Aswath Damodaran. INVESTMENT VALUATION: SECOND EDITION. Chapter 1: Introduction to Valuation. 3. Chapter 2: Approaches to Valuation. Chapter 3. Aswath Damodaran INVESTMENT VALUATION Rich Dad's Guide to Investing- Robert inevazablu.ml Real Estate Market Valuation and inevazablu.ml Aswath Damodaran. 3. I. Discounted Cash Flow Valuation. □ What is it: In discounted cash flow valuation, the value of an asset is the present value of the.

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Aswath. Damodaran. 3. A philosophical basis for Valuation. “Valuation is often not a helpful tool in determining when to sell hyper-growth stocks”, Henry Blodget . pdf. Ebook Investment Valuation 3rd Aswath Damodaran. Pages . tools and techniques for determining the value of any asset / Aswath Damodaran. Library of Congress Cataloging in Publication Data: Damodaran, Aswath. Applied corporate inance / Aswath Damodaran. – Fourth edition. pages cm Includes.

Vice President, Publisher: Amy Neidlinger Executive Editor: Jim Boyd Editorial Assistants: Russ Hall Operations Manager: Gina Kanouse Senior Marketing Manager: Julie Phifer Publicity Manager: Laura Czaja Assistant Marketing Manager: Megan Colvin Cover Designer: Alan Clements Managing Editor:

Trying to estimate "one" growth rate for a firm can be difficult to do. Seeing the Dark Side of Valuation When confronted with estimation challenges. The healthy response is to confront the challenge and adapt existing models to reflect the differences in the company being valued.

All too often. Input Phase In the input phase. As we noted earlier. Breakdown of earnings global company that can be maintained over and operating variables time is an exercise in futility. We see some standard patterns in valuations: Q Base year fixation: Analysts often treat the current year as the base year in valuation and build these numbers in making forecasts.

The more common response is to bend the rules of valuation and use shortcuts to justify whatever price they are predisposed to pay for the company. They underestimate the dangers of the unknown.

Higher growth or risk in some businesses will be offset by lower growth or risk in other businesses. While this is understandable. Q Ignoring the scaling effect: As firms get larger. Q Paradigm shifts: When analysts abandon age-old principles of economics and valua- tion. In making forecasts. The fact that Wal-Mart was able to continue growing. Analysts point to companies like Coca-Cola and Microsoft to justify assumptions about maintaining high margins and returns on investment for small-growth companies.

This is especially true with younger companies that have significant growth prospects. This is especially true with equity risk premiums and betas. Q Valuing for the exception: Analysts often draw on anecdotal evidence to justify their assumptions.

When managers offer to provide forecasts of these numbers. At this stage in the process. It is worth nothing that Wal-Mart. It is true that economies and markets change. Valuation Phase The inputs feed into valuation models and metrics to provide the final judgments on value. As you will see in the coming chapters. With technology and human capital companies. What they fail to consider is that these forecasts are likely to be biased.

Q Inconsistencies in the accounting treatment of operating and capital expenditures are skewing current values for earnings and book value. Q Trusting management forecasts: The most difficult task in valuing a company is forecasting future revenues. Estimating high growth rates with little or no reinvest- ment into the business to generate this growth may be possible.

Q Outsourcing key inputs: When it comes to macroeconomic inputs. While this may give analysts someone else to blame if things go wrong. In the process of dealing with this uncer- tainty. Q Inconsistencies in valuation: Good valuations should be internally consistent. One is the fact that they require far more inputs to arrive at a number. Q Rules of thumb: If one response to complexity is to build bigger and better models. The valuations we arrive at for individual businesses reflect the errors and biases we have built into the process.

It is not uncommon in acquisition valuations. Q Market feedback: With publicly traded companies. Conclusion Some companies are easier to value than others. Two problems come out of more detailed models. When we have to leave the comfort zone of companies with solid earnings and predictable futures. Uncertainty often multiplies as we add more detail. When analysts are uncertain about the numbers that go into their valuations. Here we invent new principles.

At least two common practices wreak havoc on valuations: Q Valuation garnishing: This is the all-too-common practice of adding premiums and discounts to estimated value to reflect what the analyst believes are missed components. In many valuations. As inputs change. The net result of these adjustments is that the value reflects whatever preconceptions the analyst might have had about the company.

If we believe that markets are right. Q Black-box models: As data becomes more easily accessible and building bigger models becomes more feasible. Post-Valuation Phase In many cases. An analyst faced with a particu- larly troublesome set of inputs may decide to value a company at three times revenues because that is what investors have traditionally paid for companies in this sector. While using these shortcuts may provide the illusion of precision.

For declining firms. Cyclical and commodity companies have vola- tile operating results. In the last part of the chapter. Companies with intangible assets have earnings that are skewed by how accountants treat investments in these assets.

The risk in emerging-market and global companies can be difficult to assess. With growth firms. With mature firms. This chapter described the four inputs that we have to estimate to value any company: Restructuring the firm to make it run better may dramatically alter value. The dark side of valuation manifests itself at each phase of a valuation. For young and start-up firms. The estimation challenges we face can also be different for different subsets of companies.

The Theory of Interest.. Recent Literature on Interest. The Rate of Interest. Principles of Economics. Many analysts claim that when significant uncertainty about the future exists. But we disagree. This section looks at the foundations of the approach and some of the preliminary details of how we estimate its inputs.

New York. Put simply. The value of an asset is not what someone perceives it to be worth. In the last 50 years. The earliest interest rate tables date back to In dis- counted cash flow valuation.

Notwithstanding this uncertainty. The notion that the value of an asset is the present value of the cash flows that you expect to generate by holding it is neither new nor revolutionary. This chapter considers how discounted cash flow valuation models attempt to estimate intrinsic value and describes estimation details and possible limitations. The cash flows after debt payments and reinvestment needs are called free cash flows to equity. Growth Assets Equity Present value is the value of the entire firm and reflects the value of all claims on the firm.

We believe that every asset has an intrinsic value. Using discounted cash flow models is in some sense an act of faith. The problem lies in the fact that none of us ever gets to see the true intrinsic value of an asset.

Note also that we can always get from the former firm value to the latter equity value by net- ting out the value of all nonequity claims from firm value. Figure 2. No such analyst exists. Here we use higher discount rates to discount expected cash flows when valuing riskier assets and lower discount rates when valuing safer assets.

We can approach discounted cash flow valuation in two ways. Equity Versus Firm Valuation Of the approaches for adjusting for risk in discounted cash flow valuation. Valuing a Firm Business The cash flows before debt payments and after reinvestment needs are called free cash flows to the firm. What is intrinsic value? Consider it the value that would be attached to an asset by an all-knowing analyst with access to all information available right now and a perfect valuation model.

Done right. With publicly traded firms. The second way is to value just the equity stake in the business.

The second input is growth. Growth in operating income is the key input when valuing the entire business. Determinants of Value The first input is the cash flow from existing assets. With equity cash flows. This is defined as either pre-debt and to the firm or post-debt and to equity earnings. Discount rate reflects only the after debt payments and cost of raising equity financing. High-Growth Period net of any reinvestments needed to Stable growth firm.

Growth Assets Equity Present value is the value of just the equity claims on the firm. How we define the inputs will differ depending on whether we do firm or equity valuation. One simple way of adjusting for this is to augment the dividend with stock downloadbacks and look at the cumulative cash returned to stockholders: The rest of this section will focus on estimating the inputs into discounted cash flow models.

Augmented Dividends One of the limitations of focusing on dividends is that many companies. Since many firms do not pay dividends. The third input is the discount rate.

Then it will move to more expansive measures of cash flows. Focusing only on dividends will result in the undervaluation of equity. Cash Flows Leading up to this section. We will start with cash flows and then move on to risk and discount rates. We will close with a discussion of how best to estimate the growth rate for the high-growth period and the value at the end of that period. Dividends When an investor downloads stock in a publicly traded company. The final input. While only stockholders who sell back their stock receive cash.

If we accept this premise. Since this expected price is itself determined by future dividends. Estimating that dividend for the last period should be a simple exercise. This section begins with the strictest measure of cash flow to equity—the dividends received by investors.

Focusing on just debt cash flows allows us to zero in on a way to simplify this computation. Our distinction is between wasting cash which would include currency or cash earning below-market rate returns and nonwasting cash. These investments earn a low but fair rate of return and therefore are not wasting assets. To estimate what managers could have returned to equity investors.

Reinvestment reduces cash flow to equity investors. If old debt is replaced with new debt of exactly the same magnitude. We will reconsider whether the net effect is positive or negative after we consider how best to estimate growth. We begin with net income. We net the latter because it is not a cash expense and hence can be added back to net income.

The final input into the process are the negative cash flows associated with the repayment of old debt and the positive cash flows to equity investors from raising new debt. We compute what the firm has to rein- vest in two parts: Q Reinvestment in long-lived assets is measured as the difference between capital expendi- tures the amount invested in long-lived assets during the period and depreciation the accounting expense generated by capital expenditures in prior periods.

It is measured as follows: We are assuming that the former will be a small or negligible number at a publicly traded company. The overall change in noncash working capital therefore is investment in short-term assets. As with downloadbacks. The first is that the net income could be negative. If we define the por- tion of the net income that equity investors reinvest into the firm as the equity reinvestment rate.

The former is before interest expenses. The cash flow to the firm can be measured in two ways. Since a firm raises capital from debt and equity investors. The third reason is that large debt repay- ments coming due that have to be funded with equity cash flows can cause negative FCFE. The second reason is that reinvestment needs can overwhelm net income. There is one more way in which we can present the free cash flow to equity. The other approach is to start with operating earnings and to estimate the cash flows to the firm prior to debt payments but after reinvestment needs have been met: The fourth reason is that the quirks of the reinvestment process.

If the FCFE is negative. Cash Flow to the Firm The cash flow to the firm should be both after taxes and after all reinvestment needs have been met. Highly levered firms that are trying to bring down their debt ratios can go through years of negative FCFE. One is to add up the cash flows to all the different claim holders in the firm. Unlike those measures. Estimating Cash Flows for a Firm: If the FCFF is negative. This is because we will be counting the tax benefits from debt in the cost of capital through the use of an after-tax cost of debt.

Another way of presenting the same equation is to cumulate the net capital expenditures and working capital change into one number and state it as a percentage of the after-tax operating income.

The effective tax rate during the year was A few final thoughts about free cash flow to the firm are worth noting before we move on to discount rates. This ratio of reinvestment to after-tax operating income is called the reinvestment rate.

If we use actual taxes paid or reflect the tax benefits from interest expenses in the cash flows. The reinvestment rate can also be less than zero for firms that are divesting assets and shrinking capital.

The free cash flow to the firm for can also be computed. With this data. Free Cash Flows to Equity Note that the net debt issued reflects the new debt issues. Net capital expenditures includes acquisitions. Free Cash Flow to 3M Figure 2. Comparison of Cash Flow Estimates: During The equity in a safe business can be rendered risky if the firm uses substantial debt to fund that business.

Risk Cash flows that are riskier should be assessed a lower value than more stable cash flows. In the first. This section begins by contrasting how the risk in equity can vary from the risk in a business. We use higher discount rates on riskier cash flows and lower discount rates on safer cash flows. In the second. Business Risk Versus Equity Risk Before we delve into the details of risk measurement and discount rates.

Then it consid- ers the mechanics of estimating the cost of equity and capital. In conventional discounted cash flow valuation mod- els.

Note that the risk in the equity investment in a business is determined partly by the risk of the business the firm is in and partly by its choice of how much debt to use to fund that business. As with any other aspect of the balance sheet. We would measure the risk to the investor of investing in equity in that company. The common theme shared by risk-and-return models in finance is that the marginal investor is diversified.

In corporate finance and valuation. The latter is a weighted average of the cost of equity and the cost of debt. In a publicly traded company. Measuring Equity Risk and the Cost of Equity Measuring the risk in equity investments and converting that risk measure into a cost of equity is rendered difficult by two factors. The Diversified Marginal Investor If a company had only one equity investor.

Let us consider the alternatives: The marginal investor in a publicly traded stock has to own enough stock in the company to make a difference and must be willing to trade on that stock. Models for Expected Return Cost of Equity It is on the issue of how best to measure this nondiversifiable risk that the different risk-and- return models in finance part ways. They vary not only in size. Then we would assess a reasonable rate of return. That number has the burden of measuring exposure to all the com- ponents of market risk.

The first is that equity has an implicit cost. The second factor is that risk in the eyes of the beholder and different equity investors in the same business can be very different.

We need to come up with a risk-free rate and an equity risk premium or pre- miums in the multifactor models to use across all investments. The expected return on an investment can be written as a function of the multiple betas relative to each market risk factor and the risk premium for that factor.

Future chapters will return to the details of how best to make these estimates for different types of businesses. The open question. Using the historical data. A beta of 1 represents an average risk investment. Then we use the common characteristic s they share as a measure of risk. Stocks with small market capitalization and low price-to-book ratios have historically earned higher returns than large market stocks with higher price-to-book ratios. With these models.

Betas above or below 1 indicate investments that are riskier or safer than the average risk investment in the market.

This section lays out the broad principles that govern these estimates. If the model has k factors. Once we have these market-wide estimates. One solution is to replace the regression beta with a bottom-up beta—one that is based on industry averages for the businesses that the firm is in. Q The equity risk premium is the premium that investors demand for investing in risky assets or equities as a class.

The first is that the entity making the guarantee can have no default risk. As you will see in Chapter 6. The conventional practice for estimating equity risk premiums is to use the historical risk premium—the premium investors have earned over long periods say.

Chapter 7. To estimate betas in the arbitrage pricing model. The second condition is that the time horizon matters. The slope captures how much the stock moves for any given market move. Since the return is guaranteed.

As a consequence. The standard approach for estimating the CAPM beta is to run a regression of returns on a stock against returns on a broad equity market index. A six-month Treasury bill is not risk-free if you are looking at a five-year time horizon. Regression betas are equity betas and thus are levered.

It also follows that the equity risk premium can change over time. It is a function not only of how much risk investors perceive in equities as a class. Q The risk-free rate is the expected return on an investment with guaranteed returns. The debt-to-equity ratio over the regression period is embedded in the beta. The regression results would have been very different if we had run the regression using a different time period say. To yield a contrasting value.

The regression raw beta is 0. Regression Beta for 3M Although we do have a regression beta. It is backward-looking for the last two years and has a standard error albeit a small one of 0. The Cost of Debt While equity investors receive residual cash flows and bear the bulk of the operating risk in most firms. The other dimension on which debt and equity can vary is in their treatment for tax purposes. Table 2. To cover this default risk. A simple.

To estimate the cost of debt for a firm. In the U. The after-tax cost of debt for a firm therefore is as follows: The second component is the default spread. Q If the firm is unrated and has debt outstanding bank loans. Since interest expenses save you taxes at the margin. Three approaches are used.

The first is the risk-free rate. As a general rule. The final input needed to estimate the cost of debt is the tax rate. In September Q If the firm has traded bonds outstanding. If the cost of equity is based on a long-term risk-free rate. In making this estimate. To come up with this value. Adding this spread to the ten-year Treasury bond rate of 3. Just as a contrast. In the third sidebar. Estimating the market value of debt usually is a more difficult exercise. Estimating the Cost of Capital for 3M In the second sidebar.

As passive investors in publicly traded firms. This section looks at why growth rates can be different for equity and operating earnings. Once we have the current market value weights for debt and equity for use in the cost of capital.

In this case. This section closes with a discussion of the fundamentals that determine growth. We estimated the market values of equity and debt for the firm in September with the resulting weights and overall costs of capital and derived the cost of capital for the firm. If we assume that they will change. Though many practitioners fall back on book value of debt as a proxy of market value.

It examines two of the standard approaches for estimating growth looking at the past. In an acquisition. For publicly traded firms. Unlike cash flows and discount rates. As companies change over time. Growth Rates No other ingredient in discounted cash flow valuation evokes as much angst as estimating future growth. Firms that use increasing amounts of debt to fund their operations generally report higher growth rates in operating income than net income. This is especially true of growth firms and firms in transition.

Firms that gen- erate excess cash flows and use these cash flows to download back stock register higher growth rates in earnings per share than in net income. Q Financial leverage: The growth rates in operating and net income can diverge if the net interest expense interest expense minus interest income grows at a rate different from operating income. Q Share issues and downloadbacks: If the number of shares remains fixed.

The growth rates in different measures of earnings operating income. To make the distinction. Equity Versus Operating Earnings As with cash flows and discount rates. A debate on how best to estimate historical growth makes sense only if it is a good predictor of future growth. Before we put this practice under the microscope.

Q Period of analysis: The higher the proportion of the costs that are fixed higher operating lever- age. On the minus side. On the plus side. Q Scaling matters. Q Firms and sectors grow through growth cycles.

Q Averaging approach: Even if we agree on an earnings measure and time period for the analysis. Q Operating leverage: The growth in operating income can also be very different from the growth in revenues. Historical and Forecasted Growth Rates When confronted with the task of estimating growth.

We can draw on those who know the firm better than we do—equity research analysts who have tracked the firm for years. We could. If historical growth is not a useful predictor of future growth. Q Earnings measure: As we noted. For firms with volatile earnings. And equity research analysts have sector experience and informed sources they can draw on for better infor- mation. It to be the investment at the start of period t.

Decomposing Growth The best way to consider earnings growth is to break it down algebraically into its constituent parts. As with historical growth.

The more general scenario is one in which the return on investment does change from period to period. If we allow the return on new investments. The expected growth rate in earnings for this firm is as follows: This section considers the two sources of growth—new investments that expand the business.

The answer lies in the fundamentals within a firm that ultimately determine its growth rate. Define Et to be the earnings in period t. The second term captures the effect of changes in the return on investment on existing assets.

Fundamental Growth Rates If we cannot draw on history or trust managers and analysts. In the cash flow definitions introduced at the start of this chapter. When looking at operating earnings. In dividend discount models. When looking at equity earnings. Growth from New Investments While investment and return on investment are generic terms. Increasing the return on investment improving efficiency will create additional earnings growth. In free cash flow to equity firm models.

Central to any estimate of fundamental growth is the estimate of return on capital or equity. Return on Invested Capital and Return on Equity: Measurement and Implications. It should as come as no surprise. While we often use the same value for both numbers in valuation.

Unlike growth from new investments. This is true for two reasons. Efficiency Growth For many mature firms with limited investment opportunities. The return on exist- ing assets is an average return on a portfolio of investments already made. Accounting choices on restructuring charges. While the potential for efficiency growth is always there.

These firms cannot maintain a high reinvestment rate and deliver a high return on capital with that reinvestment. Stated again in terms of different measures of earnings.

Table The problem with accounting measures on both dimensions is well documented. Note that the return on investment that we use to compute the growth from new investments should be the return earned on those investments alone—a marginal return. Q Mature firms have more potential for efficiency growth. In discounted cash flow valuation. Once the inefficiencies. In closing. Q You can draw on increased efficiency to justify growth only for finite periods.

Estimating Growth for 3M It makes sense to start with an estimate of historical growth in earnings at 3M. You can draw on both efficiency and new investments to justify growth during the high-growth period. It is. Three approaches generally are used to estimate the terminal value. This reinvestment. Two more legitimate ways of estimating terminal value exist. Terminal Value Publicly traded firms do not have finite lives.

The other is to estimate a going concern or a terminal value. Net Income. Liquidation Value If we assume that the business will be ended in the terminal year and that its assets will be liq- uidated at that time. Since these multiples are usually obtained by look- ing at what comparable firms are trading at in the market today. Note the wildly divergent numbers that we get for past growth.

Looking at the fundamentals. We cannot estimate cash flows forever. Fundamentals In the Last Financial Year. The most common approach. Note that the riskless rate can be written as follows: For other firms. One approach is to use the estimated book value of the assets as a starting point and to estimate the liquidation value based on the book value. The perpetual growth model is a powerful one. Since no firm can grow forever at a rate higher than the growth rate of the economy in which it operates.

For firms that have finite lives and marketable assets like real estate. The discount rate is the cost of equity for the first two and the cost of capital for the last. Going Concern or Terminal Value If we treat the firm as a going concern at the end of the estimation period. This perpetual growth model draws on a simple present-value equation to arrive at terminal value: Small changes in the inputs can alter the terminal value dramatically.

The fact that a stable-growth rate is constant forever. With the former. The answer depends on whether the valuation is being done in real or nominal terms. With the latter. Q Cap the growth rate: Small changes in the stable-growth rate can change the terminal value significantly. Although increasing the stable-growth rate while holding all else constant can dramatically increase value.

Q Use mature company risk characteristics: Whether value increases or decreases as the stable growth increases depends entirely on what you assume about excess returns. If the return on capital is higher than the cost of capital in the stable-growth period. Given the relationship between growth. It is critical that we both capture the effects of lower growth on reinvestment and ensure that the firm reinvests enough to sustain its stable-growth rate in the terminal phase.

Q Reinvestment and excess-return assumptions: Stable-growth firms tend to reinvest less than high-growth firms. Substituting the stable-growth rate as a function of the reinvestment rate from before. If the return on capital is equal to the cost of capital in stable growth. In general. As a simple rule of thumb. If you assume no excess returns. Some valuation experts believe that this is the only sustainable assumption.

Setting the return on capital equal to the cost of capital. Expected Growth 3. If the cash flows are based on operating income free cash flow to the firm or noncash net income. The present value we arrive at when we dis- count the cash flows at the risk-adjusted rates should yield an estimate of value. Is this cash balance already incorporated into the present value? The answer depends on how we estimated cash flows.

But getting from that number to what we would be willing to pay per share for equity does require us to consider a few other factors: Q Cash and marketable securities: Most companies have cash balances that are not insignificant in magnitude. Since the cost of debt is relatively low. The income from cash is part of the final cash flow.

Q Cross-holdings in other companies: Q Employee options: Having arrived at the value of equity in the firm. Cross-holdings Ignore.

While analysts often use shortcuts such as adjusting the number of shares for dilution to deal with these options. With majority holdings. Since many of these options will still be outstanding.

Q Potential liabilities not treated as debt: Staying consistent with the parameters Subtract value of Subtract value of equity equity options options outstanding.

The assumption Subtract expected Subtract underfunded is that the firm considers litigation costs. We first use the expected growth rate of 7. A Valuation of 3M In the earlier sidebars. Employee options Ignore. This section begins with a model in which we adjust the cash flows for risk.

Using the cost of capital of 8. Then we move on to the adjusted present-value model where the effect of debt on value is separated from the operating assets and excess-return models where value is derived from earning excess returns on new investments.

We valued these options using a Black-Scholes option pricing model. Value of Operating Asset: Variations on DCF Valuation The discounted cash flow model described so far in this chapter is still the standard approach for estimating intrinsic value. Misunderstanding Risk Adjustment At the outset of this section.

To see why. The first is that specifying a utility function for an individual or analyst is very difficult. While it is true that bad outcomes have been weighted to arrive at this cash flow. If we can specify the utility function of wealth for an individual. In the first one. Ways of Computing Certainty Equivalent Cash Flows The practical question that we will address in this section is how best to convert uncertain expected cash flows into guaranteed certainty equivalents.

This process can be repeated for more complicated assets. Some consider the cash flows of an asset under a variety of scenarios. One quirk of using utility models to estimate certainty equivalents is that the certainty equivalent of a positive expected cash flow can be negative. Risk Adjustments Based on Utility Models The first and oldest approach to computing certainty equivalents is rooted in the utility func- tions for individuals.

While we do not disagree with the notion that it should be a function of risk aversion. With this approach. This makes the certainty equivalents of uncertain cash flows further into the future lower than uncertain cash flows that will occur sooner.

The first is that expected cash flows with higher uncertainty associated with them have lower certainty equivalents than more predictable cash flows at the same point in time. The second effect is that the effect of uncertainty compounds over time. Not surprisingly. The second problem is that. Risk-and-Return Models A more practical approach to converting uncertain cash flows into certainty equivalents is offered by risk-and-return models.

Warren Buffet expresses his disdain for the CAPM and other risk-and-return models and claims to use the risk- free rate as the discount rate. This weapon is commonly employed by analysts who are forced to use the same discount rate for projects of different risk levels and who want to level the playing field. For example. In that case.

If we use the risk premiums from risk-and-return models to compute certainty equivalents. In a variation on this approach. We suspect that he can get away with doing so because of a combi- nation of the types of companies he chooses to invest in and his inherent conservatism when it comes to estimating the cash flows.

Assume that r is the risk-adjusted cash flow. While cash flow haircuts retain their intuitive appeal. If so. They haircut the cash flows of riskier projects to make them lower. Risk-Adjusted Discount Rate or Certainty Equivalent Cash Flow Adjusting the discount rate for risk or replacing uncertain expected cash flows with certainty equivalents are alternative approaches to adjusting for risk. To see this. The absence of transparency about the risk adjustment can also lead to the double counting of risk.

The answer lies in how we compute certainty equivalents. As we add debt to the firm. It is easy to double-count risk in these cases. There are other scenarios in which the two approaches yield different values for the same risky asset.

The risk-adjusted discount rate discounts negative cash flows at a higher rate. In contrast to the conventional approach. The other scenario is when the certainty equivalents are computed from utility functions or sub- jectively. If certainty equivalents are computed from utility functions. The biggest dangers arise when analysts use an amalgam of approaches. They valued the present value of the tax savings in debt as a perpetuity using the cost of debt as the discount rate.

The two approaches can yield different estimates of value for a risky asset. The adjusted present-value approach in its current form was first presented in Myers in the context of examining the interrelationship between investment and financing decisions.

The first is when the risk-free rates and risk premiums change from time period to time period. Corporation Finance and the Theory of Investment. Some argue that the certainty equivalent approach yields more precise estimates of value in this case. The second is the dollar debt to use in computing the tax savings and whether that amount can vary across time. The inputs needed for this valuation are the expected cash flows. In other versions of the models. The first is what tax rate to use in computing the tax benefit and whether that rate can change over time.

The first step in this approach is estimating the value of the unlevered firm. We then consider the present value of the interest tax savings generated by borrowing a given amount of money. The final issue relates to what discount rate to use to compute the present value of the tax benefits. The second step in this approach is calculating the expected tax benefit from a given level of debt. In the more general case. The argument about which one of these rates is right is really one about how predictable the tax benefits from debt are.

In the early itera- tions of APV. In the special case where cash flows grow at a constant rate in perpetuity. Measuring APV In the adjusted present value approach. This can be accom- plished by valuing the firm as if it has no debt—by discounting the expected free cash flow to the firm at the unlevered cost of equity. The tax benefit is incorporated into the after- tax cost of debt and the bankruptcy costs in both the levered beta and the pre-tax cost of debt.

In theory. One is to estimate a bond rating. The probability of bankruptcy can be estimated indirectly in two basic ways.. These indirect bankruptcy costs can be catastrophic for many firms and essentially make the perception of distress into a reality. There are institutional factors that add to this already substantial bias. For instance, it is an acknowledged fact that equity research analysts are more likely to issue download rather than sell recommendations, i.

The reward and punishment structure associated with finding companies to be under and over valued is also a contributor to bias.

An analyst whose compensation is dependent upon whether she finds a firm is under or over valued will be biased in her conclusions. This should explain why acquisition valuations are so often biased upwards. The analysis of the deal, which is usually done by the acquiring firms investment banker, who also happens to be responsible for carrying the deal to its successful conclusion, can come to one of two conclusions.

One is to find that the deal is seriously over priced and recommend rejection, in which case the analyst receives the eternal gratitude of the stockholders of the acquiring firm but little else.

The other is to find that the deal makes sense no matter what the price and to reap the ample financial windfall from getting the deal done. There are three ways in which your views on a company and the biases we have can manifest themselves in value.

The first is in the inputs that you use in the valuation. When you value companies, you constantly come to forks in the road where you have to make assumptions to move on. These assumptions can be optimistic or pessimistic. For a company with high operating margins now, you can either assume that competition will drive the margins down to industry averages very quickly pessimistic or that the company will be able to maintain its margins for an extended period optimistic.

The path you 3 There are approximately five times as many download recommendations issued by analysts on Wall Street as there are sell recommendations. It should come as no surprise then that the end value that you arrive at is reflective of the optimistic or pessimistic choices we made along the way. The second is in what we will call post-valuation garnishing, where analysts revisit assumptions after a valuation in an attempt to get a value closer to what they had expected to obtain starting off.

The third is to leave the value as is but attribute the difference between the value you estimate and the value you think is the right one to a qualitative factor such as synergy or strategic considerations. This is a common device in acquisition valuation where analysts are often called upon to justify the unjustifiable.

Bias cannot be regulated or legislated out of existence. Analysts are human and bring their biases to the table.

As investors, what are the lessons you can drawn from this discussion? If you are valuing companies, try to be honest about your own biases; in fact, put them 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 companys financial statements than reading equity research reports about the company. If you are looking at someone elses valuation of a company, always consider the source of the valuation and potential biases that may affect their judgments.

As a general rule, the more bias there is in the process, the less weight you should attach to the valuation. All valuations are wrong, but it is not always your fault Starting early in life, you are taught that if you do the right things, you will get the right answers.

In other words, the precision of the answer is used as a measure of the quality of the process that yielded the answer. While this may be appropriate in mathematics or physics, it is a poor measure of quality in valuation. Barring a very small subset of assets, there will always be uncertainty associated with valuations, and even the best valuations come with a substantial margin for error.

When valuing an asset at any point in time, you make forecasts for the future. Since none of us possess crystal balls, you have to make your best estimates, given the information that you have at the time of the valuation. Our estimates of value can be wrong for a number of reasons, and you can categorize these reasons into three groups. Estimation Uncertainty: Even if our information sources are impeccable, you have to convert raw information into inputs and use these inputs in models.

Any mistakes that we make at either stage of this process will cause estimation error.

Firm-specific Uncertainty: The path that you envision for a firm can prove to be hopelessly wrong. The firm may do much better or much worse than you expected it to perform, and the resulting earnings and cash flows will be very different from your estimates.

Macroeconomic Uncertainty: Even if a firm evolves exactly the way you expected it to, the macro economic environment can change in unpredictable ways. Interest rates can go up or down and the economy can do much better or worse than expected. These macro economic changes will affect value.

The contribution of each type of uncertainty to the overall uncertainty associated with a valuation can vary across companies. When valuing a mature cyclical or commodity company, it may be macroeconomic uncertainty that is the biggest factor causing actual numbers to deviate from expectations. Valuing a young technology company can expose you to far more estimation and firm-specific uncertainty. Even if you feel comfortable with your estimates of an assets values at any point in time, that value itself will change over time, as a consequence of new information that comes out both about the firm and about the overall market..

Given the constant flow of information into financial markets, a valuation done on a firm ages quickly, and has to be updated to reflect current information. Thus, technology companies that were valued highly in late , on the assumption that the high growth from the nineties would continue into the future, would have been valued much less in early , as the prospects of future growth dimmed.

With the benefit of hindsight, the valuations of these companies and the analyst recommendations made in can be criticized, but they may well have been reasonable, given the information available at that time. The advantage of breaking uncertainty down into estimation uncertainty, firm-specific and macroeconomic uncertainty is that it gives us a window on what you can manage, what you can control and what you should just let pass through into the valuation.

Building better models and accessing superior information will reduce estimation uncertainty but will do little to reduce exposure to firm-specific or macro-economic risk.

Even the best-constructed model will be susceptible to these uncertainties. More detail and complexity does not always result in better valuations Valuation models have become more and more complex over the last two decades, as a consequence of two developments.

On the one side, computers and calculators have become far more powerful and accessible in the last few decades. With technology as our ally, tasks that would have taken us days in the pre- computer days can be accomplished in minutes. On the other side, information is both more plentiful, and easier to access and use. We can download detailed historical data on thousands of companies and use them as we see fit.

The complexity, though, has come at a cost. A fundamental question that we all face when doing valuations is how much detail we should break a valuation down into. There are some who believe that more detail is always better than less detail and that the resulting valuations are more precise.

We disagree. The trade off on adding detail is a simple one. On the one hand, more detail gives you a chance to use specific information to make better forecasts on each individual item. On the other hand, more detail creates the need for more inputs, with the potential for error on each one, and generates more complicated models.

In the physical sciences, the principle of parsimony dictates that we try the simplest possible explanation for a phenomenon before we move on to more complicated ones. We would be well served adopting a similar principle in valuation. When valuing an asset, use the simplest model that you can get away with. In other words, if you can value an asset with three inputs, you should not be using five. If you can value a company with 3 years of cash flow forecasts, forecasting ten years of cash flows is asking for trouble.

Conclusion When faced with the question of whether to invest in a stock, a bond or any asset, you can either choose to make your decisions based upon the actions or recommendations of others that you view as more informed or make your own assessment of value. Most investors choose not to do the latter and offer a variety of excuses: that valuation models are too complex, that there is insufficient information or that there is too much uncertainty about the future.

While all of these reasons have a core of truth to them, there is no reason why they should stop you from valuing assets. Valuation models can be simplified, you can make do with the information that you have rather than wish you had and you can make your best estimates about an uncertain future. Will you be wrong? Of course, but so will everyone else.

Success in investing comes not from being right but from being less wrong than everyone else playing the game. Section 1: Laying the groundwork Chapter 2: The Tools of the trade There are a few basic tools that should be part of every valuation toolkit. While all of these tools have common sense underpinnings, they can take complex forms in some analyses. In this chapter, we will navigate our way through the basics of these tools, while steering away from the complexities that may or may not improve valuations at the margin.

Valuation Tools: An overview Before we start looking at valuation models and metrics, there are four tools that we focus on as essential for our pursuit: a. Estimating time value of money: An investment generates cash flows over many years and a dollar today is worth more than a dollar in the future. True, but to convert this common sense proposition to value, we have to first understand why time has value and then develop ways in which we can make this notion specific.

Measuring risk and estimating expected return: When investing, we face uncertainty about future cash flows. The basic principle that more risky or uncertainty cash flows should be worth less than less risky cash flows is intuitive.

To put this principle to work in valuation, we need to be clear about what comprises risk, how to measure that risk and how we adjust value for that risk. Making sense of accounting data: When valuing companies, much of the information that we use comes from financial statements.

To the extent that this data is misread, our valuations will run off course. We look at the questions that we would like accounting statements to address and how we might be able to eke out answers from the numbers. Understanding relationships between data: The biggest problem that we face in investing today is not that we have too little information but that we have too much.

The data is often contradictory and pulls us in different directions on whether an asset is under or over valued.

Statistical measures such as standard deviation can help us consolidate data and understand relationships. The Time Value of Money The simplest tools in finance are often the most powerful.

The notion that a dollar today is preferable to a dollar some time 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 some time in the future is worth in todays dollars and to move cash flows across time. Why money has time value There are three reasons why a cash flow in the future is worth less than a similar cash flow today.

Individuals prefer present consumption to future consumption. People would have to be offered more in the future to give up present consumption. If the preference for current consumption increases, individuals will have to be offered much more in terms of future consumption to give up current consumption, a trade-off that is captured by a high real rate of return or discount rate.

When there is monetary inflation, the value of currency decreases over time.