sexta-feira, outubro 14, 2005

Análise Lexmark

A segunda marca mundial de impressoras vem comunicando reduções sucessivas nas vendas e correspondentes lucros. A grande rival, a HP, tem vindo a pressionar bastante os preços numa estratégia de reestruturação que envolve despedimentos de pessoal, fecho de departamentos e reduções de preços e margens. No entanto, estas reduções não são sustentáveis e a estabilidade há-de regressar ao sector.

A Lexmark possui um historial de resultados muito bom como podem comprovar os dados fundamentais abaixo. Por outro lado, só este ano já caiu quase 50%! Os múltiplos encontram-se em níveis historicamente baixos.

Neste momento tenho uma posição de $3000 mas vou reforçar.

Ficam os dados fundamentais, os gráficos, uma avalição do seu valor intrínseco recorrendo ao modelo dos free cash flows descontados e os movimento efectuados até hoje.

Avaliação do Valor Íntrinseco da Lexmark assumindo um custo do capital de 9.93% e uma LT Growth Rate de 10.5% durante 10 anos.

Através deste método podemos concluir que cada acção da Lexmark vale $99.57, ou seja, 133.95% acima do preço actual!

Ficam os movimentos no título:

quinta-feira, setembro 15, 2005

Análise Capital One Financial

Dando continuação à análise da semana passada, hoje vou apresentar alguns dados de outra empresa de cartões de crédito na qual entrei depois do negócio da MBNA. O sector encontra-se em concentração e esta é uma empresa apetecível de rentabilidades impressionantes. A Capital One vai comprar um banco (Hibernia) sendo este mais um movimento estratégico para potenciar o escoar dos seus cartões de crédito.

Entrei a 80.30 e só reforço no suporte dos 75. Isto porque caso recue tem um gap grande que só pára nesses valores.

Ficam os dados fundamentais e os gráficos. Deixo, também, um modelo de avaliação extremamente simples e bastante conservador que assume crescimento perpétuo estável.

O seguinte modelo de avaliação pressupõe crescimento estável no longo prazo. São utilizadas três medidas de avaliação: Os Earnings per Share, os Earnings per Share from Continuous Operations (excluindo resultados extraordinánios) e o Free Cash Flow. Por outro lado, também são definidas três taxas de desconto dos resultados no longo prazo: Taxa Juro sem Risco (com crescimento lucros nulo), WACC - Weight Average Cost Capital (com crescimento lucros nulo) e WACC menos taxa de crescimento de longo prazo constante. Deste modo, são calculadas 9 medidas de avaliação (umas mais conservadoras que outras) fazendo simplemente a medida dos resultados a dividir pela taxa de desconto dos mesmos.

Pode-se ver que em todas as medidas de avaliação (mesmo nas mais conservadoras) a acção encontra-se a desconto. Por exempo, se tivermos em conta o EPS/WACC que pressupõe o mesmo resultado do último ano para sempre actualizados para a data de hoje à taxa WACC, aponta para um valor intrínseco de 95.80, ou seja, 19.26% acima da cotação actual.

terça-feira, setembro 13, 2005

Value Isn't Just a Number

By Stephen D. Simpson, CFA September 12, 2005

It's all too appealing to try to reduce investing to simple numbers. An undervalued ratio here, an above-average metric there, and you're good to go, right? Well, maybe not. Although numbers have their place, they must be kept in their place -- that is, as an aid to analysis and decision making, but not a driving factor. I believe that when investors look back on the history of successful companies and winning stock picks, they will see that true value is not just a sequence of numbers.

Numbers don't tell the whole truthMany different dead people are reported to have originally uttered the line "lies, damn lies, and statistics." Whoever actually said it was on to something. Numbers may be a convenient measurement tool, but what happens when management decides to tinker a bit with them? How many people bought into the Enron or WorldCom stories because they were seduced by the numbers?

Apart from these two examples of outright fraud, there are numerous companies that actively attempt to manage their earnings. A change in inventory valuation here or a readjustment of depreciation schedules there and you can smooth over quarter-by-quarter or year-by-year comparisons. Maybe this isn't a blatantly "bad" thing -- after all, investors seem to like steady growth in earnings and stock prices -- but it does point to a reason as to why you might not want to place undue reliance on the numbers.

Let's also not forget that accounting isn't necessarily meant to be used in the way that many investors try to use it. Modern accounting principles are mostly built for the purpose of tracking the movement of cash into, around, and out of a business entity. As such, it has certain limitations.

For instance, accounting treats most research and development as an expense, yet clearly companies view R&D as at least partially an investment in future products and competitiveness. If R&D is simply an expense and not a cumulative asset, why then are biotech, med-tech, and some technology companies acquired when they have no earnings and no products yet on the market?

Likewise, why aren't capital expenditures treated as an expense? Sure, you can argue that depreciation is a proxy for the need to replenish the company's capital base, but there is no requirement for a company to distinguish between "maintenance" capital expenditures and growth capital expenditures. Likewise, assets are frequently depreciated irrespective of their actual current values -- meaning that some companies may hold property that is worth little on the balance sheet (because it has been depreciated), but worth quite a bit in real life.

Simply put, modern accounting is not concerned with what really matters in evaluating a successful business -- producing an economic return on capital that is in excess of the cost of that capital. Sure, you can (and have to) use accounting inputs like pre-tax profit in your calculations, but ultimately you need to leave accounting behind to establish reasonable estimates of discounted cash flow, economic value added, or many other methods of company valuation.

Management trumps numbersIt seems as though some people forget that numbers don't run businesses -- people do. And above-average people have proved time and time again that they are capable of doing far more than what mere numbers would suggest. In other words, good management trumps numbers.

Airlines are a lousy business -- but Herb Kelleher created a winner with Southwest Airlines (NYSE: LUV). Biotechnology is the graveyard of investor dreams, but George Rathman has founded two winners -- the incredible Amgen (Nasdaq: AMGN), as well as ICOS (Nasdaq: ICOS). I couldn't count the number of failed e-businesses, but Jeff Bezos' (Nasdaq: AMZN) is still thriving. Could you have identified all (or any) of these winners based on solid numbers alone? I'd argue "no."

Simply put, you can't quantify the above-average opportunities that are created by talented and visionary managers. Unfortunately there is no price-to-creativity ratio, nor a way to measure return on management vision. Sustainable competitive advantages and economic moats are hard to quantify much beyond "I know 'em when I see 'em," and yet they are critical components to long-term stock market success.

In the absence of a Michael Dell ratio, remember that numbers are either reflective (looking back on reported results) or prospective (projecting future results), but they themselves don't produce anything. One person may build a model showing (Nasdaq: OSTK) to be overvalued by 50%, another person can produce a model showing the stock to be undervalued by 50%. In either case, the numbers themselves don't make it so; management and competition ultimately write the story.

Cheap can be cheap for a reasonPerhaps it's because I identify myself with the value crowd, but I happen to think that value investing is the most misunderstood investment philosophy. Look at a lot of popular investment books and you get the sense that value investing is all about numbers -- P/Es, price-to-book ratios, and so on. This not only gives short shrift to what real value investing is all about, but it can be dangerous for the novice or lazy investor.
Too often investors look only at a P/E ratio or maybe an enterprise value-to-free cash flow (EV/FCF) ratio and declare a company "cheap" or a "value stock." Unfortunately, these cheap numbers are easily misunderstood. Cheap is not cheap if the company is at a cyclical peak and earnings are about to go into decline. Cheap is not cheap if the company or industry are no longer competitive and are instead doomed to eventual decline (consider Berkshire Hathaway's namesake investment in the textile industry).

Likewise, a company about to begin a cyclical upswing will not look cheap. A company that has staunched the bleeding and begun a turnaround will not look cheap. A company with a proven competitive advantage and a solid growth outlook will not look cheap. And yet, all three of these archtypes can certainly be core value investment ideas.

What "real value" isSo if value isn't to be found hidden in a ratio or buried in a formula, where do you find it? Ideally, real value is a long-term competitive advantage purchased at a good price that includes a margin of error. I say "ideally" because cyclical companies and turnaround candidates can also be true value stocks if purchased correctly -- the long-term sustainable competitive advantage may be lacking, but a large enough discount to intrinsic value can make up the difference.

Identifying quality turnaround and cyclical opportunities is a subject for another day, so I'll instead focus on some thoughts about core value companies. These are companies with strong economic moats -- sustainable competitive advantages that help to insulate the company from competitors and allow for above-average earnings growth. These are also companies that produce real economic value -- meaning that they can take a pool of capital and reliably achieve financial returns well in excess of the cost of that capital. That might seem simple and obvious, but not many companies manage to do it for the long term.

Last, but not least, real value is a company that has a great management team with access to reasonably priced capital and free economic opportunities to expand. Don't overlook this latter point, as few companies can match Motley Fool Inside Value pick Coca-Cola (NYSE: KO) and do basically the same thing for decades on end. Microsoft (Nasdaq: MSFT) has expanded far beyond computer operating systems, IBM has long since grown beyond adding machines, and AIG is not "just" an insurance company.

We look for real valueDon't worry -- you're not out on your own looking for true value opportunities. We have an entire team at The Motley Fool that does little else but look for high-quality companies trading at very attractive prices. This Inside Value team has already done quite well for its subscribers, and I believe that any investors who want to appreciate true value investing should at least take a 30-day trial subscription to the newsletter service.

Bottom lineRemember, value isn't a number. There is no ratio or combination of formulas that can reliably guide you to true value opportunities. Successful investing is not mechanical -- it's subjective and qualitative. Numbers are a crucial part of the process and can reveal important information, but they must be kept in context. Like light reflecting off a mirror, investors should remember that numbers can reflect the state of a company -- but they aren't themselves the company. By looking beyond the numbers and appreciating them in context, investors can unearth the true values in the stock market and beat the conventional averages.


quinta-feira, setembro 08, 2005

Análise MBNA

Hoje vou apresentar a análise a uma empresa que já fez parte da carteira mas cuja posição fechei entretanto: a MBNA (Ticker: KRB). Trata-se de uma empresa de cartões de crédito com rentabilidades impressionantes e crescimento de resultados incrivelmente consistentes.

Este caso é, ao mesmo tempo, um excelente exemplo do que procuro demonstar com este método de investimento mas, também, uma situação que pode iludir os investidores mais ansiosos.

O gráfico da cotação vinha variando entre 23.5 e os 29 e face ao PER que estava na altura (cerca de 11) esperei que viesse retestar o suporte para entrar. Assim aconteceu, quando entrei no dia 18/04, precisamente nos 23.5 com $5000. Exactamente passados 3 dias, na divulgação de resultados da empresa, ela anuncia que as perspectivas de crescimento de resultados para os próximos trimestres serão abaixo do previsto, uma vez que muito do crédito concedido estava a ser, extraordinariamente, liquidado. As acções caíram mais de 18%.

Nesta altura com uma posição a perder tanto o que deve fazer o investidor fundamental?
R: Com calma, analisar os dados divulgados e ver se, através deles, se podia induzir alguma alteração estrutural do negócio que pudesse justificar a correcção ocorrida. Não era o caso. Evidentemente, que a empresa sofreria algumas contrariedades de curto-prazo mas o contexto de crescimento de longo prazo mantinha-se/mantém-se intacto.

Resultado: A empresa estava a um PER ainda mais atractivo (cerca de 9.5) e portanto decidi reforçar. Reforcei a 19.41, a 20.22 e a 21.29 construindo uma posição de aproximadamente $16.000. Por essa altura começam a surgir rumores de que a empresa poderia a vir ser adquirida por um dos maiores banco dos USA.

A 30/06 o Bank of America anunciou o acordo para aquisição da MBNA com um prémio superior a 30%. Os seus administradores demonstraram o seu entusiasmo por uma aquisição de $35 biliões de dólares numa empresa com uma larga base de clientes, com enorme potencial de crescimento e uma excelente administração.

É claro que assim dá gosto analisar fundamentais. Mas é aqui que eu chamo a atenção do potencial investidor fundamental. Não nos podemos deixar iludir pois esta foi uma situação extraordinária. Caso a OPA não tivesse ocorrido teria de esperar muito mais tempo antes de a ver atingir aqueles preços. É preciso calma, acreditar nos fundamentais e esperar.

Com a venda da posição deste título abri uma nova numa concorrente da MBNA: a Capital One Financial. Também se fala que poderá vir a ser comprada, mas isso pouco interessa. Não abro posições com base em rumores. Tenho é confiança nos fundamentais.

Ficam os dados da MBNA, o gráfico e os movimentos no título. No final, deixo também um quadro com alguns dados comparativos de empresas do sector onde se pode ver, actualmente, a boa posição da Capital One Financial.

quarta-feira, agosto 31, 2005

Análise Pfizer

Más notícias no sector e na própria acção têm castigado a cotação levando-a a valores de 1998 e a PERs mínimos dos últimos 10 anos!

A retirado do mercado de seu medicamento Celabrex bem como o desafio dos medicamentos genéricos têm pressionado este negócio de excelentes rentabilidades e crescimentos de resultados.

Ficam os dados fundamentais aos quais adicionei uma avaliação do seu valor intrínseco recorrendo a uma calculadora da SmatMoney que podem encontrar em (Basta digitar o código do título).

quarta-feira, agosto 10, 2005

Análise Anheuser-Busch

Maior cervejeira do mundo, dona de marcas líder como Budweiser. Um ano mais fraco nas vendas está a castigar a cotação. Estão a perder vendas para outras bebidas como o vinho. Fala-se dum efeito "SideWays", o filme de Alexander Payne nomeado para os óscares 2005 e que tem como pano de fundo o mundo dos vinhos.

Agora eu pergunto. Acham que este efeito conjuntural de curto-prazo vai ter algum efeito estrutural de longo-prazo no negócio de rentabilidades excelentes e com marcas muito fortes da Anheuser-Busch?

A empresa está a transaccionar com um PER de 17, o mais baixo dos últimos 9 anos!

A empresa tem um suporte relevante nos 44.5-45 que foi quebrado na apresentação de resultados do dia 27/07/2005. Já tenho uma boa posição no título da ordem dos $5.000. Abaixo dos 44.5 só reforço se for aos 41.5.

É verdade! O Warren Buffet anda a comprar disto. Anunciou-o em 21/04/2005.

Fica a análise fundamental, a técnica e os movimentos efectuados no título.

+ Dados Fundamentais em (NOTA: Vão ter é que se registar - gratuitamente - no site. Mas vão ver que vale a pena):

Profile - Descrição mais pormenorizada da empresa

Ratios - Comparação de Múltiplos / Taxas de Crescimento / Rentabilidades / Rácios de Dívida com Sector / Indústria / S&P

PS: Nos últimos dias comprei um pouco ($1.000) de Pfizer e de Avon. Hoje vendi $1.000 de Lincare na resistência dos 43.5.

segunda-feira, agosto 01, 2005

Análise Harley-Davidson

Quem não conhece esta marca? Uma empresa de rentabilidades impressionantes e de crescimento de resultados galopantes. No dia do anúncio de resultados (13/04) dilvulgou uma redução da produção de motos para o ano e foi castigada por uns severos 18%/19%. Óptimo. Ficou a preços apetitosos relativamente ao seu valor intrínseco.

Esperei pelo momento técnico ideal que aconteceu numa ruptura com volume em alta de um triângulo ascendente. Como tem um gap por fechar ainda possui um grande caminho a percorrer.

Fica a análise fundamental, a técnica e os movimentos efectuados no título.

quinta-feira, julho 28, 2005

Análise Biomet

Uma excelente empresa com grandes perspectivas futuras afectada por questões técnicas de curto prazo e notícias negativas no que diz respeito a eventuais aliciamentos, já negados pela empresa, de médicos para subscrição dos seus produtos. Representa praticamente 10% da carteira e espero mantê-la e às suas rentabilidades por muito tempo.

Fica a análise fundamental, a técnica e os movimentos efectuados no título.

PS: Continuo a reforçar na Timberland (na zona de suporte dos 34) e vendi um pouco de AIG. Amanhã volto a publicar a carteira actualizada.

sábado, maio 21, 2005


O melhor livro sobre o método de investimento de Buffet elaborado com a colaboração de uma sua ex-nora.

Buffettology: The Previously Unexplained Techniques That Have Made Warren Buffett The Worlds

Americans are infatuated with the stock market. The number of households that own stock has increased from around 20 percent in the early 1980s to over 40 percent today. The market offers the hope of quick wealth and early retirement, and just about everyone who is in the market is looking for an edge, from sources such as CNBC and Wall Street Week to the Beardstown Ladies and "The Motley Fool." So it should be no surprise the most successful investor of our time--Warren Buffett--has been the subject of dozens of books and magazine articles. The value of Buffett's company, Berkshire Hathaway, has increased from $18 per share in 1965 to over $70,000 per share today. The interest in Buffett has spawned an approach to investing called "Buffettology," which is the subject of a book by the same name written by Buffett's former daughter-in-law, Mary Buffett.
In Buffettology, Mary Buffett, with the help of David Clark, details Warren Buffett's approach to investing. It's a style of investing based on the work of Benjamin Graham and one that requires a quality that most investors lack--discipline. Mary Buffett writes, "As you read through this book you will come to see that having a business perspective on investing is more about discipline than philosophy.... In short, other people's follies, brought on by fear and greed, will offer you, the investor, the opportunity to take advantage of their mistakes and benefit from the discipline of committing capital to investment only when it makes sense from a business perspective.... You will find that almost everything that relates to business perspective investing is alien to Wall Street folklore.

Buffettology examines Buffett's methods for valuing companies and selecting stocks--it even encourages you to buy a calculator and work through the valuation formulas that Buffett uses when researching companies to buy. The book not only serves as a useful guide to understanding how Buffett invests, it's an excellent primer to investing in stocks, whether you plan to become a Buffettologist or not. Highly recommended. --Harry C. Edwards, Business editor--This text refers to the Hardcover edition.

Stevin Hoover Hoover Capital Management
Absolutely the best book ever written on Warren Buffett's investment methods.

Outros Livros:
The New Buffettology by Mary Buffet
The Warren Buffett Way, Second Edition by Robert G. Hagstrom
How to Think Like Benjamin Graham and Invest Like Warren Buffett by Lawrence A. Cunningham
The Warren Buffett Portfolio : Mastering the Power of the Focus Investment Strategy by Robert G. Hagstrom
The New Buffettology: How Warren Buffett Got and Stayed Rich in Markets Like This and How You Can Too! by David Clark
Trade Like Warren Buffett (Wiley Trading) by James Altucher

A minha análise fundamental!

Aprendi finanças na Faculdade de Economia do Porto. Balanço, Demonstrações de Resultados, Cash Flows, Múltiplos de Mercado, ...

No entanto, toda essa matéria dada em série aos alunos só começou a fazer sentido quando comecei a vasculhar em livros e artigos (muito mais práticos do que os manuais da Faculdade) sobre o método de investimento fundamental utilizado por Warren Buffet (este inspirado pelos ensinamentos de Benjamin Graham). Aí tudo se simplicou na minha cabeça. Descobri um guia, uma linha de pensamento que me organizou e instituiu um método.

Nos próximos posts vou falar sobre esses ensinamentos...

terça-feira, maio 17, 2005

Stock Market Lies

Stock Market Lies
By Richard Gibbons May 2, 2005

Value investors are independent thinkers. They don't need the crowd to validate their ideas, nor do they act contrarian simply for the sake of being different. While Sun Microsystems (Nasdaq: SUNW) and JDS Uniphase (Nasdaq: JDSU) were zooming up at the height of the tech bubble in the late 1990s, Warren Buffett was criticized as being out of touch with the realities of the new economy. Now that the bubble has popped, Buffett's company, Berkshire Hathaway, is close to all-time highs, while Sun and JDS Uniphase investors have been slaughtered.

Buffett wasn't avoiding technology just to be a contrarian. Berkshire's portfolio has piles of great businesses bought at reasonable prices, not just cheap businesses bought when nobody else wanted them. Companies like American Express (NYSE: AXP) and Moody's (NYSE: MCO) can hardly be considered cigar butts, but they've made Buffett wealthy nevertheless. Buffett's success can be attributed to well-reasoned purchases made within an investing framework based on value principles.

This approach sharply contrasts with most of the financial industry, which is why it is an interesting exercise to examine, from a value perspective, the disinformation that the financial industry pitches at investors every day.

"If you were out of the market for the best 30 days in the past decade, you would have lost money."
Mutual fund advisors often use this statistic to urge investors to stick with them for the long term, despite the fact that advisors themselves tend to be traders -- the typical managed mutual fund has an average turnover rate of 85%. But while being shocked and appalled at such hypocrisy is an entertaining hobby, it's also worthwhile to analyze the reasoning behind the claim.

The statistic is accurate: $10,000 invested in the S&P 500 a decade ago grew to almost $25,000 today (excluding dividends), while without the best 30 days, it would be worth only $7,700. But before making conclusions about market timing, consider the opposite statistic: If you were out of the market for the worst 30 days, you would have made $76,000. If the first statistic is saying that you should remain invested at all times, this statistic seems to be saying that trading to avoid bad days is critical. What gives?

Neither case is accurate. Rather, the statistic is used as propaganda to help fund companies pitch their funds and discourage investors from selling. There are many good reasons to be a long-term investor, including tax-free compounding, reduced expenses, and reduced risk. But this statistic is not a good reason.

What do these statistics mean to the individual investor? It's not clear, except that if you're a trader, some bad or good luck on a few select days could have very dramatic effects on your portfolio. But as a value investor, I think of some potential benefits of a margin of safety. By buying a stock at a discount to its intrinsic value, I'm likely to avoid the worst of the fallout on those worst 30 days, and my long-term performance should be superior.

"The trend is your friend."
This catchy one-liner reflects the momentum that stocks gather: Stocks going up tend to keep ascending, while stocks going down tend to keep falling. The logic driving the claim is a combination of psychology and faith. The psychology is that investors would prefer to buy a stock that's going up and therefore keep pushing it up. The faith is the belief that if something's going up, there must be some reason for it, so it will probably continue to do so.

This reasoning might work for day traders, but it is quite bizarre from a value perspective. First, if a stock is going up, then, all else being equal, it becomes less attractive to value investors because it is approaching -- or exceeding -- its intrinsic value. The upside is less and the downside is greater. Conversely, a stock going down becomes more attractive because both the margin of safety and potential return increase. Value investors love to buy goods when they're on sale. So the trend isn't a value investor's friend, but actually an enemy, like an evil maharaja, Jar Jar Binks, or a berserk koala.

The value investor's true friends are competitive advantages and a margin of safety. Competitive advantages ensure that the company will outperform others for a long time, while a margin of safety dramatically reduces the chance that the value investor will suffer significant losses.

"Run your profits, cut your losses."
This expression is the bedfellow of the "friendly trend" from above -- and with such a nickname, it has many bedfellows, including "buy high, sell higher" and "don't catch a falling knife." It means that if you're making money on an investment, don't sell quickly, but if you're losing money, then run for the hills. Frequently, it's implemented with some sort of stop-loss rule, such as "sell any stock that falls by 10%." The idea holds some appeal, since if you have the same number of winners and losers, but make more on the winners, then you will come out ahead.

However, this reasoning trips over the same stumbling block as momentum investing: It ignores valuation. If a stock has fallen 10% below your purchase price, that does not imply anything about the intrinsic value of the company. If the stock is down on negative news that decreases your estimate of intrinsic value, such as Merck (NYSE: MRK) after its Vioxx withdrawal, or Doral (NYSE: DRL) taking a hit to its balance sheet and changing its business model because of troubles with interest-only strips, then it makes sense to reevaluate the position.

But if the stock falls with no fundamental change, or falls further than is justified by the change in the intrinsic value, then a value investor would be more inclined to increase the position than decrease it. After all, the upside has become bigger and the downside smaller. The intrinsic value of Martha Stewart Living Omnimedia (NYSE: MSO) fell when Martha Stewart went to court, but the share price declined far more than the intrinsic value. Now that the homemaker's troubles seem to be behind her, shareholders who bought during the trial have tripled their investment.

"The market is always right."
Traders say this when the market is not doing what they expect it to do. It generally means that the trader believes his or her reasoning to be incorrect, since the market isn't acting as planned. Consequently, the traders should cut their losses. I love this expression because it's so pessimistic. It reminds me of Eeyore, blue-grey donkey and portfolio manager: "I was just kind of guessing where the stock was going anyway, and I was wrong. Oh, well."

Value investors think this expression is quaint. The market is right occasionally, but overall it tends to be pretty bipolar, with individual stocks priced both above and below intrinsic value. Really, if a stock is priced at less than the discounted value of its expected future returns, then the market is wrong. In such cases, value investors are able to make extraordinary profits both from long-term growth in the business and from the stock returning to intrinsic value. In fact, identifying such stocks is Motley Fool Inside Value's primary goal.

In conclusion
Many common investing expressions don't hold up when examined from a value perspective. However, this can be a great thing, as those who do believe in such maxims may push stocks away from intrinsic values, providing an opportunity for value investors to profit.

Profit From Panic

By Richard Gibbons
April 15, 2005

The mission of Motley Fool Inside Value is simple: We want to find companies trading at prices less than their fair value. In some cases, companies are below fair value simply because the market has failed to appreciate the sustainability of a company's competitive advantage. At other times, companies fall below their fair value during a crisis, when panicked investors flee.

The latter case has the potential for quick returns, but also comes with greater risk. When looking at companies in crises, such as AIG and Doral Financial (NYSE: DRL) right now, it can be challenging distinguishing between a company just suffering a flesh wound and one on its deathbed.

When you do identify a potential turnaround, it can be quite lucrative. Consider Martha Stewart Living Omnimedia (NYSE: MSO). When Martha Stewart's insider-trading fiasco first made the news, it was possible to pick up shares at less than $7. These shares traded above $35 this year, for a pleasant 400% return. Much larger multibaggers over the course of years are easily within reach. The difficulty, though, is determining who will survive and prosper. With that goal in mind, here are some of the issues I consider when trying to profit from panic.

LiquidityIn a crisis, cash gives a company the time and flexibility to survive a rough patch and reorganize its business. It's critical to get a good feeling for the degree to which cash on the balance sheet and future cash inflows are able to cover future cash outflows. Of course, the event causing the crisis often reduces operating cash flows, so using historical cash flow numbers can be deceptive. Instead, start with historical numbers and come up with a pessimistic approximation of the extent to which the negative event will impact cash flows, and how much cash outflows can be reduced over the short term, through, say, delaying capital expenditures.

If the company is close to the edge, there's a good chance it will topple over, so it should be avoided.

Even if the cash flow looks good, another liquidity issue to consider is debt. Even if it seems clear to shareholders that the company has enough cash flow to survive, banks and other lenders can be skittish. So it's a good idea to examine absolute levels of debt and future debt maturities. If the company is highly leveraged, or a substantial portion of its debt is coming due in the next few years, then the company may be unable to roll that debt over to future maturities. Often, it's not the slow draining of cash resources that leads to bankruptcy, but rather a large debt maturity that the company is unable to roll over or repay.

Asset strengthWhen it comes to turnarounds, the balance sheet can count more than the income statement. I've already talked about debt. Another factor to consider is the strength of the assets, because all assets are not equal. Cash is the best asset, since it gives maximum flexibility.

Other good assets include securities and non-depreciating physical assets that can potentially be sold, such as real estate. Because of the rules of accounting, real estate can be particularly strong because it may be listed on the balance sheet at significantly less than its present value.

However, there are also bad assets that generally cannot easily be sold or generate cash. Such assets include goodwill and tax assets. Goodwill is useless because it's intangible, while tax assets can only be converted into cash when the company has operating profits, generally after the crisis has passed. So when considering a company's survival prospects, it's best to heavily discount the value of these assets.

The competitive positionPreferably, we're buying the beaten-down company not just for its assets but also for its future operating performance. Ideally, the company is suffering from temporary bad news, but its long-term competitive position is intact. Maybe the company will show poor results for a year or two, but is likely to prosper after that time. Or perhaps the company has suffered a permanent setback but is still strong enough to be a viable business.

In late 2001, terrorism fears hit the travel industry. At the time, people were talking about how far the airlines would fall, and which airlines would survive. But really, the travel recovery play wasn't in airlines. Sure, people who perfectly timed AMR's (NYSE: AMR) crisis in 2003 could have earned 500% returns. But they would have been assuming a lot of risk buying into an extremely volatile industry with fleeting competitive advantages.

Instead, the simple and safe travel industry play was the hotels. Hotels have competitive advantages both in terms of location and brand. Plus, hotels often own real estate that can provide a cushion to help avoid liquidity concerns. A September 2001 purchase of Starwood Hotels and Resorts (NYSE: HOT) or Hilton Hotels (NYSE: HLT), two of the largest hoteliers, would have returned 100% within a year, or 200% had you decided to hold until now.

Bringing it togetherA good example of all these issues is National Health Investors (NYSE: NHI), a REIT that primarily owns nursing homes. As you can see in this chart, National Heath Investors was flying along quite happily when it hit the perfect storm. The Balanced Budget Act of 1997 cut Medicare revenues to its nursing home operators, the companies that lease National Health Investors' buildings. Consequently, many operators went bankrupt. Plus, it was affected by overbuilding and labor shortages. Finally, lawsuits in Florida were destroying the business there.

Confronted with these challenges, National Health collapsed like Mr. Bean sparring with Evander Holyfield. I became interested, and bought some at $15. This was a wee bit early, since it cratered below $5 when the company discontinued its dividend only six months later. But this wasn't a technology company. It had solid real estate assets in a time of falling interest rates.

Cash flow was still positive. The entire industry was unlikely to vanish: Somehow, someone would take care of the elderly. So I bought more at $5, and it started to look like the industry was recovering.

But National Health owed money to the banks. And the banks panicked, demanding repayment. So National Health was forced to sell convertible preferreds at a time when the stock was low, diluting existing shareholders. I bought more in the $6 range. Cash flow was still good, nursing home operators were coming out of bankruptcy, and the balance sheet, never really overleveraged to begin with, now looked quite clean. It was difficult to see how National Health could fail.

Now, four years later, the stock is trading around $25. That's lower than it would be if it hadn't been forced to issue the convertible, but it's still a decent return. For months, value investors bought in the $6 range, and those investors have seen a 400% return. What's more, since National Heath has a $1.80 dividend, investors at $6 are now seeing an annual dividend of 30% on their original investment. I sold out at $22.

The keys in this case were that cash flow was positive, leverage was reasonable, the assets were strong, and there were signs that the industry would turn around. Even then, the debt maturity hurt shareholders significantly, because nobody wanted to lend to companies in the sector. This is why, when analyzing these turnaround situations, it is critical to consider debt maturities.ConclusionEvaluating these factors can help you find and identify turnaround plays that lead to extraordinary profits. For instance, in 2002, both Philip Durell, Inside Value's chief analyst, and I independently recognized that Providian Financial (NYSE: PVN) had a decent chance of rebounding, and we both bought well under $5. It's now around $17. If you want to learn about what Philip sees as the great value plays right now, and see all of his historical recommendations, a free 30-day trial is available. Or, for a limited time, Philip is offering Inside Value at a 25% discount to the regular price. To find out more, click here.

Selecting Stocks Using ROE

Have you ever wondered why two similar companies can have vastly different prospects and returns? You could look at earnings per share, but knowing if a company is underperforming is less important than figuring out why. Breaking apart return on equity can determine that a company's operations are improving before the market notices.

By Bill Mann (TMF Otter)
April 28, 2004

Ever wonder why some companies succeed while similar companies fail to generate the same returns for shareholders? One of the key elements is a company's ability to turn the shareholder equity it holds into profits. It's one of the key elements that Mathew Emmert looks for in his dividend-paying stocks featured in Motley Fool Income Investor. In fact, it's an element that every investor should keep in the ol' toolbox for evaluating securities.

It doesn't get the same treatment as earnings per share, it doesn't gain much cult status like free cash flow, and you'll never, ever hear the folks on Bubblevision using the term. But return on equity (ROE) matters. It shows how good a company is at generating money based on the retained shareholder equity, also known as money that the company could return to you. This is an important number for dividend payers as it shows how well the company is generating returns for the next dividend. A consistently low ROE is a sign that the company's management isn't effectively deploying the resources at its command.

Moreover, relative return on equity within an industry can tell investors which companies are well run, and which are not. Ever wonder why Ralph Lauren (NYSE: RL) was such a lousy investment for so many years even though everyone seemed to have one or two pieces of Polo clothing in their closets? Look no farther than a chronically anemic ROE.

The basic calculation for return on equity is dazzlingly simple: net income divided by shareholders' equity (book value). But this calculation hides some more nuanced information that not only indicates a company is generating poor returns, but also why. The return on equity calculation, as simple as it appears, is actually a combination of several critical components relating to profit margins, asset turnover, debt, and debt servicing. Break this calculation down into its elements and you'll get an astounding amount of information about a company, its trends, and its performance relative to its competition.

Permit me to demonstrate by looking at two similar companies: American Eagle Outfitters (Nasdaq: AEOS) and Abercrombie & Fitch (NYSE: ANF). American Eagle has 800 stores, Abercrombie 700. American Eagle's trailing 12-month revenues exceeded $1.5 billion, Abercrombie's $1.7 billion. These are not huge differences, and yet Abercrombie is valued 50% higher than American Eagle Outfitters. One hint why: Abercrombie & Fitch has an ROE exceeding 25%, while American Eagle Outfitters' is less than 10%.

Does this mean that the companies' book values are wide apart? Again, no -- they are quite close. Obviously, the return component for American Eagle is far inferior to that of Abercrombie. Let's dig in and figure out why. Keep in mind this formula for ROE: [(operating profit margin)(asset turnover) - (interest expense rate)](leverage)(tax retention rate).

Item 1. Operating profit marginSimple enough. By dividing EBIT (earnings before interest and taxes) by sales, you find out how much money the company made from operating activities before the taxman and the noteholders get their lucre, and you want to see how much in revenues it took to generate this amount. A company could sell billions of dollars' worth of product, but if its expenses consistently equal or exceed its revenues, it's more like a turnstile than a business. Right out of the gate, we can see a big discrepancy between our two case-study companies. Abercrombie has an operating profit margin of 19.4%, while American Eagle's is 6.9%. At those rates, it would take American Eagle nearly three times the sales to generate the same gross operating profit.

Item 2. Asset turnoverI love this measure -- it's where places like Costco (Nasdaq: COST), Claire's (NYSE: CLE), and Home Depot (NYSE: HD) really shine. Compared to the level of assets, how much in revenues did the company generate? So we use this formula: sales divided by average assets. (Note we're talking average assets, not the raw number at the end of the reporting period.) For American Eagle, the turnover is 1.89 times, while for Abercrombie it's 1.53 times, so American Eagle is actually better in this regard.

Item 3. Interest expense rateRemember, in Item 1 we backed out interest payments. That's because we want to be able to view leverage separately from operations. If a company is operating well but is simply drowning in debt, that would be useful information -- and if in future periods you notice the debt level dropping, you might have yourself an underappreciated stock. Stranger things have happened. What we're looking for here is how much interest the company is paying to maintain its asset base, so the formula is interest expense divided by assets. Abercrombie, rather than paying interest, generates it from the cash in the bank, so it actually has an interest expense rate of negative 0.3%. Ditto American Eagle, which comes in at minus 0.4% Nice.

Item 4. LeverageWait a minute, didn't we just get finished determining that neither company had any interest expenses? I guess that means we can scribble in a zero for both and move on, right? Not so fast. While neither had interest-bearing debt, both have plenty of operating, short-term leverage -- accrued expenses, accounts payable, even unredeemed gift cards. Still, this component's pretty simple to calculate. The formula is average assets divided by average shareholders' equity (remember the average part). American Eagle comes in at 1.31, while Abercrombie & Fitch is 1.37 times -- nearly identical.

Item 5. Tax retention rateCan you hear Billy Bragg talking with the taxman about poetry? No? Well, Uncle wants his cut, and although we'd love to be able to quote returns net of tax, that doesn't really capture the whole picture. The calculation here is the reciprocal of the tax bite, that is: 1 minus the tax rate. To calculate, take the provision for income taxes and divide it by the income before income taxes, then take this sum and subtract it from 1. Abercrombie's tax rate is 38.8%, so its retention rate is 61.2%. American Eagle's tax rate is 43.4% (yikes!), so it retains 56.6%.

In sum we have the following equations:

Abercrombie & Fitch:[(0.194)(1.53)-(-0.003)](1.37)(0.612) = 0.2514, or 25.1%

American Eagle:[(0.069)(1.89)-(-0.004)](1.31)(0.566) = 0.0997, or a smidge below 10%

A look at most of these component numbers shows something striking. They're dramatically similar for the two companies with one glaring exception -- operating profit margins (though, I must admit I'm a bit perplexed by the high tax rate at American Eagle). Abercrombie is far more efficient at keeping costs down, and it shows in net profits -- and in return on equity.

Here's where else it shows: On marginally higher annual sales, Abercrombie is valued at a billion dollars more in market capitalization than American Eagle. What's tougher for American Eagle shareholders is that the ROE has declined from well above 29% in 2001 to today's 10%. You can see this trend quite clearly in the most recent 10-K with the company having added more than 10% new retail space only to capture 3.9% higher revenues.One thing to keep in mind is that companies granting tons of stock options without expensing them (neither of the two in the example) can skew results in two ways. First, earnings -- the numerator -- will be overstated.

Second, many companies counteract the impact of options dilution by buying back shares. The money for this comes straight from the equity account, so the denominator may be substantially understated. I always read the management discussion and add back every penny to equity that was used to buy back shares to hide dilution. They don't call it shareholders' equity for nothing.

Risky Business?

By Mike Klein
May 10, 2005

Risk isn't easy to define. I won't skydive, even if the data says my parachute will open every time. The downside is just not OK with me. But other people do it all the time -- they accept the risk. Some people won't fly on airplanes, but to me the data shows it's one of the safest forms of transportation. That let me fly to Omaha for the Berkshire Hathaway annual meeting.

There is a lot made about investing risks. Much of this is to sell you investment products that make money for someone else. But there is a simple investing strategy that reduces risk and delivers market-beating results. Read on...

You can't beat the marketThe investing concepts of risk/return trade-off, diversification, and the inability to beat an efficient market all have their roots in a 1952 paper written by MIT economics graduate student Harry Markowitz titled "Portfolio Construction." Markowitz set forth the relationship between returns and volatility, concluding that investors must subject their portfolios to higher volatility in order to earn higher returns. He also found that strategic diversification -- based on reducing correlation between investments -- reduces a portfolio's volatility but also cuts into gains. Markowitz won a Nobel Prize for his work.

His ideas have taken hold in the financial world, far beyond what Markowitz ever dreamed. You can see those ideas at work when the Wall Street elite talk about asset allocation, risk tolerance, and efficient markets. Your local financial planner will probably tell you that owning individual stocks is risky and that you should invest in index funds and diversify still further with bonds and cash. Furthermore, you will hear that in the long run, you cannot beat the market.

Return without the risk?Markowitz may have won a Nobel Prize, but Warren Buffett has beaten the market soundly for 50 years running. The handful of other investors who use Buffett's basic principles have market-beating records of 20, 30, or more years. What's more, Buffett and those who follow his principles have achieved their gains without subjecting themselves to enormous risk. How can this be? Are these accidents, freaks of probability, or luck?

None of the above. These extraordinary investors have told us for decades how they achieve their results. Charlie Munger, Berkshire Hathaway's vice chairman and Buffett's business partner, didn't mince words last year: "Diversified portfolios are madness! It's taught in all the business schools, and it's wrong." Excuse Charlie for being blunt, but he sure gets his point across, and he's right.

What's the secret?How can an individual investor achieve great returns while cutting risk? Let's detour for a moment to understand why investment firms sell diversification. They need to make a consistent profit to keep their own shareholders happy. In the 1970s, seeing the opportunity to sell a broad range of products under the guise of diversification, brokerages latched onto Markowitz's ideas and commercialized them.

Investment houses sell investing as a science -- follow our formula and you'll do fine, they say. They collect 1% or 2% a year to let you use their science, whether or not your investments perform well. And the more you trade -- in accord with their science -- the more they make in commissions. This approach achieved two things for these firms: they got more money to manage and they tapped a consistent source for revenue and profits. Unfortunately, this approach prevents people like you and me from getting the best possible return on our money.

Volatility is your friend!The most important difference between Buffett, Munger, and other value investors and Markowitz's followers is their definition of risk. In most of the financial community, stocks that go up and down a lot are considered "risky." Cisco (Nasdaq: CSCO), JDS Uniphase (Nasdaq: JDSU), and all manner of troubled companies are examples. Wall Street trades these stocks under the assumption that you have to ride the wave of these volatile stocks to get great returns -- all the while ignoring whether these companies are financially sound.

Conversely, Buffett and other value investors buy stock in high-quality companies when they are selling for less than they are worth. Value investors wait patiently for volatility to bring the stock price down well below its true value, then they buy it. In other words, they use volatility to their advantage. With this strategy, volatility can be used to lower risk! That's completely opposite conventional wisdom.

So where's the risk? There has to be some -- but when you buy shares for less than they're worth, there isn't as much of it. The stock could fall more, but it's much more likely to go up. The risk is even further reduced by considering only high-quality companies. Buffett loves it when the markets slide because it lets him find great companies selling at discount prices. That is value investing in a nutshell, and it works.

Diversification? Or diworsification?According to Markowitz, diversification reduces risk. But Markowitz looked only at volatility. He didn't examine buying stocks at a discount or the quality of a company. By using the principles of value investing, we reduce risk by buying low and considering only good companies. That changes the assumptions underlying the trade-off between risk and reward and reduces the need for the products investment firms try to sell.

Some diversification is still important to ensure that if something very unusual happens to one or two stocks, your portfolio isn't wiped out. But instead of needing to own a broad index fund, or hundreds of stocks, you can diversify with 10 to 20 well-picked stocks. For starters, a free trial to Motley Fool Inside Value will provide a list of attractive investments, along with intelligent analysis and commentary on the active Inside Value discussion boards.

Find attractive value stocksFrequently, stock prices are pushed down by the overreactions of short-term investors. Look no further than pharmaceutical giants Merck (NYSE: MRK) and Inside Value pick Pfizer (NYSE: PFE) for evidence. While they have had real problems recently, investors have overreacted and the stocks are good buys today for long-term owners. The stock of soft-drink behemoth and Inside Value recommendation Coca-Cola (NYSE: KO), with brand-name strength and a global distribution network second to none, is also selling at unusually low prices. Although we have yet to hear the second shoe drop, AIG (NYSE: AIG) is a fundamentally solid business whose stock price has been punished by short-term events.

Motorcycle maker Harley-Davidson (NYSE: HDI) is another potential example: a great brand with growing revenues, excellent profitability, a strong balance sheet, and a unique product.

Harley's stock was knocked down about 20% a couple of weeks ago because of a reduced earnings forecast.The hardest part of value investing is figuring out what a stock such as AIG is worth. This is where Inside Value comes to the rescue. Every month, Philip Durell recommends two stocks that have passed his rigorous value screening and analysis based on business fundamentals. His past picks range across industries and provide the only diversification a portfolio needs: 20 high-gain, low-risk companies.

Using DCF Foolishly

Just because you have a set of tools does not mean you can build a house. You have to know how to use the tools properly by understanding where they work and where they don't. The same applies for Fools using the discounted cash flow (DCF) analysis tool.

By David Meier March 28, 2005

I consider myself a value investor. To me, all that means is that I am price-conscious. It doesn't matter what type of company I look at or what its situation is. The bottom line is that I refuse to pay more than an investment is worth.

If I am not going to pay too much, then I have to make an estimate of an investment's value. There are different ways to calculate value; you have probably seen many of them in the Fool's School. But today I want to focus on the discounted cash flow analysis.

John Burr Williams developed the idea in the '50s, and Warren Buffett has evangelized it in the years since. Despite its power and simplicity, there are areas where we need to tread carefully. Used Foolishly, DCF can be a great friend; used foolishly, DCF can be our worst enemy. So let's look at DCF carefully, because I don't want you to pay too much for an investment.

Here's what we're up againstFirst, we need the equation. You may already know it, but I'll present it here for reference:

Value = Sum[Cash Flow(t)/(1+k)^t] from t = 1 to infinity

We'll call this the long form. All you need to do is predict all of the future cash flows and discount them back to the present at the rate of k. What could be easier? For simplicity, we'll define "cash flow" as cash flow from operations minus capital expenditures.

Pitfall No. 1: We don't know jackI know that sounds harsh, but it's the truth. We cannot consistently predict the cash flows and their growth rates with any accuracy; the business environment is far too dynamic. Of course, we should try to make the best estimates we can. And that means being careful about our assumptions and predictions because we don't want to have the pitfalls of the equation work against us.

Merck (NYSE: MRK) has been getting the attention of many value investors lately. The Vioxx problems and the court ruling about early patent expirations have caused lots of uncertainty, knocking down the stock price. Using our definition, Merck earned $7 billion in cash flow in 2004. Should that be the starting point? No. Do we know the cash flow reduction from the two issues stated above? I read one report that said the Vioxx lawsuit could cost $4 billion to $30 billion. No precision there. Will two people using the same information predict the same value? Not likely.

The equation is not for calculating precise answers, like in physics and engineering. I think it is Foolish for making estimates based on personal judgments. The better the judgment, the better the estimate.

Pitfall No. 2: Stay away from critical mass situationsThere is a simplified form of this equation, assuming constant growth and a constant discount rate.

Value = Cash Flow(t = 0)*(1+g)/(k-g) where
g = growthk = discount ratet = 0 is the cash flow from the previous year

One reason we cannot rely on the equation for precise answers is that there is a point of critical mass. In 1946, scientist Louis Slotin died from radiation poisoning after he accidentally let two half-spheres of beryllium-coated plutonium touch during an experiment. When the two halves touched, they reached the critical mass required to sustain a nuclear reaction.

The equation above is valid only if the discount rate is greater than the growth rate (k > g). If k is less than or equal to g, the equation is undefined. Our critical mass pitfall comes when g starts to get close to k. As this happens, value starts to get really big, really fast.

For illustration, let's look at Google (Nasdaq: GOOG). My gut tells me that Google is overvalued. But my gut and a quarter won't get me a cup of Starbucks coffee. From 2004 financial statements, we know everything in the upper half of the table. We don't know the growth rate.

So let's assume a discount rate and solve for growth.

(on 12/31/2004)

Diluted Shares
Market Cap


Enterprise Value

Assume k
Solve for g
k - g
Note: Dollar values in millions.

The results tell us that cash flow needs to grow at 23.4% per year from now until infinity to achieve a 25% annual return. So in year 19, Google will have to generate $35.7 billion in cash. For comparison, Microsoft (Nasdaq: MSFT) generated $13.5 billion of cash in its 19th year as a publicly traded company. That's a lofty goal. Does it mean that Google is overvalued? I don't think we can say from this equation. The validity of the answer breaks down because we are too close to the critical mass point, where k equals g.

Pitfall No. 3: Money for nothing…So if the simplified form of the equation is breaking down, what about using the long form? We can break the equation into parts: a fast-growth part and a slower-growth part. Let's assume that Google can grow cash flow at 100% per year for the next five years and at a slower rate after that. Again, let's use a discount rate of 25%. I know you Fools are wondering how I can have a growth rate higher than the discount rate. In the long form of the equation, there's nothing that says we can't. But let's think carefully about what that means.

Essentially, it means that we are getting money for nothing. It implies that the cash flows are more valuable simply because they are growing. It also implies that our investment has infinite value and that we are guaranteed a return no matter what price we pay. We both know those are foolish notions.

At the Berkshire Hathaway annual meeting, Warren Buffett referred to this as the St. Petersburg Paradox, based on a paper by David Durand. No investment has infinite value. So we have to be very careful using g > k for extended periods of time.

Should we throw DCF out the window?An emphatic no! We just need to use it Foolishly. Here's what I recommend:

1. Be conservative.Aggressive analyses can lead to inflated values and cause you to pay too much. Pay too much, just like incurring high transaction costs, and you get lower returns.

2. Think about your assumptions and gather contrasting viewpoints.Poor assumptions based on viewpoints that are the same as yours can lead to aggressive analysis. And we know where that can lead.

3. Use a margin of safety.Sorry. Despite the fact that you are conservative doesn't mean your answers are more accurate. Have the courage to pay significantly less than your estimate of value. Your family will thank you down the road.At the Inside Value website, Philip Durell has a wonderful DCF calculator to help you with your analyses. Take a free trial of the newsletter for 30 days to access the tool and see how Philip is using it to value his recommendations. Not coincidentally, he is outperforming the market.

Buffett by Numbers

Want to invest like Buffett? We derive the method Buffett uses to analyze the quantitative worth of a company.

By Jim Schoettler May 10, 2005

My last article provided an overview of Warren Buffett and the evolution of his investment philosophy. But what specifically led Warren Buffett to invest in such diverse companies as Coke (NYSE: KO), The Washington Post (NYSE: WPO), Gillette (NYSE: G), General Dynamics (NYSE: GD), Freddie Mac (NYSE: FRE), and others?

Today, we begin to answer that question by deriving the method Buffett uses to analyze the quantitative worth of a company: the Discounted Cash Flow equation.

DisclaimerBefore we go any further, you should know that this article is all about math. If you are the type of person who simply turns to the back of the book for answers, then the following may not be for you. But if you're the type of person who just has to know the ins and outs of the equations you rely on to value companies (or if you just love math), then read on.

Derivation of the DCFLet's get started with a definition:

The Discounted Cash Flow model determines the present value of a company by estimating its future cash flows, discounting those cash flows to present value, and summing these discounted values.

Well, that seems pretty straightforward! Fortunately, we can make this much more complicated by looking at the details. Let's take the definition one part at a time.

Estimating future cash flowsLet's say Company X has a current cash flow of $100 per year, and its cash flows are growing at 10% for each of the next five years. All we have to do to estimate the future cash flows is multiply each yearly value by (1 + growth rate), or 1.10:
Cash Flow* (prior year)
x Growth factor
Cash flow*
*Cash values are rounded to the nearest dollar.

Mathematically, given a growth factor (g), the future value (FV) in year n can be calculated from the present value (PV) with the equation:

FV = PV x (1 + g)n (Equation 1)

For year four in the above table, this gives us:

100 x (1 + 0.10)4 = $146

Present value in the DCF modelFor a clear description on the concept of present value, please check out James Early's recent article. We'll skip ahead and simply present the present value equation:

PV = FV x [1/(1 + r)n] (Equation 2)

Notice that this equation is the inverse of Equation 1. The only difference is that we now use r (expected rate of return) rather than g (growth). This is an important distinction.

The expected rate of return refers to the risk-free return we could expect to get on our money (if we invested in a certificate of deposit, for example).

We use the expected rate of return (or expected return) to calculate the present value of any future amount. For example, say our friend Barney offered to pay us $150 in five years if we gave him $100 today. And let's say our local bank is offering a five-year certificate of deposit paying 5% interest. We can then calculate the present value of that $150:

PV = $150 x [1 / (1 + 0.05)5] = $150 x [1 / 1.055] = $150 x (0.784) = $117

That $150 is actually worth $117 to us today. Assuming we know Barney will pay us back (which we do because he is the most trustworthy talking elephant we know), then loaning him the $100 is a good deal.

The discount factorThe discount factor (DF) is simply the term we use to refer to [1/(1 + r)n]. In the Barney example, our discount factor equals 0.784. By using the concept of a discount factor, Equation 2 simplifies to:

PV = FV x DF (isn't that pretty?)

Don't forget where the discount factor comes from, because we will rely heavily on it later on (in this article and the next).

Discounting future cash flowsLet's run through an example.

Assume Company X is growing cash flow at 10% per year and our (risk-free) expected return is 5% (as above). To find the discounted cash flow from year n (DCFn), we multiply the expected cash flow in year n (CFn ) by our discount factor for year n (DFn):

DCF(n) = CFn x DFn (Equation 3)

The simplest way to complete this for a series of years is in a spreadsheet:

Year (n)
Cash flow (CFn)
x discount factor (DFn)
Discounted cash flow (DCFn)
*Cash values are rounded to the nearest dollar.

Summing discounted valuesThe discounted cash flow valuation is simply a sum of the discounted values:

DCFtotal = $105 + $110 + $115 + $120 + $126 = $576.

Assuming Company X produces no more cash flow after five years (perhaps they go out of business), we would say that Company X is worth $576 today. We can determine whether Company X is fully valued by comparing this calculated value to Company X's actual market value.

The whole shebang: The DCF equation As we saw above, DCFtotal is the summation of the individually discounted values, so we can say:

DCFtotal = DCF(1) + DCF(2) + DCF(3) + ... + DCF(n)

Where n represents the last year of the company's existence (i.e. 50 years from now).
By flushing out Equation 3, we get a specific equation for each DCF(n).

DCF(n) = CFn x DFn = CF0 x (1 + g)n x [1 / (1 + r)n] = CF0 x [(1 + g) / (1 + r)]n

And in summation (chuckle), we can write:

DCFtotal = CF0 x SUM[(1 + g) / (1 + r)]x for x = 0 to n (Equation 4)

And that is our Discounted Cash Flow equation!

NOTE: Under specific conditions we can simplify this equation to calculate values far into the future. We take a look at the assumptions this requires in my next article.

Strengths of the DCF modelThe DCF model is very flexible. By employing different growth and discount factors, we can easily model companies going through lifecycle transitions (from high growth to average growth, for example). Since the model accounts for expected growth, we can use it as a universal comparison metric: A high-growth company can be compared to a low growth company (or any other company) by analyzing how its calculated value compares with its actual value. This comparison also allows us to estimate an expected return on our investment and can help us limit risk by investing in more established companies with more consistent operating histories (we'll look at this more in a future article).

Weaknesses of the DCF modelThe further into the future we look, the more uncertain our estimates. The chief weakness of the DCF model is its sensitivity to these estimates. Small changes in assumptions can lead to large changes in calculated value. To temper this effect, we should always be conservative in our assumptions. This "glass half empty" approach will increase the likelihood that we will be pleasantly surprised rather than sorely disappointed.
For more on the benefits and pitfalls of the DCF model, read David Meier's illuminating column, "Using DCF Foolishly."

What's next?As a Foolish investor, you must certainly be wondering about the actual values we use in the DCF equation: What cash flow numbers? Where do we find growth values? What is my risk free expected rate of return?Deriving the DCF equation and answering all of those questions in the same article would just be too much fun. Have heart. My next article covers all of those questions (with much less math).

sexta-feira, maio 13, 2005


Serve o presente para declarar o blog soperdequemtem aberto. Pretende-se com este blog expôr bitaites bolsistas decorrentes da análise técnica e fundamental.

Esperem por novidades e recordem essas oito grandes máximas da bolsa:

"Só perde quem tem!"
"É pô-lo e vê-lo ir..."
"É preciso é calma e descontraccione!"
"Isto é tudo muito complexo!"
"Isto é só para burros que sabem ler!"
"Estava-se mesmo a ver!"
"Isto sobe de escadinha e desce de elevador!"
"Quem sabe, sabe!"