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FIN449 Valuation

FIN449 Valuation. Michael Dimond. Beta. What is beta? What does it measure? How do we find it? Is it important? Is it accurate?. Estimating Beta ( β ). The standard procedure for estimating beta is to regress stock returns ( R j ) against market returns ( R m ) - R j = a + b R m

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FIN449 Valuation

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  1. FIN449Valuation Michael Dimond

  2. Beta • What is beta? • What does it measure? • How do we find it? • Is it important? • Is it accurate?

  3. Estimating Beta (β) • The standard procedure for estimating beta is to regress stock returns (Rj) against market returns (Rm) - Rj = a + b Rm where a is the intercept and b is the slope of the regression • The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock. β is the slope of the regression line.

  4. Issues to watch in regression analysis • R-squared measures goodness of fit: How well the regression formula explains the data points which created it. • Standard Error measures the ± value of any particular point predicted by the regression formula within a degree of certainty (95% in the example below). • Relevant Range is the range of values in which these data have a valid relationship.

  5. How do risk & value relate? • As risk increases, the value of an asset diminishes. Conversely, as the risk of an asset decreases, the value should increase. • Risk is represented in the CAPM by beta (β), so as β changes, the present value of an asset also changes because of the effect on Ke: PVPERP = CF/(ke-g) • How far can the beta:value relationship be taken?

  6. Interestingly, beta can be negative. If beta is found by regressing the return of a single asset against the returns of the market and the returns move in the opposite direction (i.e. the stock is countercyclical), beta will be negative.

  7. What a negative beta indicates is that as returns on the market rise, returns on the asset decline, and vice versa.

  8. What are the implications of a negative beta? Ke = Rf + β(Rm – Rf) • β = 1.0 suggests an asset is equal in risk to the market. Ke = Rm • β < 1.0 suggests an asset is less risky (uncertain, volatile) than the market itself. Ke < Rm • β = 0.0 suggests an asset is equal in risk to the risk-free assetKe = Rf • Negative beta (β < 0.0) suggests an asset is less risky than the risk-free assetKe < Rf • Would you lend at less than the risk-free rate? • Could you borrow at less than the risk-free rate?

  9. Consider the effect of beta on the value of a zero-growth perpetuity • Fundamentally, as risk diminishes, the price one would pay for an asset increases. • Formulaically, as β diminishes the value increases, but the computation makes less sense when β gets below zero. • Where β(MRP) = -Rf, the value is undefined (Ke = 0) There are only certain circumstances when one would pay a significant premium for a counter-cyclical stock

  10. Regression Beta Problems Regressed beta has several problems: It has a low R-squared. It has a high standard error. It may produce a value which is not practical (such as negative beta). It reflects the firm’s business mix over the period of the regression, not the current mix. It reflects the firm’s average financial leverage over the period rather than the current leverage.

  11. Beta Estimation: The Noise Problem

  12. Beta Estimation: The Index Effect This regression shows a better fit (R2 = 0.94) and a fairly low standard error (0.03), but at the time of the regression Nokia was 70% of the index against which it was regressed. The solution is to regress against an index which does not include this company but is subject to the same economic forces.

  13. Solutions to the Regression Beta Problem Modify the regression beta by changing the index used to estimate the beta adjusting the regression beta estimate, by bringing in information about the fundamentals of the company Estimate the beta for the firm using the standard deviation in stock prices instead of a regression against an index. accounting earnings or revenues, which are less noisy than market prices. Estimate the beta for the firm from the bottom up without employing the regression technique. This will require understanding the business mix of the firm estimating the financial leverage of the firm Use an alternative measure of market risk that does not need a regression.

  14. Fundamental Drivers of Beta Ultimately beta & Ke need to make sense for the asset being valued. The riskier the asset is, the higher the required rate of return must be. Considering fundamentals is a good way to frame these thoughts. Product or Service: The beta value for a firm depends upon the sensitivity of the demand for its products and services and of its costs to macroeconomic factors that affect the overall market. Cyclical companies have higher betas than non-cyclical firms Firms which sell more discretionary products will have higher betas than firms that sell less discretionary products Operating Leverage: The greater the proportion of fixed costs in the cost structure of a business, the higher the beta will be of that business. This is because higher fixed costs increase your exposure to all risk, including market risk. Financial Leverage: The more debt a firm takes on, the higher the beta will be of the equity in that business. Debt creates a fixed cost, interest expenses, that increases exposure to market risk.

  15. Comparable Firms • Considering the fundamentals will help choose appropriately comparable firms and then develop a risk model (beta) based on them. • For investment purposes, is one stream of cash flows much like another? What matters about those cash flows? • Size • Growth Expectations • Cash Flows • Volatility • Exposure to economic inputs

  16. Comparable Firms • Given the firm that we are valuing, what is a “comparable” firm? • It is impossible to find an exactly identical firm to the one you are valuing. • While traditional analysis is built on the premise that firms in the same sector are comparable firms, valuation theory would suggest that a comparable firm is one which is similar to the one being analyzed in terms of fundamentals. • Damodaran says, “There is no reason why a firm cannot be compared with another firm in a very different business, if the two firms have the same risk, growth and cash flow characteristics.” This is not necessarily the case. Legal requirements may dictate limits in some applications but, more importantly, the underlying economics must make sense.

  17. Capital Structure Credit Status Depth of Management Personnel Experience Nature of Competition Maturity of the Business Products Markets Management Earnings Dividend-paying Capacity Book Value Position in Industry Criteria to Identify Comparable Firms SOURCE: Pratt et al, Valuing A Business (4th edition)

  18. Choosing Comparable Firms (1) • In valuing a manufacturer of electronic control equipment for the forest products industry, we found plenty of manufacturers of electronic control equipment but none for whom the forest products industry was a significant part of their market. • What to do? • For guideline companies, we selected manufacturers of other types of industrial equipment and supplies which sold to the forest products and related cyclical industries. We decided the markets served were more of an economic driving force than the physical nature of the products produced. Adapted from: Pratt et al, Valuing A Business (4th edition)

  19. Choosing Comparable Firms (2) • At the valuation date in the estate of Mark Gallo, there was only one publicly traded wine company stock, a tiny midget compared with the huge Gallo and, for other reasons as well, not a good guideline company. • What to do? • Experts for the taxpayer and for the IRS agreed it was appropriate to use guideline companies which were distillers, brewers, soft drink bottlers, and food companies with strong brand recognitions and which were subject to seasonal crop conditions and grower contracts. Adapted from: Pratt et al, Valuing A Business (4th edition)

  20. Equity Betas and Leverage The beta of equity alone can be written as a function of the unlevered beta and the debt-equity ratio L = u (1+ ((1-t)D/E)) where L = Levered or Equity Beta u = Unlevered Beta (Asset Beta) t = Corporate marginal tax rate D = Market Value of Debt E = Market Value of Equity While this beta is estimated on the assumption that debt carries no market risk (and has a beta of zero), you can have a modified version: L = u (1+ ((1-t)D/E)) - debt (1-t) (D/E)

  21. Relevered (Bottom-up) Betas The bottom up beta can be estimated by : Taking a weighted (by sales or operating income) average of the unlevered betas of the different businesses a firm is in. (The unlevered beta of a business can be estimated by looking at other firms in the same business) Lever up using the firm’s debt/equity ratio The bottom up beta will give you a better estimate of the true beta when It has lower standard error (SEaverage = SEfirm / √n (n = number of firms) It reflects the firm’s current business mix and financial leverage It can be estimated for divisions and private firms.

  22. Bottom-up Beta: Firm in Multiple Businesses (Boeing in 1998) Segment Estimated Value Unlevered Beta Segment Weight Commercial Aircraft 30,160.48 0.91 70.39% Defense 12,687.50 0.80 29.61% Estimated Value = Revenues of division * Enterprise Value/SalesBusiness Unlevered Beta of firm = 0.91 (.7039) + 0.80 (.2961) = 0.88 Levered Beta Calculation Market Value of Equity = $ 33,401 Market Value of Debt = $8,143 Market Debt/Equity Ratio = 24.38% Tax Rate = 35% Levered Beta for Boeing = 0.88 (1 + (1 - .35) (.2438)) = 1.02

  23. Alternatives to CAPM • APM • Fama-French

  24. Cost of Capital Ke Kd WACC

  25. 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

  26. Cost of Equity The cost of equity should be higher for riskier investments and lower for safer investments While risk is usually defined in terms of the variance of actual returns around an expected return, risk and return models in finance assume that the risk that should be rewarded (and thus built into the discount rate) in valuation should be the risk perceived by the marginal investor in the investment Most risk and return models in finance also assume that the marginal investor is well diversified, and that the only risk that he or she perceives in an investment is risk that cannot be diversified away (i.e, market or non-diversifiable risk)

  27. The CAPM: Cost of Equity Consider the standard approach to estimating cost of equity: Cost of Equity = Rf + Equity Beta * (E(Rm) - Rf) where, Rf = Riskfree rate E(Rm) = Expected Return on the Market Index (Diversified Portfolio) In practice, Short term government security rates are used as risk free rates Historical risk premiums are used for the risk premium Betas might be estimated by regressing stock returns against market returns

  28. Short term Government bonds are not riskfree On a riskfree asset, the actual return is equal to the expected return. Therefore, there is no variance around the expected return. For an investment to be riskfree, then, it has to have No default risk No reinvestment risk Thus, the riskfree rates in valuation will depend upon when the cash flow is expected to occur and will vary across time A simpler approach is to match the duration of the analysis (generally long term) to the duration of the riskfree rate (also long term) In emerging markets, there are two problems: The government might not be viewed as riskfree (Brazil, Indonesia) There might be no market-based long term government rate (China)

  29. Everyone uses historical premiums, but.. The historical premium is the premium that stocks have historically earned over riskless securities. Practitioners never seem to agree on the premium; it is sensitive to How far back you go in history… Whether you use T.bill rates or T.Bond rates Whether you use geometric or arithmetic averages. For instance, looking at the US: Arithmetic Average Geometric Average Period T.Bills T.Bonds T.Bills T.Bonds 1928-2001 8.09% 6.84% 6.21% 5.17% 1962-2001 5.89% 4.68% 4.74% 3.90% 1991-2001 10.62% 6.90% 9.44% 6.17%

  30. Historic US Risk-Free Rates

  31. 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

  32. Cost of Equity The cost of equity should be higher for riskier investments and lower for safer investments While risk is usually defined in terms of the variance of actual returns around an expected return, risk and return models in finance assume that the risk that should be rewarded (and thus built into the discount rate) in valuation should be the risk perceived by the marginal investor in the investment Most risk and return models in finance also assume that the marginal investor is well diversified, and that the only risk that he or she perceives in an investment is risk that cannot be diversified away (i.e, market or non-diversifiable risk)

  33. The CAPM: Cost of Equity Consider the standard approach to estimating cost of equity: Cost of Equity = Rf + Equity Beta * (E(Rm) - Rf) where, Rf = Riskfree rate E(Rm) = Expected Return on the Market Index (Diversified Portfolio) In practice, Short term government security rates are used as risk free rates Historical risk premiums are used for the risk premium Betas might be estimated by regressing stock returns against market returns

  34. If you choose to use historical premiums…. Go back as far as you can. A risk premium comes with a standard error. Given the annual standard deviation in stock prices is about 25%, the standard error in a historical premium estimated over 25 years is roughly: Standard Error in Premium = 25%/√25 = 25%/5 = 5% Be consistent in your use of the riskfree rate. Since we argued for long term bond rates, the premium should be the one over T.Bonds Use the geometric risk premium. It is closer to how investors think about risk premiums over long periods.

  35. Implied Equity Premiums If we use a basic discounted cash flow model, we can estimate the implied risk premium from the current level of stock prices. For instance, if stock prices are determined by a variation of the simple Gordon Growth Model: Value = Expected Dividends next year/ (Required Returns on Stocks - Expected Growth Rate) Dividends can be extended to included expected stock buybacks and a high growth period. Plugging in the current level of the index, the dividends on the index and expected growth rate will yield a “implied” expected return on stocks. Subtracting out the riskfree rate will yield the implied premium. This model can be extended to allow for two stages of growth - an initial period where the entire market will have earnings growth greater than that of the economy, and then a stable growth period.

  36. Estimating Implied Premium for U.S. Market: Jan 1, 2002 Level of the index = 1148 Treasury bond rate = 5.05% Expected Growth rate in earnings (next 5 years) = 10.3% (Consensus estimate for S&P 500) Expected growth rate after year 5 = 5.05% Dividends + stock buybacks = 2.74% of index (Current year) Year 1 Year 2 Year 3 Year 4 Year 5 Expected Dividends = $34.72 $38.30 $42.24 $46.59 $51.39 + Stock Buybacks Expected dividends + buybacks in year 6 = 51.39 (1.0505) = $ 54.73 1148 = 34.72/(1+r) + 38.30/(1+r)2+ + 42.24/(1+r)3 + 46.59/(1+r)4 + (51.39+(54.73/(r-.0505))/(1+r)5 Solving for r, r = 8.67%. (Only way to do this is trial and error) Implied risk premium = 8.67% - 5.05% = 3.62%

  37. Estimating Beta The standard procedure for estimating betas is to regress stock returns (Rj) against market returns (Rm) - Rj = a + b Rm where a is the intercept and b is the slope of the regression. The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock.

  38. Regressing Beta

  39. Regressing Beta

  40. Estimating Beta The standard procedure for estimating betas is to regress stock returns (Rj) against market returns (Rm) - Rj = a + b Rm where a is the intercept and b is the slope of the regression. The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock. This beta has three problems: It has high standard error and a low R-squared It reflects the firm’s business mix over the period of the regression, not the current mix It reflects the firm’s average financial leverage over the period rather than the current leverage.

  41. Beta Estimation: The Noise Problem

  42. Beta Estimation: The Index Effect

  43. Fundamental Drivers of Beta Product or Service: The beta value for a firm depends upon the sensitivity of the demand for its products and services and of its costs to macroeconomic factors that affect the overall market. Cyclical companies have higher betas than non-cyclical firms Firms which sell more discretionary products will have higher betas than firms that sell less discretionary products Operating Leverage: The greater the proportion of fixed costs in the cost structure of a business, the higher the beta will be of that business. This is because higher fixed costs increase your exposure to all risk, including market risk. Financial Leverage: The more debt a firm takes on, the higher the beta will be of the equity in that business. Debt creates a fixed cost, interest expenses, that increases exposure to market risk.

  44. Solutions to the Regression Beta Problem Modify the regression beta by changing the index used to estimate the beta adjusting the regression beta estimate, by bringing in information about the fundamentals of the company Estimate the beta for the firm using the standard deviation in stock prices instead of a regression against an index. accounting earnings or revenues, which are less noisy than market prices. Estimate the beta for the firm from the bottom up without employing the regression technique. This will require understanding the business mix of the firm estimating the financial leverage of the firm Use an alternative measure of market risk that does not need a regression.

  45. Equity Betas and Leverage The beta of equity alone can be written as a function of the unlevered beta and the debt-equity ratio L = u (1+ ((1-t)D/E)) where L = Levered or Equity Beta u = Unlevered Beta (Asset Beta) t = Corporate marginal tax rate D = Market Value of Debt E = Market Value of Equity While this beta is estimated on the assumption that debt carries no market risk (and has a beta of zero), you can have a modified version: L = u (1+ ((1-t)D/E)) - debt (1-t) (D/E)

  46. Bottom-up Betas The bottom up beta can be estimated by : Taking a weighted (by sales or operating income) average of the unlevered betas of the different businesses a firm is in. (The unlevered beta of a business can be estimated by looking at other firms in the same business) Lever up using the firm’s debt/equity ratio The bottom up beta will give you a better estimate of the true beta when It has lower standard error (SEaverage = SEfirm / √n (n = number of firms) It reflects the firm’s current business mix and financial leverage It can be estimated for divisions and private firms.

  47. Comparable Firms • For investment purposes, is one stream of cash flows much like another? • Size • Growth Expectations • Cash Flows • Volatility • Exposure to economic inputs

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