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Doctoral Dissertation

It is only an estimate: Imprecision and Uncertainty in Valuation

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Value first, Valuation to follow: Bias in Valuation

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We may, however, disclose Your information to unaffiliated third-parties as follows: We may disclose Personal Information about You to third-parties with Your consent. The advantage of breaking uncertainty down into estimation uncertainty, firm-specific and macroeconomic uncertainty is that it gives us a window on what we can manage, what we can control and what we 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. In general, analysts should try to focus on making their best estimates of firm-specific information — how long will the firm be able to maintain high growth?

How fast will earnings grow during that period? What type of excess returns will the firm earn? To see why, assume that you believe that interest rates today are too low and that they will go up by about 1. If you build in the expected rise in interest rates into your discounted cash flow valuations, they will all yield low values for the companies that you are analyzing.

A person using these valuations will be faced with a conundrum because she will have no way of knowing how much of this over valuation is attributable to your macroeconomic views and how much to your views of the company. In summary, analysts should concentrate on building the best models they can with as much information as they can legally access, trying to make their best estimates of firm-specific components and being as neutral as they can on macro economic variables.

As new information comes in, they should update their valuations to reflect the new information. There is no place for false pride in this process. Valuations can change dramatically over time and they should if the information warrants such a change.

Even at the end of the most careful and detailed valuation, there will be uncertainty about the final numbers, colored as they are by assumptions that we make about the future of the company and the economy in which it operates. It is unrealistic to expect or demand absolute certainty in valuation, since the inputs are estimated with error. This also means that analysts have to give themselves reasonable margins for error in making recommendations on the basis of valuations.

The corollary to this statement is that a valuation cannot be judged by its precision. Some companies can be valued more precisely than others simply because there is less uncertainty about the future. We can value a mature company with relatively few assumptions and be reasonably comfortable with the estimated value. Valuing a technology firm will require far more assumptions, as will valuing an emerging market company. A scientist looking at the valuations of these companies and the associated estimation errors may very well consider the mature company valuation the better one, since it is the most precise, and the technology firms and emerging market company valuations to be inferior because there is most uncertainty associated with the estimated values.

The irony is that the payoff to valuation will actually be highest when you are most uncertain about the numbers. After all, it is not how precise a valuation is that determines its usefulness but how precise the value is relative to the estimates of other investors trying to value the same company. Any one can value a zero-coupon default-free bond with absolute precision.

Valuing a young technology firm or an emerging market firm requires a blend of forecasting skills, tolerance for ambiguity and willingness to make mistakes that many analysts do not have. Since most analysts tend to give up in the face of such uncertainty, the analyst who perseveres and makes her best estimates error-prone though they might be will have a differential edge.

We do not want to leave the impression that we are completely helpless in the face of uncertainty. Simulations, decision trees and sensitivity analyses are tools that help us deal with uncertainty but not eliminate it. 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.

In this section, we will consider the trade off on complexity and how analysts can decide how much to build into models. 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.

The trade off on adding detail is a simple one. On the one hand, more detail gives analysts 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. Thus, breaking working capital down into its individual components — accounts receivable, inventory, accounts payable, supplier credit etc.

A parallel and related question to how much detail there should be in a valuation is the one of how complex a valuation model should be. There are clear costs that we pay as models become more complex and require more information. More information does not always lead to better valuations.

In fact, analysts can become overwhelmed when faced with vast amounts of conflicting information and this can lead to poor input choices. The problem is exacerbated by the fact that analysts often operate under time pressure when valuing companies. Models that require dozens of inputs to value a single company often get short shrift from users. The models become so complicated that the analysts using them no longer understand their inner workings.

Of particular concern should be models where portions of the models are proprietary and cannot be accessed or modified by analysts.

This is often the case with commercial valuation models, where vendors have to keep a part of the model out of bounds to make their services indispensable. Big versus Small Assumptions: Complex models often generate voluminous and detailed output and it becomes very difficult to separate the big assumptions from the small assumptions. 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, we want to use the simplest model we can get away with.

In other words, if we can value an asset with three inputs, we should not be using five. If we can value a company with 3 years of cashflow forecasts, forecasting ten years of cash flows is asking for trouble.

The problem with all-in-one models that are designed to value all companies is that they have to be set up to value the most complicated companies that we will face and not the least complicated.

Thus, we are forced to enter inputs and forecast values for simpler companies that we really do not need to estimate. In the process, we can mangle the values of assets that should be easy to value. Consider, for instance, the cash and marketable securities held by firms as part of their assets. The simplest way to value this cash is to take it at face value. Analysts who try to build discounted cash flow or relative valuation models to value cash often mis-value it, either by using the wrong discount rate for the cash income or by using the wrong multiple for cash earnings.

Analysts use a wide spectrum of models, ranging from the simple to the sophisticated. These models often make very different assumptions about the fundamentals that determine value, but they do share some common characteristics and can be classified in broader terms.

There are several advantages to such a classification -- it makes it is easier to understand where individual models fit in to the big picture, why they provide different results and when they have fundamental errors in logic. In general terms, there are three approaches to valuation. The first, discounted cashflow valuation, relates the value of an asset to the present value of expected future cashflows on that asset.

The second, relative valuation, estimates the value of an asset by looking at the pricing of 'comparable' assets relative to a common variable like earnings, cashflows, book value or sales. The third, contingent claim valuation, uses option pricing models to measure the value of assets that share option characteristics. While they can yield different estimates of value, one of the objectives of discussing valuation models is to explain the reasons for such differences, and to help in picking the right model to use for a specific task.

In discounted cashflows valuation, the value of an asset is the present value of the expected cashflows on the asset, discounted back at a rate that reflects the riskiness of these cashflows. This approach gets the most play in classrooms and comes with the best theoretical credentials. In this section, we will look at the foundations of the approach and some of the preliminary details on how we estimate its inputs.

We buy most assets because we expect them to generate cash flows for us in the future. In discounted cash flow valuation, we begin with a simple proposition. The value of an asset is not what someone perceives it to be worth but it is a function of the expected cash flows on that asset.

Put simply, assets with high and predictable cash flows should have higher values than assets with low and volatile cash flows. In discounted cash flow valuation, we estimate the value of an asset as the present value of the expected cash flows on it. The cashflows will vary from asset to asset -- dividends for stocks, coupons interest and the face value for bonds and after-tax cashflows for a business.

The discount rate will be a function of the riskiness of the estimated cashflows, with higher rates for riskier assets and lower rates for safer ones. Using discounted cash flow models is in some sense an act of faith. 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.

No such analyst exists, of course, but we all aspire to be as close as we can to this perfect analyst. The problem lies in the fact that none of us ever gets to see what the true intrinsic value of an asset is and we therefore have no way of knowing whether our discounted cash flow valuations are close to the mark or not.

There are three distinct ways in which we can categorize discounted cash flow models. In the first, we differentiate between valuing a business as a going concern as opposed to a collection of assets. In the second, we draw a distinction between valuing the equity in a business and valuing the business itself. In the third, we lay out three different and equivalent ways of doing discounted cash flow valuation — the expected cash flow approach, a value based upon excess returns and adjusted present value.

The value of an asset in the discounted cash flow framework is the present value of the expected cash flows on that asset. Extending this proposition to valuing a business, it can be argued that the value of a business is the sum of the values of the individual assets owned by the business. While this may be technically right, there is a key difference between valuing a collection of assets and a business.

A business or a company is an on-going entity with assets that it already owns and assets it expects to invest in the future. This can be best seen when we look at the financial balance sheet as opposed to an accounting balance sheet for an ongoing company in figure 1. Note that investments that have already been made are categorized as assets in place, but investments that we expect the business to make in the future are growth assets.

A financial balance sheet provides a good framework to draw out the differences between valuing a business as a going concern and valuing it as a collection of assets.

In a going concern valuation, we have to make our best judgments not only on existing investments but also on expected future investments and their profitability.

While this may seem to be foolhardy, a large proportion of the market value of growth companies comes from their growth assets. In an asset-based valuation, we focus primarily on the assets in place and estimate the value of each asset separately.

Adding the asset values together yields the value of the business. For companies with lucrative growth opportunities, asset-based valuations will yield lower values than going concern valuations. One special case of asset-based valuation is liquidation valuation, where we value assets based upon the presumption that they have to be sold now.

In theory, this should be equal to the value obtained from discounted cash flow valuations of individual assets but the urgency associated with liquidating assets quickly may result in a discount on the value.

How large the discount will be will depend upon the number of potential buyers for the assets, the asset characteristics and the state of the economy. There are two ways in which we can approach discounted cash flow valuation. The first is to value the entire business, with both assets-in-place and growth assets; this is often termed firm or enterprise valuation.

The cash flows before debt payments and after reinvestment needs are called free cash flows to the firm , and the discount rate that reflects the composite cost of financing from all sources of capital is called the cost of capital. The second way is to just value the equity stake in the business, and this is called equity valuation. The cash flows after debt payments and reinvestment needs are called free cash flows to equity, and the discount rate that reflects just the cost of equity financing is the cost of equity.

Note also that we can always get from the former firm value to the latter equity value by netting out the value of all non-equity claims from firm value. Done right, the value of equity should be the same whether it is valued directly by discounting cash flows to equity a the cost of equity or indirectly by valuing the firm and subtracting out the value of all non-equity claims.

The model that we have presented in this section, where expected cash flows are discounted back at a risk-adjusted discount rate, is the most commonly used discounted cash flow approach but there are two widely used variants.

In the first, we separate the cash flows into excess return cash flows and normal return cash flows. Earning the risk-adjusted required return cost of capital or equity is considered a normal return cash flow but any cash flows above or below this number are categorized as excess returns; excess returns can therefore be either positive or negative.

With the excess return valuation framework, the value of a business can be written as the sum of two components: If we make the assumption that the accounting measure of capital invested book value of capital is a good measure of capital invested in assets today, this approach implies that firms that earn positive excess return cash flows will trade at market values higher than their book values and that the reverse will be true for firms that earn negative excess return cash flows.

In the second variation, called the adjusted present value APV approach , we separate the effects on value of debt financing from the value of the assets of a business.

In the APV approach, the value of a firm can be written as follows: In contrast to the conventional approach, where the effects of debt financing are captured in the discount rate, the APV approach attempts to estimate the expected dollar value of debt benefits and costs separately from the value of the operating assets. While proponents of each approach like to claim that their approach is the best and most precise, we will argue that the three approaches yield the same estimates of value, if we make consistent assumptions.

There are three inputs that are required to value any asset in this model - the expected cash flow , the timing of the cash flow and the discount rate that is appropriate given the riskiness of these cash flows.

In valuation, we begin with the fundamental notion that the discount rate used on a cash flow should reflect its riskiness, with higher risk cash flows having higher discount rates. There are two ways of viewing risk. The first is purely in terms of the likelihood that an entity will default on a commitment to make a payment, such as interest or principal due, and this is called default risk.

When looking at debt, the cost of debt is the rate that reflects this default risk. The second way of viewing risk is in terms of the variation of actual returns around expected returns. The actual returns on a risky investment can be very different from expected returns; the greater the variation, the greater the risk.

When looking at equity, we tend to use measures of risk based upon return variance. While the discussion of risk and return models elsewhere in this site will look at the different models that attempt to do this in far more detail, there are some basic points on which these models agree.

The first is that risk in an investment has to perceived through the eyes of the marginal investor in that investment, and this marginal investor is assumed to be well diversified across multiple investments. Therefore, the risk in an investment that should determine discount rates is the non-diversifiable or market risk of that investment. The second is that the expected return on any investment can be obtained starting with the expected return on a riskless investment, and adding to it a premium to reflect the amount of market risk in that investment.

This expected return yields the cost of equity. The cost of capital can be obtained by taking an average of the cost of equity, estimated as above, and the after-tax cost of borrowing, based upon default risk, and weighting by the proportions used by each.

We will argue that the weights used, when valuing an on-going business, should be based upon the market values of debt and equity. While there are some analysts who use book value weights, doing so violates a basic principle of valuation, which is that at a fair value [3] , one should be indifferent between buying and selling an asset. In the strictest sense, the only cash flow an equity investor gets out of a publicly traded firm is the dividend; models that use the dividends as cash flows are called dividend discount models.

A broader definition of cash flows to equity would be the cash flows left over after the cash flow claims of non-equity investors in the firm have been met interest and principal payments to debt holders and preferred dividends and after enough of these cash flows has been reinvested into the firm to sustain the projected growth in cash flows. The cashflow to the firm is the cumulated cash flow to all claimholders in the firm. One way to obtain this cashflow is to add the free cash flows to equity to the cash flows to lenders debt and preferred stockholders.

It is while estimating the expected growth in cash flows in the future that analysts confront uncertainty most directly. There are three generic ways of estimating growth. The peril is that past growth may provide little indication of future growth. The second is to obtain estimates of growth from more informed sources.

The bias associated with both these sources should raise questions about the resulting valuations. We will promote a third way, where the expected growth rate is tied to two variables that are determined by the firm being valued - how much of the earnings are reinvested back into the firm and how well those earnings are reinvested.

In the equity valuation model, this expected growth rate is a product of the retention ratio, i. In the firm valuation model, the expected growth rate is a product of the reinvestment rate, which is the proportion of after-tax operating income that goes into net new investments and the return on capital earned on these investments. The advantages of using these fundamental growth rates are two fold. The first is that the resulting valuations will be internally consistent and companies that are assumed to have high growth are required to pay for the growth with more reinvestment.

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