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## Cost of Capital in Valuation and Corporate Models

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**Cost of Capital Contents**• Actual Cost of Capital Process • WACC Computation and Theory • Alternative Models • Capital Asset Pricing Model • Beta Measurement • Market Premium • Asset Beta**Financial Management and Finance Theory**• A crucial issue in financial analysis is establishing the discount rate and risk measurement using capital asset pricing models. • Financial principles of efficient markets, market expectations and event studies lie behind a number of modeling and financial management concepts. • The general opinion is that cost of capital is over-estimated and compensated for with optimistic assumptions. • Recent work on cost of capital • Lower equity risk premium • CAPM discredited • Analyst growth rates are too high**Example of Discount Rates in Merger Analysis**• In order to determine the value of Pennzoil-Quaker State's common stock, Morgan Stanley performed a 5-year discounted cash flow analysis that included the use of two different scenarios, or case assumptions. The Management Case reflects Pennzoil-Quaker State management's estimates of the company's future financial performance, excluding any future acquisitions. • The Market Case reflects publicly available estimates of Pennzoil-Quaker State's future performance of certain securities research analysts. These cases were used to project future cash flows which were discounted back to a present value using a range of discount rates of 8% to 10%. • The range was determined based upon a calculation of Pennzoil-Quaker State's weighted average cost of capital (WACC), which was calculated based upon the WACC for comparable companies in three industry segments: Mid-Cap Consumer Products, Auto Aftermarket and Auto OEM. • Morgan Stanley also applied a terminal EBITDA multiple of 7.0x to 9.0x to the projected 2006 EBITDA, for purposes of calculating a terminal value of Pennzoil-Quaker State at the end of 2006. This terminal value together with the projected annual un-levered free cash flows from 2002 through 2006 was then discounted to the present, assuming cash flows occurred mid-year, using discount rates of 8% to 10%.**Cost of Capital Example**• The estimated after-tax free cash flows for BellSouth’s Wireline segment for calendar years 2006 through 2008 and the terminal values calculated for BellSouth’s Wireline segment were then discounted to the present value using discount rates of 7.0% to 8.0%. • The estimated after-tax free cash flows for Cingular for calendar years 2006 through 2008 and the terminal values calculated for Cingular were then discounted to the present value using discount rates of 8.5% to 9.5% and multiplied by 40%. The estimated after-tax free cash flows for BellSouth’s Directories segment for calendar years 2006 through 2008 and the terminal values calculated for BellSouth’s Directories segment were then discounted to the present value using discount rates of 7.0% to 8.0%. • Lehman Brothers and Evercore discounted the unlevered free cash flow streams and the estimated terminal value to a present value at a range of discount rates from 7.5% to 8.5%. The discount rates utilized in this analysis were chosen by Lehman Brothers and Evercore based on their expertise and experience with the telecommunications industry and also on an analysis of the weighted average cost of capital of BellSouth and other comparable companies.**Late Fifties**Payback period Sixties Present Value Seventies (Fremgen) Internal rate of return Net Present Value Eighties Mean Cost of Capital 14.2% Gordon model and CAPM Nineties CAPM Most popular Risk premium of 6% Current Equity premium of 5% or less 27 Highly Regarded Corporations and 10 Leading Investment Banks DCF with WACC is dominant valuation technique WACC uses market rather than book weights Debt cost from marginal cost and statutory tax rates CAPM is predominant model for cost of equity Most use treasury as long-term treasury rate Equity premium Majority less than 6% 11% use lower than 4.5% 10% use 5% 50% use 7.0% to 7.4% Current Equity Premium 5% or Less Surveys of Managers**Use Correct Discount Rate for Correct Cash Flow**The key is to match the right cash flow with the right discount rate And to the thing being valued**Common Problems in Applying Cost of Capital to Cash Flow**• Given difficulties in estimating cost of capital, present a range in cost of capital in valuations. • Discount rate should reflect project characteristics • Contracts • Risks • Generally companies over-estimate the cost of capital (McKinsey) • 2001 Survey – managers use 12.2% • Actual market premium is much less • Optimistic assumptions to compensate for high required return • Over-payment for acquisitions • Mis-timing of investments in commodity price businesses**WACC Points**• Use target capital structure • Use nominal cost of capital in currency consistent with the free cash flow • Should be market weights and incremental cost of capital • Tricky Items • Convertible Bonds • Lower rate is due to equity value • Bond value • Equity Option • Term of Debt • Credit Spread on Debt • Callable and No callable debt (effect on cash flow)**WACC Computation**• In the WACC formula, we know • Debt percent • Equity percent • Cost of new debt • Income tax rate • The hard part is the cost of equity • If the capital structure changes, the cost of equity should change • In theory, if the capital structure changes, the cost of equity should change to maintain the same overall WACC • Therefore, if the capital structure changes in the model, careful with assumption about how the WACC changes.**Weighted Average Cost of Capital**• Step 1: • Equity Cost from Asset Cost • Ke = Be x Rm + Rf • Ke = (Ba x (V/E)) x Rm + Rf • Step 2 • Debt Cost from Rf plus Credit Spread • Kd = Rf + CS • After tax Kd • Step 3 • WACC = (D/V) * Kd x (1-t) + (E/V) * Ke**Alternative Approaches to Computing the Cost of Capital**• Dividend growth model (analogous to P/E ratio) • Works if there are stable dividends • A variant is P/E = (1-g/r)/(k-g) • Debt capacity model (project finance) • Risk premium method (analogous to the CAPM) • K = Rf + Risk Premium • Implied cost of capital in EBITDA ratios • Arbitrage Pricing Model (extension of CAPM and related to risk neutral valuation) • Implied cost of capital from reverse engineering financial models (described in the M&A discussion)**.**MM without Tax and WACC – Increasing Interest Cost**MM with increasing Debt Cost – Equity Cost Decreases**because of Option in Equity Cost Higher Interest Rate with Higher Probability of Default**CAPM Inputs**• Rf,i is the risk free rate for the current period (i) and it is the only variable directly affected by movements in the overall cost of capital in the economy. • βi is the covariance between returns on the security and the market returns divided by the overall variance of market returns. This parameter is the only input affected by the risk of the security in question and the βi parameter is not expected to vary over time unless there is a change in business and/or the financial risk of the company. • EMRP is the expected return on a fully diversified portfolio of equity securities over and above the rate of return on risk free securities. This variable is a function only of aggregate preferences by people in the economy for risky investments versus risk free investments. It is not affected by current interest rates, the risk of the security, or movements in the overall stock market.**Geared EquityBe**Asset/Ungeared equity – Ba x Market Market Premium Average Debt Inflation Plus Real Rate - Rf Real CAPM and Real and Risk Free Rate**CAPM Theory**• CAPM has many problems, but the basic theory upon which the CAPM is built is a foundation of finance. • The foundation of the CAPM is: • Risk is measured by variation and standard deviation in returns • Standard deviation is reduced from diversification • Variance (a + b) where the portfolio if a and b are have a weight of .5 is: • .25 variance (a) + .25 variance (b) + .5 covariance(a,b) • If the covariance is zero, the variance of the portfolio is much lower than the variance without diversification**CAPM Problems**• Problems with the CAPM theory are recounted by Ravi Jagannathan and Iwan Meier in their 2001 article “Do We Need CAPM for Capital Budgeting:” • The CAPM as a model has been seriously challenged in the academic literature…. [S]ince the critique by Fama and French (1992) there is consensus in the academic literature that the CAPM as taught in MBA classes is not a good model – it provides a very imprecise estimate of the cost of capital…. [T]here is overwhelming evidence in the academic literature that for over two decades business schools have been teaching the wrong model – or at least recommending the use of the wrong inputs – for calculating the cost of capital.[1] • [1] Jagannathan, R. and Meier, I. 2001, “Do We Need CAPM For Capital Budgeting?”, Kellogg School of Management, Finance Department, pp 1-3.**CAPM Problems**• “Not only has the CAPM proved wrong, but we do not even know that the market premium is.” • Ravi Jagannathan and Iwan Meyer, “Do We Need CAPM for Capital Budgeting” Kellog School of Management • Fama and French: • Statistical analysis showing no relation between returns and beta • Statistical modeling: Time series to compute the Beta and then cross section to compute the significance • Statistical problems: errors in variables and all variables should be based on expectations rather than actual • CAPM may be un-testable**Cost of Capital and the CAPM**• Use of CAPM to compute equity cost of capital and cost of capital to apply to free cash flow • Risk free rate to apply in the CAPM • Alternative methods to evaluate the risk premium for the overall market • Data sources and computation of Beta • Adjustments to Beta to compute Beta for application to free cash flow • Adjustments to CAPM for interest tax shield • Theoretical problems with the CAPM • Alternative approaches to the CAPM**Discussion of CAPM Components**• The CAPM requires estimation of three components (Rf, Rm and Beta). Each of these has some controversy. • Rf • Should the long-term treasury rate be used • Country premiums • Rm • Method of estimation expected returns • Actual use in practice • Beta • Estimation • Accuracy**Risk Free Rate Discussion**• There are debates concerning implementation of the risk free rate in the CAPM. • Some suggest using long-term Treasury bond yields, some advocate short-term Treasury Bills and still others argue for use of the yield on inflation indexed bonds plus the expected rate of inflation. • The primary argument against using long-term Treasury Bond yields as a proxy for the risk free rate is that holders of long-term bonds accept inflation risk and those yields are therefore not risk-free. • Further, during times at which an inverted yield curve exists, the long-term treasury yield will produce a lower risk free parameter than the Treasury Bill rate. • Those opposed to use of a short-term rate contend that the duration of cash flows from short-term investments does not match the duration of cash flows received from an investment in a stock.**CAPM - Risk Free Rate**• The primary issue in estimating the risk free rate is what risk free security should be used: • Common equity pays cash flow to investors over a long period • In theory the duration of dividends could be computed • Use t-bill yield to maturity of 10 years • Example • Treasury Bond Yield -- 2016 -- 5.53% • Treasury Bond Yield -- 2011 -- 4.98%**General Points on EMRP**• The EMRP is expressed in real terms and is not a nominal number. This means the EMRP does not increase or decrease when interest rates change or when the expected rate of inflation changes. It would be wrong, for example, to update this number in the midst of a case because of changes in the interest rate. • The EMRP comes from the general risk preferences of agents in an economy for equities relative to risk free securities. If people did not have risk aversion for equities relative to risk free bonds, the EMRP would be zero. This means changes in the EMRP are driven by changes in general preferences for equities relative to risk free securities. Because the EMRP comes from risk preferences, it should be stable over long time periods as risk preferences do not swing from month to month or year to year. • Third, the EMRP is an expected number rather than a number that can be directly measured from actual realized returns. The fact that the EMRP is an expected number means that it does not change when the stock market goes up or down because realized earnings change or because general economic activity is robust or depressed. • Fourth, the EMRP is an economy wide number not unique to ComEd. Unlike Beta which measures the risk associated with a specific company, the EMRP is the same whether it is used in valuing a paper company, gauging the rate of return for an oil project or assessing the share price of an airline company. • Fifth, the EMRP has been the subject of a very large body of research. This research has been performed by people who are not funded by parties who have a vested interest in producing a particularly high or a particularly low risk premium number. Since the EMRP is not unique to ComEd, since it is an expected number difficult to calculate, and since it is not expected to change over short time periods, the EMRP research is directly relevant to this and other regulatory proceedings.**Current Opinions with Respect to EMRP**• Enrique Arzac recaps a wide body of research by stating “We show that both the historic record, financial theory, and prospective estimates based on stock prices and growth expectations, all indicate that the future equity premium in developed capital markets is likely between 3 and 5%...” • Seth Artimage summarizes many different studies by noting: “Consensus is lacking at present on the best way of estimating the equity premium, and reasonable estimates lie in the rage of 1% or 5%...” • Koller et al. describe the general biases in EMRP: “Historical estimates found in most textbooks (and locked in the mind of many), which often report numbers near 8% are too high for valuation purposes because they compare the market risk premium versus short-term bonds, use only 75 years of data, and are biased by the historical strength of the U.S. market.**Historic EMRP**• Enrique Arzac refers to research by Blanchard who “developed a dynamic model of the expectations of real returns on stocks and bonds. He found that the risk premium during the 1930’s and 1940’s was unusually high ranging from 3 to 5% in the early 1930’s to more than 10% in the 1940’s. Afterwards, it started a gradual decline with some relatively minor fluctuations and reached between 2 and 3% in the early 1990’s.” • Claus and Thomas emphasize the notion that historic returns exceed the expected amounts: “Despite substantial variation in the underlying fundamentals across markets and over time, observing that every one of our 69 country-year estimates lies well below eight percent suggests that the Ibbotson estimate is too high for our sample period.”**Use of DCF to Estimate EMRP**• Seth Armitage describes the DCF studies as follows: “The arithmetic mean real premium between 1900 and 2000 was … 7.0% for the United States, measured against the yield on long-term bonds. But a simple forward looking estimate based on applying the dividend discount model to the market suggests a risk premium of 3% to 4%. This is why many people do not expect the premium in the future to be as large as it has been in the past, especially in the second half of the twentieth century. They place more faith in reasonable expectations about the future than in outcomes observed in recent decades. Furthermore, several researchers have argued recently that investors did not expect premiums as large as they got in the twentieth century. Armitage concludes that Most of the studies indicate a range for historic ex ante premiums … of between 1.5% and 4.5% -- considerably below the actual arithmetic mean premium since 1920…” • Enrique Arzac uses a DCF model to estimate the equity market premium of between 3.08% and 3.32%. • In their widely cited 2002 article, Fama and French state that “the equity premium estimates from the dividend and earnings growth models, 2.55 percent and 4.32 percent, are far below the estimate from the average return, 7.43 percent….The expected return estimates from the dividend and earnings growth models are more precise than the average return. The standard error of the dividend growth estimate of the expected return for 1951 to 2000 is 0.74 percent, versus 2.43 percent for the average stock return….The earnings growth model is not, however, clearly superior to the dividend growth model.”**Surveys of Investors**• “In the US, Merrill Lynch publishes ‘bottom up’ expected returns on the Standard and Poor’s 500, derived by averaging expected return estimates for stocks in the Standard & Poor’s 500….In recent years, the Merrill Lynch expected return estimates have indicated an EMRP in the region of 4% to 5%. • “The Value Line projected market risk premia are somewhat more volatile than those from the Merrill Lynch DDM model. In recent years they have generally ranged from 2% to 6%....” • Greenwich Associates had published the results of an annual survey of pension plan officers regarding expected returns on the Standard and Poor’s 500 for a five-year holding period. The Greenwich Associates survey has generally indicated and EMRP in a 2%-3% range.” • Claus and Thomas also cite investor expectations. They summarize the information as follows: “Surveys of institutional investors also suggest an equity premium substantially below eight percent (e.g., Burr (1998)), and there are indications that this belief has been held for many years (e.g., Benore (1983)) . Also, the weighted average cost of capital used in discounted cash flow valuations provided in analysts’ research reports usually implies an equity premium below five percent.”**Risk Premium**• There is a wide range in premiums used in theory and practice. The following shows results from one study.**Equity Market Risk Premium**• A well known study by Fama and French, published in 2002, finds that “estimates [of the equity market risk premium] for 1951 to 2000, 2.55 percent and 4.32 percent, are much lower than the equity premium produced by the average stock return, 7.43 percent.” • In another oft cited paper published in 2001 by Claus and Thomas titled “Equity Premia as Low as Three Percent? Evidence from Analysts’ Earnings Forecasts for Domestic and International Stock Markets,” the authors conclude that “for each year between 1985 and 1998, we find that the equity premium is around three percent (or less) in the United States and five other markets.” • “The Cost of Capital: Intermediate Theory” which was published in 2005 summarizes the current research as follows: “Almost all researchers on this question agree that the premium in the twentieth century in the United States … has turned out to be larger than investors expected it to be.”**Estimated Risk Premiums from Actual Returns**• The market premium is unobservable • Studies have attempted to measure the expected market premium using the PE method • Actual Market Risk Premiums • 1926-1998 • Arithmetic 7.8% • Geometric 5.9% • 1974 – 1998 • Arithmetic 5.5% • Geometric 4.9% • 1964 – 1998 • Arithmetic 4.7% • Geometric 3.6%**CAPM - Market Premium**• McKinsey -- 4.50% • Investment Bank Low -- 3.5% • Investment Bank High -- 5.5% • Brealy and Meyers – 6% to 8.5% • Gordon’s model – 2.9% • Exelon Rate Case -- 9.98% • Issue: Sample Bias from Bankruptcy**Equity Risk Premium in Hong Kong**The median estimate of ERP is in the 4-5% range for mature markets**Problems with historic data in estimating market premium**• The problem with market premium estimates is that the market premium should be an expected return rather than the historical actual returns that may or may not have been expected: • Real time now matters more than historic periods. • Samples drawn from the past have little relevance to what investors expect now. • What was 75% probable yesterday has an unknown probability tomorrow.**Sources of Beta and Differences in Measurement**• The table below shows that beta measurement can be dramatically different for the same companies.**Beta Measurement**• Beta is measured from historic returns • Beta is cov(Rm,Rt)/variance(Rm)**Beta Adjustments**• Value Line computes its beta from a regression equation that measures an unadjusted beta. Then, Value Line adds an adjustment to move the beta toward 1.0 using the following equation[1]: • Adjusted beta = 2/3 x Unadjusted beta + 1/3 x 1.0 • or • Unadjusted beta = Adjusted beta x 3/2 – 1/2 • [1] Patterson, C.S., 1995, The Cost of Capital: Theory and Estimation, Westport CT: Quorum Books, p. 130.**Beta Adjustments for Mean Reversion**• The adjustment for betas is generally accepted in cost of capital literature for companies with betas above 1.0 because of a tendency of betas to revert to the mean. Statistical studies have demonstrated that “there appeared to be greater measurement error associated with the betas of extreme values.”[1] The mean reversion adjustment is accepted for companies with observed high betas. The risk of these high beta companies often moves towards 1.0 over time due to statistical measurement problems and due to the tendency of high business risk companies to eventually moderate. However, the mean reversion is far less accepted for utility companies with betas of below 1.0. [1] Ogier, T, Rugman, J., Spicer, L., 2004, The Real Cost of Capital A Business Field Guide to Better Financial Decisions, Great Britain: FT Prentice Hall, page 54.**Example of Beta Adjustments**• The case of NICOR demonstrates that using a mean reversion adjustment wherein betas are pushed towards 1.0 to correct statistical irregularity is inappropriate for utility companies. Instead, the statistical anomalies should push the beta back to the industry average beta for utility companies. The 1.10 beta obviously does not measure prospective risk and making a correction by moving the beta towards 1.0 would not help. The NICOR example effectively demonstrates that mean reversion adjustments of utility betas are not appropriate. These adjustments do not improve the measurement of beta but instead simply result in increased cost of equity numbers. • .**Asset Beta versus Equity Beta**• Without Taxes • Ba = (D/V)*Bd + (E/V)*Be • Be measured with stock prices • D,V,E are debt, enterprise value and equity value measured at market value. • Often assume Bd = 0 • Or, Be = (Ba – (D/V)*Bd) * V/E • With taxes • Ba = (D x (1-t))/(E+D*(1-t)) * Bd + (E/(D*(1-t) + E *(1-t))*Be • Assumes that all cash flows from debt are tax deductible**Example of Asset and Equity Beta**• Cathay Pacific has an observed beta of 1.3 and a debt to equity ratio of 50%. Singapore Airlines has a debt equity ratio of 25%. Calculate the equity beta of Singapore Airlines. The tax rates in Hong Kong and Singapore are 15 and 20% respectively.