Contents Foreword Introduction Hit the Ground Running—Valuation Basics Chapter 1 : Value—More Than a Number! Two Approaches to Valuation Why Should You Care? Some Truths about Valuation Start Your Engines! Chapter 2 : Power Tools of the Trade Time Is Money Grappling with Risk Accounting 101 Making Sense of Data The Tool Box Is Full Chapter 3 : Yes, Virginia, Every Asset Has an Intrinsic Value Value the Business or Just the Equity? Inputs to Intrinsic Valuation What Do These Models Tell Us? It’s All in the Intrinsic Value! Chapter 4 : It’s All Relative! Standardized Values and Multiples Four Keys to Using Multiples Intrinsic versus Relative Value Einstein Was Right From Cradle to Grave—Life Cycle and Valuation Chapter 5 : Promise Aplenty Valuation Issues Valuation Solutions Are We Missing Something? Chapter 6 : Growing Pains Valuation Issues Valuation Solutions Chapter 7 : Valuation Viagra Valuation Issues Valuation Solutions Can Changing Management Change Value? Chapter 8 : Doomsday Valuation Issues Valuation Solutions Breaking the Mold—Special Situations in Valuation Chapter 9 : Bank on It Valuation Issues Valuation Solutions Chapter 10 : Roller-Coaster Investing Valuation Issues Valuation Solutions The Real Option Argument for Undeveloped Reserves Chapter 11 : Invisible Value Valuation Issues Valuation Solutions Conclusion Little Book Big Profits Series In the Little Book Big Profits series, the brightest icons in the financial world write on topics that range from tried-and-true investment strategies to tomorrow’s new trends. Each book offers a unique perspective on investing, allowing the reader to pick and choose from the very best in investment advice today. Books in the Little Book Big Profits series include: The Little Book That Still Beats the Market by Joel Greenblatt The Little Book of Value Investing by Christopher Browne The Little Book of Common Sense Investing by John C. Bogle The Little Book That Makes You Rich by Louis Navellier The Little Book That Builds Wealth by Pat Dorsey The Little Book That Saves Your Assets by David M. Darst The Little Book of Bull Moves by Peter D. Schiff The Little Book of Main Street Money by Jonathan Clements The Little Book of Safe Money by Jason Zweig The Little Book of Behavioral Investing by James Montier The Little Book of Big Dividends by Charles B. Carlson The Little Book of Bulletproof Investing by Ben Stein and Phil DeMuth The Little Book of Commodity Investing by John R. Stephenson The Little Book of Economics by Greg Ip The Little Book of Sideways Markets by Vitaliy N. Katsenelson The Little Book of Currency Trading by Kathy Lien The Little Book of Alternative Investments by Ben Stein and Phil DeMuth The Little Book of Valuation by Aswath Damodaran Copyright © 2011 by Aswath Damodaran. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. 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For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Damodaran, Aswath. The little book of valuation : how to value a company, pick a stock and profit / Aswath Damodaran. p. cm. — (Little book big profit) ISBN 978-1-118-00477-7 (cloth); 978-1-118-06412-2 (ebk); 978-1-118-06413-9 (ebk); 978-1-118-06414-6 (ebk) 1. Corporations—Valuation. 2. Stocks—Prices. 3. Investment analysis. I. Title. HG4028.V3D3535 2011 332.63′221—dc22 2010053543 To all of those who have been subjected to my long discourses on valuation, this is my penance. Foreword If you take a moment to think about it, stock exchanges provide a service that seems miraculous. They allow you to exchange cash that you don’t need today for a share in a claim, based on the future cash flows of a company, which should grow in value over time. You can defer consumption now in order to consume more in the future. The process also goes in reverse. You can sell shares in a company for cash, effectively trading tomorrow’s potential for a certain sum today. Valuation is the mechanism behind this wondrous ability to trade cash for claims. And if you want to invest thoughtfully, you must learn how to value. As a student and practitioner of valuation techniques throughout my career, I can say without hesitation that Aswath Damodaran is the best teacher of valuation I have ever encountered. I have attended his lectures, consulted his books, pored over his papers, and scoured his web site. He combines remarkable breadth and depth with clarity and practicality. He intimately knows valuation’s big ideas as well as its nooks and crannies, and delivers the content in a useful and sensible way. If you are looking to learn about valuation from the master, you have come to the right place. The Little Book of Valuation may not be large, but it packs a lot of punch. You’ll start off learning about the basics of discounted cash flow and quickly move to valuation multiples. Professor Damodaran also frames a proper mind-set—valuations are biased and wrong, and simpler can be better—and emphasizes the difference between intrinsic and relative approaches. His discussion of the pros and cons of popular valuation multiples is especially useful. Valuing businesses at different stages of their lives is tricky. For example, how do you compare the relative attractiveness of a hot initial public offering of a company boasting the latest whiz-bang technology to a stable but staid manufacturer of consumer products? In the heart of the book, Professor Damodaran helps you navigate the valuation issues that surround companies at different points in their life cycles, providing vivid and relevant examples that help cement the ideas. The book’s final section guides you in dealing with some of the special situations that you are likely to encounter. For instance, valuing a company that relies on a commodity that rises and falls like a roller coaster is an inherently thorny problem. So, too, is valuing a company that pours money into research and development with little that is tangible to show for it. These are some of the valuation challenges you will face as a practitioner, but are also among the most rewarding. Don’t put the book down until you have read, and internalized, the “10 Rules for the Road” in the conclusion. They effectively meld good theory and practice, and will guide you when you reach a point of uncertainty. Valuation is at the core of the economic activity in a free economy. As a consequence, a working knowledge of valuation’s broad concepts as well as its ins and outs is of great utility. Aswath Damodaran has done more to bring these ideas to life than anyone I know. I hope that you enjoy The Little Book of Valuation and profit from its lessons. Michael J. Mauboussin Michael J. Mauboussin is chief investment strategist at Legg Mason Capital Management and an adjunct professor at Columbia Business School. Introduction Do you know what a share in Google or Apple is really worth? What about that condo or house you just bought? Should you care? Knowing the value of a stock, bond, or property may not be a prerequisite for successful investing, but it does help you make more informed judgments. Most investors see valuing an asset as a daunting task—something far too complex and complicated for their skill sets. Consequently, they leave it to the professionals (equity research analysts, appraisers) or ignore it entirely. I believe that valuation, at its core, is simple, and anyone who is willing to spend time collecting and analyzing information can do it. I show you how in this book. I also hope to strip away the mystique from valuation practices and provide ways in which you can look at valuation judgments made by analysts and appraisers and decide for yourself whether they make sense or not. While valuation models can be filled with details, the value of any company rests on a few key drivers, which will vary from company to company. In the search for these value drivers, I will look not only across the life cycle from young growth firms such as Under Armour to mature companies like Hormel Foods, but also across diverse sectors from commodity companies such as Exxon Mobil, to financial service companies such as Wells Fargo, and pharmaceutical companies such as Amgen. Here is the bonus: If you understand the value drivers of a business, you can also start to identify value plays—stocks that are investment bargains. By the end of the book, I would like you to be able to assess the value of any company or business that you are interested in buying and use this understanding to become a more informed and successful investor. Not all of you will have the time or the inclination to value companies. But this book will give you the tools if you choose to try, and it will provide you with some shortcuts in case you do not. Let’s hit the road. In a web site to accompany this book (www.wiley.com/go/littlebookofvaluation), you can look at these valuation models and change or update the numbers to see the effects. Hit the Ground Running—Valuation Basics Chapter One Value—More Than a Number! Understanding the Terrain Oscar Wilde Defined a Cynic as One Who “knows the price of everything and the value of nothing.” The same can be said of many investors who regard investing as a game and define winning as staying ahead of the pack. A postulate of sound investing is that an investor does not pay more for an asset than it is worth. If you accept this proposition, it follows that you have to at least try to value whatever you are buying before buying it. I know there are those who argue that value is in the eyes of the beholder, and that any price can be justified if there are other investors who perceive an investment to be worth that amount. That is patently absurd. Perceptions may be all that matter when the asset is a painting or a sculpture, but you buy financial assets for the cash flows that you expect to receive. The price of a stock cannot be justified by merely using the argument that there will be other investors around who will pay a higher price in the future. That is the equivalent of playing an expensive game of musical chairs, and the question becomes: Where will you be when the music stops? Two Approaches to Valuation Ultimately, there are dozens of valuation models but only two valuation approaches: intrinsic and relative. In intrinsic valuation, we begin with a simple proposition: The intrinsic value of an asset is determined by the cash flows you expect that asset to generate over its life and how uncertain you feel about these cash flows. Assets with high and stable cash flows should be worth more than assets with low and volatile cash flows. You should pay more for a property that has long-term renters paying a high rent than for a more speculative property with not only lower rental income, but more variable vacancy rates from period to period. While the focus in principle should be on intrinsic valuation, most assets are valued on a relative basis. In relative valuation, assets are valued by looking at how the market prices similar assets. Thus, when determining what to pay for a house, you would look at what similar houses in the neighborhood sold for. With a stock, that means comparing its pricing to similar stocks, usually in its “peer group.” Thus, Exxon Mobil will be viewed as a stock to buy if it is trading at 8 times earnings while other oil companies trade at 12 times earnings. While there are purists in each camp who argue that the other approach is useless, there is a middle ground. Intrinsic valuation provides a fuller picture of what drives the value of a business or stock, but there are times when relative valuation will yield a more realistic estimate of value. In general, there is no reason to choose one over the other, since nothing stops you from using both approaches on the same investment. In truth, you can improve your odds by investing in stocks that are undervalued not only on an intrinsic basis but also on a relative one. Why Should You Care? Investors come to the market with a wide range of investment philosophies. Some are market timers looking to buy before market upturns, while others believe in picking stocks based on growth and future earnings potential. Some pore over price charts and classify themselves as technicians, whereas others compute financial ratios and swear by fundamental analysis, in which they drill down on the specific cash flows that a company can generate and derive a value based on these cash flows. Some invest for short-term profits and others for long-term gains. Knowing how to value assets is useful to all of these investors, though its place in the process will vary. Market timers can use valuation tools at the start of the process to determine whether a group or class of assets (stocks, bonds, or real estate) is under- or overvalued, while stock pickers can draw on valuations of individual companies to decide which stocks are cheap and which ones are expensive. Even technical analysts can use valuations to detect shifts in momentum, when a stock on an upward path changes course and starts going down or vice versa. Increasingly, though, the need to assess value has moved beyond investments and portfolio management. There is a role for valuation at every stage of a firm’s life cycle. For small private businesses thinking about expanding, valuation plays a key role when they approach venture capital and private equity investors for more capital. The share of a firm that venture capitalists will demand in exchange for a capital infusion will depend upon the value they estimate for the firm. As the companies get larger and decide to go public, valuations determine the prices at which they are offered to the market in the public offering. Once established, decisions on where to invest, how much to borrow, and how much to return to the owners will all be decisions that are affected by perceptions of their impact on value. Even accounting is not immune. The most significant global trend in accounting standards is a shift toward fair value accounting, where assets are valued on balance sheets at their fair values rather than at their original cost. Thus, even a casual perusal of financial statements requires an understanding of valuation fundamentals. Some Truths about Valuation Before delving into the details of valuation, it is worth noting some general truths about valuation that will provide you not only with perspective when looking at valuations done by others, but also with some comfort when doing your own. All Valuations Are Biased You almost never start valuing a company or stock with a blank slate. All too often, your views on a company or stock are formed before you start inputting the numbers into the models and metrics that you use and, not surprisingly, your conclusions tend to reflect your biases. The bias in the process starts with the companies you choose to value. These choices are not random. It may be that you have read something in the press (good or bad) about the company or heard from a talking head that a particular company was under- or overvalued. It continues when you collect the information you need to value the firm. The annual report and other financial statements include not only the accounting numbers but also management discussions of performance, often putting the best possible spin on the numbers. With professional analysts, there are institutional factors that add to this already substantial bias. Equity research analysts, for instance, issue more buy than sell recommendations because they need to maintain good relations with the companies they follow and also because of the pressures that they face from their own employers, who generate other business from these companies. To these institutional factors, add the reward and punishment structure associated with finding companies to be under- and overvalued. Analysts whose compensation is dependent upon whether they find a firm to be cheap or expensive will be biased in that direction. The inputs that you use in the valuation will reflect your optimistic or pessimistic bent; thus, you are more likely to use higher growth rates and see less risk in companies that you are predisposed to like. There is also post-valuation garnishing, where you increase your estimated value by adding premiums for the good stuff (synergy, control, and management quality) or reduce your estimated value by netting out discounts for the bad stuff (illiquidity and risk). Always be honest about your biases: Why did you pick this company to value? Do you like or dislike the company’s management? Do you already own stock in the company? Put these biases down on paper, if possible, before you start. In addition, confine your background research on the company to information sources rather than opinion sources; in other words, spend more time looking at a company’s financial statements than reading equity research reports about the company. If you are looking at someone else’s valuation of a company, always consider the reasons for the valuation and the potential biases that may affect the analyst’s judgments. As a general rule, the more bias there is in the process, the less weight you should attach to the valuation judgment. Most Valuations (even good ones) Are Wrong Starting early in life, you are taught that if you follow the right steps, you will get the correct answer, and that if the answer is imprecise, you must have done something wrong. While precision is a good measure of process in mathematics or physics, it is a poor measure of quality in valuation. Your best estimates for the future will not match up to the actual numbers for several reasons. First, even if your information sources are impeccable, you have to convert raw information into forecasts, and any mistakes that you make at this stage will cause estimation error. Next, the path that you envision for a firm can prove to be hopelessly off. The firm may do much better or much worse than you expected it to perform, and the resulting earnings and cash flows will be different from your estimates; consider this firm-specific uncertainty. When valuing Cisco in 2001, for instance, I seriously underestimated how difficult it would be for the company to maintain its acquisition-driven growth in the future, and I overvalued the company as a consequence. Finally, even if a firm evolves exactly the way you expected it to, the macroeconomic environment can change in unpredictable ways. Interest rates can go up or down and the economy can do much better or worse than expected. My valuation of Goldman Sachs from August 2008 looks hopelessly optimistic, in hindsight, because I did not foresee the damage wrought by the banking crisis of 2008. The amount and type of uncertainty you face can vary across companies, with consequences for investors. One implication is that you cannot judge a valuation by its precision, since you will face more uncertainty when you value a young growth company than when you value a mature company. Another is that avoiding dealing with uncertainty will not make it go away. Refusing to value a business because you are too uncertain about its future prospects makes no sense, since everyone else looking at the business faces the same uncertainty. Finally, collecting more information and doing more analysis will not necessarily translate into less uncertainty. In some cases, ironically, it can generate more uncertainty. Simpler Can Be Better Valuations have become more and more complex over the last two decades, as a consequence of two developments. On the one side, computers and calculators are more powerful and accessible than they used to be, making it easier to analyze data. On the other side, information is both more plentiful and easier to access and use. A fundamental question in valuation is how much detail to bring into the process, and the trade-off is straightforward. More detail gives you a chance to use specific information to make better forecasts, but it also creates the need for more inputs, with the potential for error on each one, and it generates more complicated and opaque models. Drawing from the principle of parsimony, common in the physical sciences, here is a simple rule: When valuing an asset, use the simplest model that you can. If you can value an asset with three inputs, don’t use five. If you can value a company with three years of forecasts, forecasting 10 years of cash flows is asking for trouble. Less is more. Start Your Engines! Most investors choose not to value companies and offer a variety of excuses: valuation models are too complex, there is insufficient information, or there is too much uncertainty. While all of these reasons have a kernel of truth to them, there is no reason why they should stop you from trying. Valuation models can be simplified and you can make do with the information you have and—yes—the future will always be uncertain. Will you be wrong sometimes? Of course, but so will everyone else. Success in investing comes not from being right but from being wrong less often than everyone else. Chapter Two Power Tools of the Trade Time Value, Risk, and Statistics Should You Buy Google (GOOG), a company that pays no dividends now but has great growth potential and lots of uncertainty about its future, or Altria (MO), a high dividend-paying company with limited growth prospects and stable income? Is Altria cheap, relative to other tobacco companies? To make these assessments, you have to compare cash flows today to cash flows in the future, to evaluate how risk affects value, and be able to deal with a large amount of information. The tools to do so are provided in this chapter. Time Is Money The simplest tools in finance are often the most powerful. The notion that a dollar today is preferable to a dollar in the future is intuitive enough for most people to grasp without the use of models and mathematics. The principles of present value enable us to calculate exactly how much a dollar sometime in the future is worth in today’s terms, and to compare cash flows across time. There are three reasons why a cash flow in the future is worth less than a similar cash flow today. 1. People prefer consuming today to consuming in the future. 2. Inflation decreases the purchasing power of cash over time. A dollar in the future will buy less than a dollar would today. 3. A promised cash flow in the future may not be delivered. There is risk in waiting. The process by which future cash flows are adjusted to reflect these factors is called discounting, and the magnitude of these factors is reflected in the discount rate. The discount rate can be viewed as a composite of the expected real return (reflecting consumption preferences), expected inflation (to capture the purchasing power of the cash flow), and a premium for uncertainty associated with the cash flow. The process of discounting converts future cash flows into cash flows in today’s terms. There are five types of cash flows—simple cash flows, annuities, growing annuities, perpetuities, and growing perpetuities. A simple cash flow is a single cash flow in a specified future time period. Discounting a cash flow converts it into today’s dollars (or present value) and enables the user to compare cash flows at different points in time. The present value of a cash flow is calculated thus: Thus, the present value of $1,000 in 10 years, with a discount rate of 8 percent, is: Other things remaining equal, the value of a dollar in the future will decrease the further into the future it is, and the more uncertain you feel about getting it. An annuity is a constant cash flow that occurs at regular intervals for a fixed period of time. While you can compute the present value by discounting each cash flow and adding up the numbers, you can also use this equation: To illustrate, assume again that you have a choice of buying a car for $10,000 cash down or paying installments of $3,000 a year, at the end of each year, for five years, for the same car. If the discount rate is 12 percent, the present value of the installment plan is: The cash-down plan costs less, in present value terms, than the installment plan. A growing annuity is a cash flow that grows at a constant rate for a specified period of time. Suppose you have the rights to a gold mine that generated $1.5 million in cash flows last year and is expected to continue to generate cash flows for the next 20 years. If you assume a growth rate of 3 percent a year in the cash flows and a discount rate of 10 percent to reflect your uncertainty about these cash flows, the present value of the gold from this mine is $16.146 million; 1 this value will increase as the growth rate increases and will decrease as the discount rate rises. A perpetuity is a constant cash flow at regular intervals forever and the present value is obtained by dividing the cash flow by the discount rate. The most common example offered for a perpetuity is a console bond, a bond that pays a fixed interest payment (or coupon) forever. The value of a console bond that pays a $60 coupon each year, if the interest rate is 9 percent, is as follows: A growing perpetuity is a cash flow that is expected to grow at a constant rate forever. The present value of a growing perpetuity can be written as: Although a growing perpetuity and a growing annuity share several features, the fact that a growing perpetuity lasts forever puts constraints on the growth rate. The growth rate has to be less than the discount rate for the equation to work, but an even tighter constraint is that the growth rate used has to be lower than the nominal growth rate of the economy, since no asset can have cash flows growing faster than that rate forever. Consider a simple example. Assume that you are assessing a stock that paid $2 as dividends last year. Assume that you expect these dividends to grow 2 percent a year in perpetuity, and that your required rate of return for investing in this stock, given its risk, is 8 percent. With these inputs, you can value the stock using a perpetual growth model: These cash flows are the essential building blocks for virtual every financial asset. Bonds, stocks, or real estate properties can ultimately be broken down into sets of cash flows. If you can discount these cash flows, you can value all of these assets. Grappling with Risk When stocks were first traded in the sixteen and seventeenth centuries, there was little access to information and few ways of processing that limited information. Only the very wealthy invested in stocks, and even they were susceptible to scams. As new investors entered the financial markets at the start of the twentieth century, services started to collect return and price data on individual securities and to compute basic measures of risk, though these measures remained for the most part simplistic. For instance, a railroad stock that paid a large dividend was considered less risky than stock in a manufacturing or shipping venture. In the early 1950s, a doctoral student at the University of Chicago named Harry Markowitz noted that the risk of a portfolio could be written as a function not only of how much was invested in each security and the risks of the individual securities, but also of how these securities moved together. If securities that move in different directions are in the same portfolio, he noted that the risk of the portfolio could be lower than the risk of individual securities, and that investors should get a much better trade-off from taking risk by holding diversified portfolios than by holding individual stocks. To illustrate this, consider the risks you are exposed to when you invest in a company such as Disney (DIS). Some of the risks you face are specific to the company: Its next animated movie may do better than expected and its newest theme park in Hong Kong may draw fewer visitors than projected. Some of the risks affect not just Disney but its competitors in the business: Legislation that changes the nature of the television business can alter the profitability of Disney’s ABC network, and the ratings at the network will be determined by the strength of its new shows relative to competitors. Still other risks come from macroeconomic factors and affect most or all companies in the market to varying degrees: Rising interest rates or an economic recession will put a dent in the profitability of all companies. Take note that you can get better or worse news than expected on each of these dimensions. If you invest all your money in Disney, you are exposed to all of these risks. If you own Disney as part of a larger portfolio of many stocks, the risks that affect one or a few firms will get averaged out in your portfolio: For every company where something worse than expected happens, there will be another company where something better than expected will happen. The macroeconomic risk that affects many or most firms cannot be diversified away. In the Markowitz world, this market risk is the only risk that you should consider, as an investor in a publicly traded company. If you accept the Markowitz proposition that the only risk you care about is the risk that you cannot diversify away, how do you measure the exposure of a company to this market-wide risk? The most widely used model is the capital asset pricing model, or the CAPM, developed in the early 1960s. In this model, you assume that investors face no transaction costs and share the same information. Since there is no cost to diversifying and no gain from not doing so, each investor holds a supremely diversified portfolio composed of all traded assets (called the market portfolio). The risk of any asset then becomes the risk added to this “market portfolio,” which is measured with a beta. The beta is a relative risk measure and it is standardized around one; a stock with a beta above one is more exposed to market risk than the average stock, and a stock with a beta below one is less exposed. The expected return on the investment can then be written as: Risk-free rate + Beta (Risk premium for average risk investment) The CAPM is intuitive and simple to use, but it is based on unrealistic assumptions. To add to the disquiet, studies over the last few decades suggest that CAPM betas do not do a very good job in explaining differences in returns across stocks. Consequently, two classes of models have developed as alternatives to the CAPM. The first are multi-beta models, which measure the risk added by an investment to a diversified portfolio, with many betas (rather than the single beta), and with each beta measuring exposure to a different type of market risk (with its own risk premium). The second are proxy models, which look at the characteristics (such as small market capitalization and price-to-book ratio) of companies that have earned high returns in the past and use those as measures of risk. It is indisputable that all these models are flawed, either because they make unrealistic assumptions or because the parameters cannot be estimated precisely. However, there is no disputing that: Risk matters. Even if you don’t agree with portfolio theory, you cannot ignore risk while investing. Some investments are riskier than others. If you don’t use beta as a measure of relative risk, you have to come up with an alternative measure of relative risk. The price of risk affects value, and markets set this price. You may not buy into the CAPM or multi-beta models, but you have to devise ways of measuring and incorporating risk into your investment decisions. Accounting 101 There are three basic accounting statements. The first is the balance sheet, which summarizes the assets owned by a firm, the value of these assets, and the mix of debt and equity used to fund them, at a point in time. The income statement provides information on the operations of the firm and its profitability over time. The statement of cash flows specifies how much cash the firm generated or spent from its operating, financing, and investing activities. How do accountants measure the value of assets? For most fixed and long-term assets, such as land, buildings, and equipment, they begin with what you originally paid for the asset (historical cost) and reduce that value for the aging of the asset (depreciation or amortization). For short-term assets (current assets), including inventory (raw materials, works in progress, and finished goods), receivables (summarizing moneys owed to the firm), and cash, accountants are more amenable to the use of an updated or market value. If a company invests in the securities or assets of another company, the investment is valued at an updated market value if the investment is held for trading and historical cost when it is not. In the special case where the holding comprises more than 50 percent of the value of another company (subsidiary), the firm has to record all of the subsidiary’s assets and liabilities on its balance sheet (this is called consolidation), with a minority interest item capturing the percentage of the subsidiary that does not belong to it. Finally, you have what are loosely categorized as intangible assets. While you would normally consider items such as brand names, customer loyalty, and a well-trained work force as intangible assets, the most commonly encountered intangible asset in accounting is goodwill. When a firm acquires another firm, the price it pays is first allocated to the existing assets of the acquired firm. Any excess paid becomes goodwill and is recorded as an asset. If the accountants determine that the value of the target company has dropped since the acquisition, this goodwill has to be decreased or impaired. Just as with the measurement of asset value, the accounting categorization of liabilities and equity is governed by a set of fairly rigid principles. Current liabilities include obligations that the firm has coming due in the next accounting period, such as accounts payable and short-term borrowing, and these items are usually recorded at their current market value. Long-term debt, including bank loans and corporate bonds, are generally recorded at the face value at the time of issue and are generally not marked-to-market. Finally, the accounting measure of equity shown on the balance sheet reflects the original proceeds received by the firm when it issued the equity, augmented by any earnings made since then (or reduced by losses, if any) and reduced by any dividends paid out and stock buybacks. Two principles underlie the measurement of accounting earnings and profitability. The first is accrual accounting, where the revenue from selling a good or service is recognized in the period in which the good is sold or the service is performed (in whole or substantially), and a corresponding effort is made to match expenses incurred to generate revenues. The second is the categorization of expenses into operating, financing, and capital expenses. Operating expenses are expenses that at least in theory provide benefits only for the current period; the cost of labor and materials expended to create products that are sold in the current period is a good example. Financing expenses are expenses arising from the non-equity financing used to raise capital for the business; the most common example is interest expenses. Capital expenses are expected to generate benefits over multiple periods; for instance, the cost of buying machinery and buildings is treated as a capital expense, and is spread over time as depreciation or amortization. Netting operating expenses and depreciation from revenues yields operating income, whereas the income after interest and taxes is termed net income. To measure profitability on a relative basis, you can scale profits to revenues to estimate margins, both from an operating standpoint (operating margin = operating income/sales) and to equity investors (net margin = net income/sales). To measure how well a firm is investing its capital, we can look at the after-tax operating income relative to the capital invested in the firm, where capital is defined as the sum of the book values (BV) of debt and equity, net of cash, and marketable securities. This is the return on capital (ROC) or return on invested capital (ROIC) and it is computed as follows: The return on capital varies widely across firms in different businesses, tending to be lower in competitive businesses. The return on equity (ROE) examines profitability from the perspective of the equity investors by relating profits to the equity investor (net profit after taxes and interest expenses) to the book value of the equity investment and can be computed as: An accounting balance sheet is useful because it provides us with information about a firm’s history of investing and raising capital, but it is backward looking. To provide a more forward-looking picture, consider an alternative, the financial balance sheet, as illustrated in Table 2.1. Table 2.1 A Financial Balance Sheet Measure Explanation Assets in place Value of investments already made, updated to reflect their current cash flow potential. + Growth assets Value of investments the company is expected to make in the future (this rests on perceptions of growth opportunities). = Value of business The value of a business is the sum of assets in place and growth assets. − Debt Lenders get first claim on cash flows, during operations, and cash proceeds, in liquidation. = Value of equity Equity investors get whatever is left over after debt payments. While a financial balance sheet bears a superficial resemblance to the accounting balance sheet, it differs on two important counts. First, rather than classify assets based on asset life or tangibility, it categorizes them into investments already made by the company (assets in place) and investments that you expect the company to make in the future (growth assets). The second is that the values reflect not what has already been invested in these assets, but their current values, based upon expectations for the future. Since the assets are recorded at current value, the debt and equity values are also updated. Both U.S. and international accounting standards are pushing towards “fair value” accounting. Put simply, this would lead to accounting balance sheets more closely resembling financial balance sheets. Making Sense of Data The problem that we face in financial analysis today is not that we have too little information but that we have too much. Making sense of large and often contradictory information is part of analyzing companies. Statistics can make this job easier. There are three ways to present data. The first and simplest is to provide the individual data items and let the user make sense of the data. Thus, an analyst, who compares the price earnings (PE) ratio for a chemical company with the PE ratios of four similar chemical companies is using individual data. As the number of data items mounts, it becomes more difficult to keep track of individual data and we look at ways to summarize the data. The most common of these summary statistics is the average across all data items, and the standard deviation, which measures the spread or deviation around the average. While summary statistics are useful, they can sometimes be misleading. Consequently, when presented with thousands of pieces of information, you can break the numbers down into individual values (or ranges of values) and indicate the number of individual data items that take on each value or range of values. This is called a frequency distribution. The advantages of presenting the data in a distribution are two-fold. First, you can summarize even the largest data set into a distribution and get a measure of what values occur most frequently and the range of high and low values. The second is that the resulting distribution can resemble one of the many common statistical distributions. The normal distribution, for instance, is a symmetric distribution, with a peak centered in the middle of the distribution, and tails that stretch to include infinite positive or negative values. Not all distributions are symmetric, though. Some are weighted towards extreme positive values and are positively skewed, and some towards extreme negative values and are negatively skewed, as indicated in Figure 2.1. Figure 2.1 Normal and Skewed Distributions Why should you care? With skewed distributions, the average may not be a good measure of what is typical. It will be pushed up (down) by the extreme positive (negative) values in a positively (negatively) skewed distribution. With these distributions, it is the median, the midpoint of the distribution (with half of all data points being higher and half being lower), which is the better indicator. When looking at two series of data it is useful to know whether and how movements in one variable affect the other. Consider, for instance, two widely followed variables, inflation and interest rates, and assume that you want to analyze how they move together. The simplest measure of this co-movement is the correlation. If interest rates go up, when inflation increases, the variables move together and have a positive correlation; if interest rates go down, when inflation increases, they have a negative correlation. A correlation close to zero indicates that interest rates and inflation have no relationship to each other. While a correlation tells you how two variables move together, a simple regression allows you to go further. Assume, for instance, that you wanted to examine how changes in inflation affect changes in interest rates. You would start by plotting 10 years of data on interest rates against inflation in a scatterplot, as shown in Figure 2.2. Figure 2.2 Scatterplot of Interest Rates against Inflation Each of the 10 points on the scatterplot represents a year of data. When the regression line is fit, two parameters emerge—one is the intercept of the regression, and the other is the slope of the regression line. Assume, in this case, that the regression output is as follows: Interest rate = 1.5% + 0.8 (Inflation rate) R Squared = 60% The intercept measures the value that interest rates will have when the inflation is zero; in this case, that value is 1.5 percent. The slope (b) of the regression measures how much interest rates will change for every 1 percent change in inflation; in this case that value is 0.8 percent. When the two variables are positively (negatively) correlated, the slope will also be positive (negative). The regression equation can be used to estimate predicted values for the dependent variable. Thus, if you expect inflation to be 2 percent, the interest rate will be 3.3 percent (1.5% + 0.8 * 2% = 3.3%). In a multiple regression, you extend this approach to try to explain a dependent variable with several independent variables. You could, for instance, attempt to explain changes in interest rates using both inflation and overall economic growth. With both simple and multiple regressions, the R-squared explains the percentage of the variation in the dependent variables that is explained by the independent variable or variables; thus, 60 percent of the variation in interest rates can be explained by changes in inflation. The Tool Box Is Full You can get a lot done with the tools developed in this chapter. Time value concepts can be used to compare and aggregate cash flows across time on investments. Risk and return models in finance allow us to derive costs of investing in companies, and by extension, to value companies in