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Estimating the Discount Rate

Estimating the Discount Rate. P.V. Viswanath Based on Damodaran’s Corporate Finance. Inputs required to use the CAPM. According to the CAPM, the required rate of return on an asset will be: Required ROR = R f + b (E(R m ) - R f ) The inputs required to estimate the required ROR are:

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Estimating the Discount Rate

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  1. Estimating the Discount Rate P.V. Viswanath Based on Damodaran’s Corporate Finance

  2. Inputs required to use the CAPM • According to the CAPM, the required rate of return on an asset will be: Required ROR = Rf + b(E(Rm) - Rf) • The inputs required to estimate the required ROR are: (a) the current risk-free rate (b) the expected market risk premium (the premium expected for investing in risky assets over the riskless asset) (c) the beta of the asset being analyzed. P.V. Viswanath

  3. The Riskfree Rate • For an investment to be riskfree, i.e., to have an actual return be equal to the expected return, there must be: • No default risk; this usually means a government-issued security; but, not all governments are default free. • No uncertainty about reinvestment rates. • In practice, therefore, the riskfree rate is the rate on a zero coupon government bond matching the time horizon of the cash flow being analyzed. • Theoretically, this means using different riskfree rates for each cash flow - the 1 year zero coupon rate for the cash flow in year 1, the 2-year zero coupon rate for the cash flow in year 2 ... • Practically, if there is substantial uncertainty about expected cash flows, it is enough to use a single riskfree rate for all flows. P.V. Viswanath

  4. 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 appropriate to use a short term government security rate as the riskfree rate. • If the analysis is being done in real terms (rather than nominal terms) use a real riskfree rate, which can be obtained in one of two ways – • from an inflation-indexed government bond, if one exists • set equal, approximately, to the long term real growth rate of the economy in which the valuation is being done. P.V. Viswanath

  5. Measurement of the risk premium • The risk premium is the premium that investors demand for investing in an average risk investment, relative to the riskfree rate. • As a general proposition, this premium should be • greater than zero • increase with the risk aversion of the investors in that market • increase with the riskiness of the “average” risk investment P.V. Viswanath

  6. Estimating Risk Premiums in Practice • Survey investors on their desired risk premiums and use the average premium from these surveys. • Surveying in practice is difficult because there is no way to ensure that the numbers that participants provide are the ones they use in their own decision making. • Assume that the actual premium delivered over long time periods is equal to the expected premium - i.e., use historical data • Estimate the implied premium in today’s asset prices. P.V. Viswanath

  7. The Historical Premium Approach • This is the default approach used by most to arrive at the premium to use in the model • In most cases, this approach does the following • it defines a time period for the estimation (1926-Present, 1962-Present....) • it calculates average returns on a stock index during the period • it calculates average returns on a riskless security over the period • it calculates the difference between the two • and uses it as a premium looking forward • The limitations of this approach are: • it assumes that the risk aversion of investors has not changed in a systematic way across time. (The risk aversion may change from year to year, but it reverts back to historical averages) • it assumes that the riskiness of the “risky” portfolio (stock index) has not changed in a systematic way across time. P.V. Viswanath

  8. Historical Average Premiums for the United States P.V. Viswanath

  9. What is the right historical premium? • Go back as far as you can, so as to reduce the standard error of the estimate. The standard error is roughly equal to • Standard Error in Risk premium = Annual Standard deviation in Stock prices / Square root of the number of years of historical data • With an annual standard deviation in stock prices of 24% and 25 years of data, for instance, the standard error would be Standard Error of Estimate = 24%/ √25 = 4.8% • Be consistent in your use of a riskfree rate -- if you use the T.Bill(T.Bond) rate, use the spread over the T.Bill (T.Bond) rate. • Use arithmetic averages for one-year estimates of costs of equity and geometric averages for estimates of long term costs of equity. P.V. Viswanath

  10. 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 the simple Gordon Growth Model: • Value = Expected Dividends next year/ (Required Returns on Stocks - Expected Growth Rate) • 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. P.V. Viswanath

  11. Implied Equity Premiums • This is a market neutral approach to estimate the implied spread, i.e., it assumes that the current level of the market is correct) • For instance, if the S&P 500 is at 1100, expected dividends next year on the index is 33 and the expected growth in the earnings/dividends is 7%: • 1100 = 33/(r - .07) • Solving for r, we find r = 10% • If the treasury bond rate is 7%, the implied Equity Premium = 10% - 7% = 3% • The problems with this approach are: • the discounted cash flow model used to value the index has to be correct. • the inputs on dividends and expected growth have to be correct • it implicitly assumes that the market is currently correctly valued P.V. Viswanath

  12. In Summary... • The historical risk premium is 6.6%, if we use a geometric risk premium, and much higher, if we use arithmetic averages. • The current implied risk premium is much lower. Even if we use liberal estimates of cashflows (dividends +stock buybacks) and high expected growth rates, the implied premium is about 4% and probably lower. • Implied risk premium using the S&P 500 Index value is ~1%! • We will use a risk premium of 5.5%, because • The historical risk premium is much too high to use in a market, where equities are priced with with premiums of 4% or lower. • The implied premium might be too low, especially if we believe that markets can become overvalued. P.V. Viswanath

  13. 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. P.V. Viswanath

  14. Estimating Performance • The intercept of the regression provides a simple measure of performance during the period of the regression, relative to the capital asset pricing model. Rj = Rf + bj (Rm - Rf) = Rf (1-bj) + b Rm ........... Capital Asset Pricing Model Rj = aj + bj Rm ........... Regression Equation • If aj > Rf (1-bj) ..Stock did better than expected during reg period aj = Rf (1-bj) ..Stock did as well as expected during regr period aj < Rf (1-bj) ..Stock did worse than expected during reg period • Jensen's alpha, a measure of stock performance, is measure as aj - Rf (1-b) P.V. Viswanath

  15. Firm Specific and Market Risk • The R squared (R2) of the regression provides an estimate of the proportion of the risk (variance) of a firm that can be attributed to market risk. • The balance (1 - R2) can be attributed to firm specific risk. P.V. Viswanath

  16. Setting up for the Estimation • Decide on an estimation period • Services use periods ranging from 2 to 5 years for the regression • Longer estimation period provides more data, but firms change. • Shorter periods can be affected more easily by significant firm-specific event that occurred during the period • Decide on a return interval - daily, weekly, monthly • Shorter intervals yield more observations, but suffer from more noise. • Noise is created by stocks not trading and biases all betas towards one. • Estimate returns (including dividends) on stock • Return = (PriceEnd - PriceBeginning + DividendsPeriod)/ PriceBeginning • Included dividends only in ex-dividend month • Choose a market index, and estimate returns (inclusive of dividends) on the index for each interval for the period. P.V. Viswanath

  17. Choosing the Parameters: Boeing • Period used: 5 years • Return Interval = Monthly • Market Index: S&P 500 Index. • For instance, to calculate returns on Boeing in May 1995, • Price for Boeing at end of April= $ 27.50 • Price for Boeing at end of May = $ 29.44 • Dividends during month = $0.125 (It was an ex-dividend month) • Return =($29.44 - $ 27.50 + $ 0.125)/$27.50= 7.50% • To estimate returns on the index in the same month • Index level (including dividends) at end of April = 514.7 • Index level (including dividends) at end of May = 533.4 • Dividends on the Index in May = 1.84 • Return =(533.4-514.7+1.84)/ 514.7 = 3.99% P.V. Viswanath

  18. Boeing’s Historical Beta Boeing versus S&P 500: 10/93-9/98 10.00% Regression line 5.00% Returns on Boeing 0.00% -25.00% -20.00% -15.00% -10.00% -5.00% 0.00% 5.00% 10.00% 15.00% 20.00% -5.00% Beta is slope of this line -10.00% -15.00% Each point represents a month of data. -20.00% Returns on S&P 500 P.V. Viswanath

  19. The Regression Output • ReturnsBoeing = -0.09% + 0.96 ReturnsS & P 500 • R squared=29.57% • Intercept = -0.09% • Slope = 0.96 P.V. Viswanath

  20. Analyzing Boeing’s Performance • Intercept = -0.09% • This is an intercept based on monthly returns. Thus, it has to be compared to a monthly riskfree rate. • Between 1993 and 1998, • Monthly Riskfree Rate = 0.4% • Riskfree Rate (1-Beta) = 0.4% (1-0.96) = .01% • The Comparison is then between Intercept versus Riskfree Rate (1 - Beta) -0.09% versus 0.4%(1-0.96)= 0.01% • Jensen’s Alpha = -0.09% -(0.01%) = -0.10% • Boeing did 0.1% worse than expected, per month, between 1993 and 1998. • Annualized, Boeing’s annual excess return = (1-.0001)12-1= -1.22% P.V. Viswanath

  21. Breaking down Boeing’s Risk • R Squared = 29.57% • This implies that • 29.57% of the risk at Boeing comes from market sources • 70.43%, therefore, comes from firm-specific sources • The firm-specific risk is diversifiable and will not be rewarded P.V. Viswanath

  22. Estimating Expected Returns: December 31, 1998 • Boeing’s Beta = 0.96 • Riskfree Rate = 5.00% (Long term Government Bond rate) • Risk Premium = 5.50% (Approximate historical premium) • Expected Return = 5.00% + 0.96 (5.50%) = 10.31% P.V. Viswanath

  23. How managers use this expected return • Managers at Boeing • need to make at least 10.31% as a return for their equity investors to break even. • this is the hurdle rate for projects, when the investment is analyzed from an equity standpoint • In other words, Boeing’s cost of equity is 10.31%. • What is the cost of not delivering this cost of equity? P.V. Viswanath

  24. Fundamental Determinants of Betas • Type of Business: Firms in more cyclical businesses or that sell products that are more discretionary to their customers will have higher betas than firms that are in non-cyclical businesses or sell products that are necessities or staples. • Operating Leverage: Firms with greater fixed costs (as a proportion of total costs) will have higher betas than firms will lower fixed costs (as a proportion of total costs) • Financial Leverage: Firms that borrow more (higher debt, relative to equity) will have higher equity betas than firms that borrow less. P.V. Viswanath

  25. Determinant 1: Product Type • Industry Effects: 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 P.V. Viswanath

  26. Determinant 2: Operating Leverage Effects • Operating leverage refers to the proportion of the total costs of the firm that are fixed. • Other things remaining equal, higher operating leverage results in greater earnings variability which in turn results in higher betas. P.V. Viswanath

  27. Measures of Operating Leverage Fixed Costs Measure = Fixed Costs / Variable Costs • This measures the relationship between fixed and variable costs. The higher the proportion, the higher the operating leverage. EBIT Variability Measure = % Change in EBIT / % Change in Revenues • This measures how quickly the earnings before interest and taxes changes as revenue changes. The higher this number, the greater the operating leverage. P.V. Viswanath

  28. A Look at The Home Depot’s Operating Leverage P.V. Viswanath

  29. Reading The Home Depot’s Operating Leverage • Operating Leverage = % Change in EBIT/ % Change in Sales = 34.94%/ 32.58% = 1.07 • This is similar to the operating leverage for other retail firms, which we computed to be 1.05. This would suggest that The Home Depot has a similar cost structure to its competitors. P.V. Viswanath

  30. A Test Assume that you are comparing a European automobile manufacturing firm with a U.S. automobile firm. European firms are generally much more constrained in terms of laying off employees, if they get into financial trouble. What implications does this have for betas, if they are estimated relative to a common index? • European firms will have much higher betas than U.S. firms • European firms will have similar betas to U.S. firms • European firms will have much lower betas than U.S. firms P.V. Viswanath

  31. Determinant 3: Financial Leverage • As firms borrow, they create fixed costs (interest payments) that make their earnings to equity investors more volatile. • This increased earnings volatility which increases the equity beta P.V. Viswanath

  32. 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 t = Corporate marginal tax rate D = Market Value of Debt E = Market Value of Equity • The unlevered beta measures the riskiness of the business that a firm is in and is often called an asset beta. P.V. Viswanath

  33. Effects of leverage on betas: Boeing • The regression beta for Boeing is 0.96. This beta is a levered beta (because it is based on stock prices, which reflect leverage) and the leverage implicit in the beta estimate is the average market debt equity ratio during the period of the regression (1993 to 1998) • The average debt equity ratio during this period was 17.88%. • The unlevered beta for Boeing can then be estimated:(using a marginal tax rate of 35%) = Current Beta / (1 + (1 - tax rate) (Average Debt/Equity)) = 0.96 / ( 1 + (1 - 0.35) (0.1788)) = 0.86 P.V. Viswanath

  34. Boeing : Beta and Leverage Debt to Debt/Equity Beta EffectCapital Ratio of Leverage 0.00% 0.00% 0.86 0.00 10.00% 11.11% 0.92 0.06 20.00% 25.00% 1.00 0.14 30.00% 42.86% 1.10 0.24 40.00% 66.67% 1.23 0.37 50.00% 100.00% 1.42 0.56 60.00% 150.00% 1.70 0.84 70.00% 233.33% 2.16 1.30 80.00% 400.00% 3.10 2.24 90.00% 900.00% 5.89 5.03 P.V. Viswanath

  35. Betas are weighted Averages • The beta of a portfolio is always the market-value weighted average of the betas of the individual investments in that portfolio. • Thus, • the beta of a mutual fund is the weighted average of the betas of the stocks and other investment in that portfolio • the beta of a firm after a merger is the market-value weighted average of the betas of the companies involved in the merger. P.V. Viswanath

  36. The Boeing/McDonnell Douglas Merger Company Beta Debt Equity Firm Value Boeing 0.95 $ 3,980 $ 32,438 $ 36,418 McDonnell Douglas 0.90 $ 2,143 $ 12,555 $ 14,698 P.V. Viswanath

  37. Beta Estimation: Step 1 • Calculate the unlevered betas for both firms Boeing = 0.95/(1+0.65*(3980/32438)) = 0.88 McDonnell Douglas = 0.90/(1+0.65*(2143/12555)) = 0.81 • Calculate the unlevered beta for the combined firm Unlevered Beta for combined firm = 0.88 (36,418/51,116) + 0.81 (14,698/51,116) = 0.86 P.V. Viswanath

  38. Beta Estimation: Step 2 • Boeing’s acquisition of McDonnell Douglas was accomplished by issuing new stock in Boeing to cover the value of McDonnell Douglas’s equity of $12,555 million. Debt = McDonnell Douglas Old Debt + Boeing’s Old Debt = $3,980 + $2,143 = $6,123 million Equity = Boeing’s Old Equity + New Equity used for Acquisition = $ 32,438 + $ 12,555 = $44,993 million D/E Ratio = $ 6,123/44,993 = 13.61% New Beta = 0.86 (1 + 0.65 (.1361)) = 0.94 P.V. Viswanath

  39. Firm Betas versus divisional Betas • Firm Betas as weighted averages: The beta of a firm is the weighted average of the betas of its individual projects. • At a broader level of aggregation, the beta of a firm is the weighted average of the betas of its individual division. P.V. Viswanath

  40. Bottom-up versus Top-down Beta • The top-down beta for a firm comes from a regression • The bottom up beta can be estimated by doing the following: • Find out the businesses that a firm operates in • Find the unlevered betas of other firms in these businesses • Take a weighted (by sales or operating income) average of these unlevered betas • Lever up using the firm’s debt/equity ratio • The bottom up beta will give you a better estimate of the true beta when • the standard error of the beta from the regression is high (and) the beta for a firm is very different from the average for the business • the firm has reorganized or restructured itself substantially during the period of the regression • when a firm is not traded P.V. Viswanath

  41. The Home Depot’s Comparable Firms P.V. Viswanath

  42. Estimating The Home Depot’s Bottom-up Beta • Average Beta of comparable firms = 0.93 • D/E ratio of comparable firms = (200+2076)/16,232 = 14.01% • Unlevered Beta for comparable firms = 0.93/(1+(1-.35)(.1401)) = 0.86 • If the Home Depot’s D/E ratio is 20%, our bottom-up estimate of Home Depot’s beta is 0.86[1+(1-.35)(.2)] = 0.9718 P.V. Viswanath

  43. Decomposing Boeing’s Beta • The values were estimated based upon the revenues in each business and the typical multiple of revenues that other firms in that business trade for. • The unlevered betas for each business were estimated by looking at other publicly traded firms in each business, averaging across the betas estimated for these firms, and then unlevering the beta using the average debt to equity ratio for firms in that business. Unlevered Beta = Average Beta / (1 + (1-tax rate) (Average D/E)) • Using Boeing’s current market debt to equity ratio of 25% Boeing’s Beta = = 0.88 (1+(1-.35)(.25)) = 1.014 P.V. Viswanath

  44. From Cost of Equity to Cost of Capital • The cost of capital is a composite cost to the firm of raising financing to fund its projects. • In addition to equity, firms can raise capital from debt P.V. Viswanath

  45. Estimating the Cost of Debt • If the firm has bonds outstanding, and the bonds are traded, the yield to maturity on a long-term, straight (no special features) bond can be used as the interest rate. • If the firm is rated, use the rating and a typical default spread on bonds with that rating to estimate the cost of debt. • If the firm is not rated, • and it has recently borrowed long term from a bank, use the interest rate on the borrowing or • estimate a synthetic rating for the company, and use the synthetic rating to arrive at a default spread and a cost of debt • The cost of debt has to be estimated in the same currency as the cost of equity and the cash flows in the valuation. P.V. Viswanath

  46. Estimating Synthetic Ratings • The rating for a firm can be estimated using the financial characteristics of the firm. In its simplest form, the rating can be estimated from the interest coverage ratio Interest Coverage Ratio = EBIT / Interest Expenses • Consider InfoSoft, a firm with EBIT of $2000 million and interest expenses of $ 315 million Interest Coverage Ratio = 2,000/315= 6.15 • Based upon the relationship between interest coverage ratios and ratings, we would estimate a rating of A for the firm. P.V. Viswanath

  47. Interest Coverage Ratios, Ratings and Default Spreads Interest Coverage Ratio Rating Default Spread > 12.5 AAA 0.20% 9.50 - 12.50 AA 0.50% 7.50 – 9.50 A+ 0.80% 6.00 – 7.50 A 1.00% 4.50 – 6.00 A- 1.25% 3.50 – 4.50 BBB 1.50% 3.00 – 3.50 BB 2.00% 2.50 – 3.00 B+ 2.50% 2.00 - 2.50 B 3.25% 1.50 – 2.00 B- 4.25% 1.25 – 1.50 CCC 5.00% 0.80 – 1.25 CC 6.00% 0.50 – 0.80 C 7.50% < 0.65 D 10.00% P.V. Viswanath

  48. Costs of Debt for Boeing, the Home Depot and InfoSoft Boeing Home Depot InfoSoft Bond Rating AA A+ A Rating is Actual Actual Synthetic Default Spread over treas. 0.50% 0.80% 1.00% Market Interest Rate 5.50% 5.80% 6.00% Marginal tax rate 35% 35% 42% Cost of Debt 3.58% 3.77% 3.48% The treasury bond rate is 5%. P.V. Viswanath

  49. Estimating Market Value Weights • Market Value of Equity should include the following • Market Value of Shares outstanding • Market Value of Warrants outstanding • Market Value of Conversion Option in Convertible Bonds • Market Value of Debt is more difficult to estimate because few firms have only publicly traded debt. There are two solutions: • Assume book value of debt is equal to market value • Estimate the market value of debt from the book value; for Boeing, the book value of debt is $6,972 million, the interest expense on the debt is $ 453 million, the average maturity of the debt is 13.76 years and the pre-tax cost of debt is 5.50%. Estimated MV of Boeing Debt = P.V. Viswanath

  50. Estimating Cost of Capital: Boeing • Equity • Cost of Equity = 5% + 1.01 (5.5%) = 10.58% • Market Value of Equity = $32.60 Billion • Equity/(Debt+Equity ) = 82% • Debt • After-tax Cost of debt = 5.50% (1-.35) = 3.58% • Market Value of Debt = $ 8.2 Billion • Debt/(Debt +Equity) = 18% • Cost of Capital = 10.58%(.80)+3.58%(.20) = 9.17% P.V. Viswanath

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