 15-20 cents worth of value incinerated; they keep pissing it away by overpaying for acquisitions, for example. however, this dynamic seems like it would be invisible to your test.

From:
http://moneycentral.msn.com/investor/invsub/results/statemnt.asp?lstStatement=10YearSummary&Symbol=mo&stmtView=Ann

1995 - 1997 EPS average = 2.43
2001 - 2004 EPS Average = 4.54

Incease in EPS = 2.11

Retained EPS 1996 - 2001 = 7.89

Return on Retained Earnings = 2.11/7.89 = 27%

This suggest to me that they are doing something right so if they are wasting money on acquisitions, they must be doing a lot of other stuff right that makes up for it.

If we require a multiple of 10.42 for dividends and 10.42 x 27/9.6 (use Max value of 20) for retained earnings, I can calculate a buy price.

Use 4.54 as the average EPS
Divide this up into 2.92 of dividends and 1.62 retained.

Buy price then is 10.42 x 2.92 + 1.62 x 20 = 62.82 At a current price of 59.14, it looks like a reasonable buy using this criteria alone, but if you look at the balance sheet, it does not measure up in a lot of the other areas = i.e. current ratio, debt / working capital, etc.

For the moment, I won't be buying.

2) MCIP (a stock i hold). have a look at that and tell me how it does by this method. there are about three problems i can see - they just emerged from bankruptcy with "fresh start" accounting, their cash flows greatly exceed their GAAP earnings, and the major driver of their bottom line is cost reductions.

I wouldn't consider them until they have some real history simply because I wouldn't know how to do so with any reasonable level of confidence.

3) REITs. they don't retain earnings. why would anybody ever be so stupid as to pay a premium to NAV for a REIT, then?

My model is based on Graham's guidelines for industrial companies. REIT's are a totally different set-up and I don't feel qualified to properly assess them.

StevnFool

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