A philosophical basis for Valuation Many investors believe that the pursuit of 'true value' based upon financial fundamentals is a fruitless one in markets where prices often seem to have little to do with value. There have always been investors in financial markets who have argued that market prices are determined by the perceptions (and misperceptions) of buyers and sellers, and not by anything as prosaic as cashflows or earnings. Perceptions matter, but they cannot be all that matter. Asset prices cannot be justified by merely using the “bigger fool” theory.
Misconceptions about Valuation • Myth 1: A valuation is an objective search for “true” value • Truth 1.1: All valuations are biased. The only questions are how much and in which direction. • Truth 1.2: The direction and magnitude of the bias in your valuation is directly proportional to who pays you and how much you are paid. • Myth 2.: A good valuation provides a precise estimate of value • Truth 2.1: There are no precise valuations • Truth 2.2: The payoff to valuation is greatest when valuation is least precise. • Myth 3: . The more quantitative a model, the better the valuation • Truth 3.1: One’s understanding of a valuation model is inversely proportional to the number of inputs required for the model. • Truth 3.2: Simpler valuation models do much better than complex ones.
Approaches to Valuation • Discounted cashflow valuation: Relates the value of an asset to the present value of expected future cashflows on that asset. • 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. • Contingent claim valuation: Uses option pricing models to measure the value of assets that share option characteristics.
Basis for all valuation approaches • The use of valuation models in investment decisions (i.e., in decisions on which assets are under valued and which are over valued) are based upon • a perception that markets are inefficient and make mistakes in assessing value • an assumption about how and when these inefficiencies will get corrected • In an efficient market, the market price is the best estimate of value. The purpose of any valuation model is then the justification of this value.
Efficient Market Hypothesis (EMH) • Definition 1: A market is said to be efficient with respect to some information set, It, if it is impossible to make economic profitson the basis of information set It. • Economic profits: Profits after adjusting for risk and transaction costs (such as, brokerage fees, investment advisory fees). • Economic profits = Actual return - Expected return - Transaction costs • Expected Return: CAPM provides one estimate of expected return. Other estimates: Arbitrage Pricing Theory, Historical Industry Returns.
EMH continued: • Models of Expected Returns • CAPM: Expected return on stock i = Riskfree rate + (Beta of i with respect to Market)*(Expected return on Market - Riskfree rate) • APT: Expected return on stock i = Riskfree rate + (Beta of i with respect to Factor 1)*(Expected return on Factor 1 - Riskfree rate) + (Beta of i with respect to Factor 2)*(Expected return on Factor 2 - Riskfree rate) + ...
EMH continued • Models of Expected Returns • Historical Industry Returns: Expected Return on stock i = Average historical return of other firms in the same industry as company i.
EMH continued: • Information set: • Weak form of EMH : Past history of prices of the particular security. • Semistrong form of EMH: All publicly available information. • Strong form of EMH: All public and private information.
Efficient Market Hypothesis • Definition 2: If capital markets are efficient then purchase or sale of any security at the prevailing market price is a zero-NPV transaction. • Definition 3 (Technical definition): The capital market is efficient with respect to an information set if and only if revealing that information to all investors would change neither equilibrium prices nor portfolios.
Discounted Cash Flow Valuation • What is it: In discounted cash flow valuation, the value of an asset is the present value of the expected cash flows on the asset. • Philosophical Basis: Every asset has an intrinsic value that can be estimated, based upon its characteristics in terms of cash flows, growth and risk. • Information Needed: To use discounted cash flow valuation, you need • to estimate the life of the asset • to estimate the cash flows during the life of the asset • to estimate the discount rate to apply to these cash flows to get present value
Advantages of DCF Valuation • Since DCF valuation, done right, is based upon an asset’s fundamentals, it should be less exposed to market moods and perceptions. • If good investors buy businesses, rather than stocks (the Warren Buffett adage), discounted cash flow valuation is the right way to think about what you are getting when you buy an asset. • DCF valuation forces you to think about the underlying characteristics of the firm, and understand its business. If nothing else, it brings you face to face with the assumptions you are making when you pay a given price for an asset.
Disadvantages of DCF valuation • Since it is an attempt to estimate intrinsic value, it requires far more inputs and information than other valuation approaches • These inputs and information are not only noisy (and difficult to estimate), but can be manipulated by the savvy analyst to provide the conclusion he or she wants. • For example: • An entrepreneur can get a high valuation by overestimating cashflows and/or underestimating discount rates. • A venture capitalist can buy equity from an entrepreneur at a lower price by underestimating cashflows. • An entrepreneur and venture capitalist can get a higher price for their IPO by overestimating cashflows and/or underestimating discount rates.
Disadvantages of DCF valuation • In an intrinsic valuation model, there is no guarantee that anything will emerge as under- or over-valued. Thus, it is possible in a DCF valuation model, to find every stock in a market to be over-valued. This can be a problem for • equity research analysts, whose job it is to follow sectors and make recommendations on the most under- and over-valued stocks in that sector • equity portfolio managers, who have to be fully (or close to fully) invested in equities
When DCF Valuation works best • This approach is easiest to use for assets (firms) whose • cashflows are currently positive and • can be estimated with some reliability for future periods, and • where a proxy for risk that can be used to obtain discount rates is available. • It works best for investors who either • have a long time horizon, allowing the market time to correct its valuation mistakes and for price to revert to “true” value or • are capable of providing the catalyst needed to move price to value, as would be the case if you were an activist investor or a potential acquirer of the whole firm
Relative Valuation • What is it?: The value of any asset can be estimated by looking at how the market prices “similar” or ‘comparable” assets. • Philosophical Basis: The intrinsic value of an asset is impossible (or close to impossible) to estimate. The value of an asset is whatever the market is willing to pay for it (based upon its characteristics) • Information Needed: To do a relative valuation, you need • an identical asset, or a group of comparable or similar assets • a standardized measure of value (in equity, this is obtained by dividing the price by a common variable, such as earnings or book value) • and if the assets are not perfectly comparable, variables to control for the differences • Market Inefficiency: Pricing errors made across similar or comparable assets are easier to spot, easier to exploit and are much more quickly corrected.
Advantages of Relative Valuation • Relative valuation is much more likely to reflect market perceptions and moods than discounted cash flow valuation. This can be an advantage when it is important that the price reflect these perceptions as is the case when • the objective is to sell a security at that price today (as in the case of an IPO) • With relative valuation, there will always be a significant proportion of securities that are under- valued and over-valued. • Since portfolio managers are judged based upon how they perform on a relative basis (to the market and other money managers), relative valuation is more tailored to their needs • Relative valuation generally requires less information than discounted cash flow valuation (especially when multiples are used as screens)
Disadvantages of Relative Valuation • A portfolio that is composed of stocks which are undervalued on a relative basis may still be overvalued, even if the analysts’ judgments are right. It is just less overvalued than other securities in the market. • Relative valuation is built on the assumption that markets are correct in the aggregate, but make mistakes on individual securities. To the degree that markets can be over or under valued in the aggregate, relative valuation will fail • Relative valuation may require less information in the way in which most analysts and portfolio managers use it. However, this is because implicit assumptions are made about other variables (that would have been required in a discounted cash flow valuation). To the extent that these implicit assumptions are wrong the relative valuation will also be wrong.
When relative valuation works best.. • This approach is easiest to use when • there are a large number of assets comparable to the one being valued • these assets are priced in a market • there exists some common variable that can be used to standardize the price • This approach tends to work best for investors • who have relatively short time horizons • are judged based upon a relative benchmark (the market, other portfolio managers following the same investment style etc.) • can take actions that can take advantage of the relative mispricing; for instance, a portfolio manager specializing in technology stocks can buy the under valued and sell the over valued assets
Contingent Claim (Option) Valuation • Options have several features • They derive their value from an underlying asset, which has value • The payoff on a call (put) option occurs only if the value of the underlying asset is greater (lesser) than an exercise price that is specified at the time the option is created. If this contingency does not occur, the option is worthless. • They have a fixed life • Any security or project that shares these features can be valued as an option.
Direct Examples of Options • Listed options, which are options on traded assets, that are issued by, listed on and traded on an option exchange. • Warrants, which are call options on traded stocks, that are issued by the company. The proceeds from the warrant issue go to the company, and the warrants are often traded on the market.
Indirect Examples of Options • Equity in a deeply troubled firm - a firm with negative earnings and high leverage - can be viewed as an option to liquidate that is held by the stockholders of the firm. Viewed as such, it is a call option on the assets of the firm. • The reserves owned by natural resource firms can be viewed as call options on the underlying resource, since the firm can decide whether and how much of the resource to extract from the reserve, • The patent owned by a firm or an exclusive license issued to a firm can be viewed as an option on the underlying product (project). The firm owns this option for the duration of the patent.
Advantages of Using Option Pricing Models • Option pricing models allow us to value assets that we otherwise would not be able to value. For instance, equity in deeply troubled firms and the stock of a small, bio-technology firm (with no revenues and profits) are difficult to value using discounted cash flow approaches or with multiples. They can be valued using option pricing. • Option pricing models provide us fresh insights into the drivers of value. In cases where an asset is deriving its value from its option characteristics, for instance, more risk or variability can increase value rather than decrease it.
Disadvantages of Option Pricing Models • When real options (which includes the natural resource options and the product patents) are valued, many of the inputs for the option pricing model are difficult to obtain. For instance, projects do not trade and thus getting a current value for a project or a variance may be a daunting task. • The option pricing models derive their value from an underlying asset. Thus, to do option pricing, you first need to value the assets. It is therefore an approach that is an addendum to another valuation approach.
Discounted Cashflow Valuation: Basis for Approach • where, • n = Life of the asset • CFt = Cashflow in period t • r = Discount rate reflecting the riskiness of the estimated cashflows
Equity Valuation versus Firm Valuation • Value just the equity stake in the business • Value the entire business, which includes, besides equity, the other claimholders in the firm
I.Equity Valuation • The value of equity is obtained by discounting expected cashflows to equity, i.e., the residual cashflows after meeting all expenses, tax obligations and interest and principal payments, at the cost of equity, i.e., the rate of return required by equity investors in the firm. where, CF to Equityt = Expected Cashflow to Equity in period t ke = Cost of Equity • The dividend discount model is a specialized case of equity valuation, and the value of a stock is the present value of expected future dividends.
II. Firm Valuation • The value of the firm is obtained by discounting expected cashflows to the firm, i.e., the residual cashflows after meeting all operating expenses and taxes, but prior to debt payments, at the weighted average cost of capital, which is the cost of the different components of financing used by the firm, weighted by their market value proportions. where, CF to Firmt = Expected Cashflow to Firm in period t WACC = Weighted Average Cost of Capital
Cash Flows and Discount Rates • Assume that you are analyzing a company with the following cashflows for the next five years. Year CF to Equity Int Exp (1-t) CF to Firm 1 $ 50 $ 40 $ 90 2 $ 60 $ 40 $ 100 3 $ 68 $ 40 $ 108 4 $ 76.2 $ 40 $ 116.2 5 $ 83.49 $ 40 $ 123.49 Terminal Value $ 1603.008 $ 2363.008 • Assume also that the cost of equity is 13.625% and the firm can borrow long term at 10%. (The tax rate for the firm is 50%.) • The current market value of equity is $1,073 and the value of debt outstanding is $800.
Equity versus Firm Valuation Method 1: Discount CF to Equity at Cost of Equity to get value of equity • Cost of Equity = 13.625% • PV of Equity = 50/1.13625 + 60/1.136252 + 68/1.136253 + 76.2/1.136254 + (83.49+1603)/1.136255 = $1073 Method 2: Discount CF to Firm at Cost of Capital to get value of firm Cost of Debt = Pre-tax rate (1- tax rate) = 10% (1-.5) = 5% WACC = 13.625% (1073/1873) + 5% (800/1873) = 9.94% PV of Firm = 90/1.0994 + 100/1.09942 + 108/1.09943 + 116.2/1.09944 + (123.49+2363)/1.09945 = $1873 • PV of Equity = PV of Firm - Market Value of Debt = $ 1873 - $ 800 = $1073
First Principle of Valuation • Never mix and match cash flows and discount rates. • The key error to avoid is mismatching cashflows and discount rates, since discounting cashflows to equity at the weighted average cost of capital will lead to an upwardly biased estimate of the value of equity, while discounting cashflows to the firm at the cost of equity will yield a downward biased estimate of the value of the firm.
Discounted Cash Flow Valuation: The Steps • Estimate the discount rate or rates to use in the valuation • Discount rate can be either a cost of equity (if doing equity valuation) or a cost of capital (if valuing the firm) • Discount rate can be in nominal terms or real terms, depending upon whether the cash flows are nominal or real • Discount rate can vary across time. • Estimate the current earnings and cashflows on the asset, to either equity investors (CF to Equity) or to all claimholders (CF to Firm) • Estimate the future earnings and cash flows on the asset being valued, generally by estimating an expected growth rate in earnings. • Estimate when the firm will reach “stable growth” and what characteristics (risk & cash flow) it will have when it does. • Choose the right DCF model for this asset and value it.
The Key Inputs in DCF Valuation • Discount Rate • Cost of Equity, in valuing equity • Cost of Capital, in valuing the firm • Cash Flows • Cash Flows to Equity • Cash Flows to Firm • Growth (to get future cash flows) • Growth in Equity Earnings • Growth in Firm Earnings (Operating Income)
I. Estimating Discount Rates DCF Valuation
Estimating Inputs: Discount Rates • Critical ingredient in discounted cashflow valuation. Errors in estimating the discount rate or mismatching cashflows and discount rates can lead to serious errors in valuation. • At an intuitive level, the discount rate used should be consistent with both the riskiness and the type of cashflow being discounted. • Equity versus Firm: If the cash flows being discounted are cash flows to equity, the appropriate discount rate is a cost of equity. If the cash flows are cash flows to the firm, the appropriate discount rate is the cost of capital. • Currency: The currency in which the cash flows are estimated should also be the currency in which the discount rate is estimated. • Nominal versus Real: If the cash flows being discounted are nominal cash flows (i.e., reflect expected inflation), the discount rate should be nominal
Estimating Inputs: Discount Rates or Cost of Capital (WACC) • It will depend upon: • (a) the components of financing: Debt, Equity • (b) the cost of each component • The cost of capital is the cost of each component weighted by its relative market value. WACC = ke (E/(D+E)) + kd (D/(D+E)) where ke is cost of equity kdis cost of debt, E is market value of equity, D is typically book value of debt.
I. Cost of Equity • The cost of equity is the rate of return that investors require to make an equity investment in a firm. There are three approaches to estimating the cost of equity; • a dividend-growth model, • a risk and return model (e.g., CAPM), • industry average model (Historical Industry Returns).
I. Cost of Equity • The dividend growth model (which specifies the cost of equity to be the sum of the dividend yield and the expected growth in earnings) is based upon the premise that the current price is equal to the value. It cannot be used in valuation, if the objective is to find out if an asset is correctly valued. • A risk and return model, on the other hand, tries to answer two questions: • How do you measure risk? • How do you translate this risk measure into a risk premium? • Industry Average Returns • Assumes future returns of the company will be similar to the past returns of firms in that industry. • Needs no estimate of risk, or risk and return model.
What is Risk? • Risk, in traditional terms, is viewed as a ‘negative’. Webster’s dictionary, for instance, defines risk as “exposing to danger or hazard”. The Chinese symbols for risk are reproduced below: • The first symbol is the symbol for “danger”, while the second is the symbol for “opportunity”, making risk a mix of danger and opportunity.
Beta’s Properties • Betas are standardized around one. • If b = 1 ... Average risk investment b > 1 ... Above Average risk investment b < 1 ... Below Average risk investment b = 0 ... Riskless investment • The average beta across all investments is one.
Limitations of the CAPM • 1. The model makes unrealistic assumptions • 2. The parameters of the model cannot be estimated precisely • Definition of a market index • Firm may have changed during the 'estimation' period' • 3. The model does not work well • If the model is right, there should be • a linear relationship between returns and betas • the only variable that should explain returns is betas • - The reality is that • the relationship between betas and returns is weak • Other variables (size, price/book value) seem to explain differences in returns better.
Inputs required to use the CAPM - (a) the current risk-free rate (b) the expected return on the market index and (c) the beta of the asset being analyzed.
Riskfree Rate in Valuation • The correct risk free rate to use in a risk and return model is • a short-term Government Security rate (eg. T.Bill), since it has no default risk or price risk • a long-term Government Security rate, since most projects are long-term.
The Riskfree Rate • On a riskfree asset, the actual return is equal to the expected return. • Therefore, there is no variance around the expected return. (Strictly speaking, for an asset to be riskfree, its returns should not co-vary with the market returns. If an asset’s return has no variance, i.e., it does not vary, then it will not vary with anything including the market; hence, it will be a riskfree asset.) • For an investment to be riskfree, i.e., to have an actual return be equal to the expected return • There has to be no default risk, which generally implies that the security has to be issued by the U.S. government. Note, however, that not all governments can be viewed as default free.
Riskfree Rate in Practice • The riskfree rate is the rate on a zero coupon government bond matching the time horizon of the cash flow being analyzed. • Theoretically, this translates into using different riskfree rates for each cash flow - the 1 year zero coupon rate for the cash flow in year 2, the 2-year zero coupon rate for the cash flow in year 2 ... • Practically speaking, if there is substantial uncertainty about expected cash flows, the present value effect of using time varying riskfree rates is small enough that it may not be worth it.
The Bottom Line on Riskfree Rates • Using a long term government rate (even on a coupon bond) as the riskfree rate on all of the cash flows in a long term analysis will yield a close approximation of the true value. • For short term analysis, it is entirely appropriate to use a short term government security rate as the riskfree rate.