Sahil Eco


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  • Cash is king. A firm with negative cash flows today can be a very valuable firm but only if there is reason to believe that cash flows in the future will be large enough to compensate for the negative cash flows today. The riskier a firm and the longer you have to wait for the cash flows, the greater the cashflows eventually have to be….
  • A business and the equity in the business can be very different numbers… A firm like GE has a value of $ 600 billion for its business but its equity is worth only $ 400 billion - the difference is due to the substantial debt that GE has used to fund its expansion. You can have valuable businesses, where the equity is worth nothing because the firm has borrowed too much….
  • In this approach, you put blinders on and consider only two questions: What cashflows can equity investors expect to make from this business? The cashflows can generally be defined as cashflows left over after a firm has met its reinvestment needs and made any debt payments… They can therefore be negative… In the strict view of equity cashflows, there are some who argue that the only cashflows to equity are dividends, which makes the dividend discount model a special case of a cashflow to equity model. What cost of equity will they attach to these cashflows? Generally should be higher for higher risk equity.
  • The easiest way to explain cashflows to the firm is to aggregate cashflows to all claim holdesr in the firm: Equity: Cashflows to Equity Debt: Interest expenses (1-t) + Principlal repayments Preferred: Preferred dividends You would discount this cumulative cashflow at the cost of capital which is a weighted average of the costs of each of these components. To get from firm value to equity value, you would subtract the market values (or estimated market values) of debt and preferred stock from firm value.
  • Treat these cashflows as given. In the pages to come, we will talk about estimating these cashflows in detail. Note that we are assuming a perpetual bond with fixed interest payments in each period. The costs of equity and debt are also given.
  • The reason the two values converge is because the market values of equity and debt for this firm happen to be equal to the estimated values of equity and debt. If this does not hold, the weights you use for your cost of capital calculation - which are based upon current market value - will not be consistent with the debt ratio you are assuming for estimating for your FCFE calculations and the two values will diverge.
  • It is a principle that is often violated because we often talk about discount rates and cashflows loosely and costs of capital and equity interchangeably. We need to be more precise about words like free cash flow (to whom? The firm? Equity?) and discount rates to avoid these problems.
  • The results of mismatching… not inconsequential… A few years I checked through acquisition valuations done at major investment banks checking for fundamental mismatches and was amazed at how many I found. Every possible combination of cashflows and discount rates had been explored with disastrous consequences for stockholders in the firms involved in the deals… (Check out the Kennecott case study in the Harvard Business School finance case book (Butter, Fruhans et al.) for a great example…)
  • The process is not always sequential. It may seem irrational to pick the DCF model after you have estimated the inputs, but you have to get a sense of the cash flows and growth potential before you pick a model.
  • The four pillars of value: Cashflows Potential for high growth Length of the high growth period (before the firm starts growing at the same rate as the economy) Discount rate Note the variations and the need for consistency: With equity -> Cashflows to equity - > Growth rate in net income -> Discount at the cost of equity With firm -> Cashflows to firm - > Growth rate in operating income -> Discount at the cost of capital
  • While discount rates are a critical ingredient in discounted cashflow valuation, I think we spend far too much time on discount rates and far too little on cashflows. The most significant errors in valuation are often the result of failures to estimate cash flows correctly…. As companies increasingly become global, and multiple listings abound (Royal Dutch has six equity listings in different markets) the consistently principle becomes very important. The currency used in estimating cash flows should also be the currency in which you estimate discount rates - Euro discount rates for Euro cashflows and peso discount rates for peso cash flows. Recently, I came across a valuation of a Mexican company, where the cashflows were in nominal pesos but the discount rate used was the dollar cost of capital of a U.S. acquirer…. As a result, the value was inflated by more than 300%….
  • Re-emphasizes a key assumption that we make in risk and return models in finance. It is not risk that matters, but non-diversifiable risk and the cost of equity will increase as the non-diversifiable risk in an investment increases. This view of the world may pose a problem for us when valuing private companies or closely held, small publicly traded firms, where the marginal investor (owner, venture capitalist….) may not be diversified.
  • Lays out the four basic models and how non-diversifiable risk is measured in each model: The capital asset pricing model makes the most restrictive assumptions (no transactions costs, no private information) and arrives at the simplest model to estimate and use. The arbitrage pricing model and multi-factor model make less restrictive assumptions but yield more complicated models (with more inputs to estimate) The proxy model is dependent upon history and the view that firms that have earned higher returns over long periods must be riskier than firms that have lower returns. The characteristics of the firms that earn high returns - small market cap and low price to book value, for example in the Fama-French study - stand in as measures for risk.
  • While this equation is set up in terms of the capital asset pricing model, the issues raised with the CAPM apply to the more complex models as well -the APM and the multi-factor model
  • Treasury bills may be default free but there is reinvestment risk when they are used as riskless rates for longer-term cashflows. A 6-month T.Bill is not riskless when looking at a 5-year cashflow. Would a 5-year treasury be riskfree? Not really. The coupons would still expose you to reinvestment risk. Only a 5-year zero-coupon treasury would be riskfree for a 5-year cash flow. If you were a purist, you would need different riskfree rates for different cashflows. A pragmatic solution would be to estimate the duration of the cashflows in a valuation and use a treasury of similar duration. (Since the duration is the weighted average of when the cashflows come in, this should be fairly long, especially when you count in the fact that the terminal value is the present value of cashflows forever).
  • Approach 1: Assume that the Indian government bond rate is 12% and that the rating assigned to the Indian government is A. If the default spread for A rated bonds is 2%, the riskless Indian rupee rate would be 10%. Riskless Rupee rate = Indian Government Bond rate – Default Spread = 12% - 2% = 10% Approach 2: If the current spot rate is 38.10 Thai Baht per US dollar, the ten-year forward rate is 61.36 Baht per dollar and the current ten-year US treasury bond rate is 5%, the ten-year Thai risk free rate (in nominal Baht) can be estimated as follows In general, while many practitioners use the last approach (working with a different, more stable currency) to avoid having to deal with inflation in the local currency, they shift the problem of making these estimates to the cashflows from the discount rates.
  • The correct riskfree rate is the treasury bond rate. The C-Bond has a default spread component -the additional country risk can be built into the equity risk premium..
  • While everyone uses historical risk premiums, the actual premium in use can vary depending upon How far back you go in time Whether you T.Bills or T.Bonds Whether you use arithmetic or geometric averages This table was developed using data that is publicly accessible on the S&P 500, treasury bills and 10-year treasury bonds on the Federal Reserve of St. Louis web site. Dataset: histretSP.xls
  • The noise in stock prices is such that you need 100-150 years of data to arrive at reasonably small standard errors. It is pointless estimating risk premiums with 10-20 years of data. Consistent with our argument of using a treasury bond rate as a riskfree rate, we would estimate the premium over the treasury bond rate. If you wanted a risk premium for the next year, you would use the arithmetic average - it is the single best estimate of next year’s premium. If you want a risk premium to use in a cost of equity which will be compounded over time, you should use a geometric average.
  • Relative Equity Market approach : Assume, for the moment, that you are using a mature market premium for the United States of 5.51% and that the annual standard deviation of U.S. stocks is 20%. If the annual standard deviation of Indonesian stocks is 35%, the estimate of a total risk premium for Indonesia would be as follows. Risk Premium for Indonesia = 5.51% (35/20) = 9.64% Problem with approach: Some very risky markets have low standard deviations because of non-trading. Country Bond Approach Brazil has dollar-denominated C-Bonds which trade at a spread of 4.83% over and above the treasury bond rate. You could treat this default spread as the country risk premium. Problem with approach: Equity is riskier than bonds. The country spread should be larger.
  • These ratings can be obtained online at both Moody’s and S&P. The ratings used are those on long-term issues (and on dollar-rated issues) The typical spread is the average spread over all countries with B1 ratings. This acts as a reality check on the market spread (which is the actual spread on dollar-denominated bonds) since country bonds are volatile. If the two numbers are very different, I would go with the typical spread. Dataset: ctryprem.xls
  • The standard deviations in equity and the C-Bond are based upon two years of weekly returns. (One is in real and the other is in dollars. If this is a potential problem, you could convert one or another into another currency using exchange rates). I am scaling up the country default spread by the relative volatility of equity. I would add this country risk premium (10.24%) to the risk premium I have for a mature equity market (5.51%, for instance). There is a chance that I am double counting some risk since you could argue that the 5.51% risk premium in U.S. already reflects some of the standard deviation in the treasury bond. This may be possibility and the country risk premium may look high, but I would change this risk premium over the forecast period - reducing it as I move towards the terminal year.
  • Fewer countries with default risk and small spreads. Note, though, that Greece and Portugal still have default risk notwithstanding the fact that they are part of the EU and plan to shift to one currency (the Euro).
  • Same process as that used for Brazil. The effect is much smaller.
  • The first approach is the bludgeon approach and treats all companies in a country as being equally exposed to risk - small and large, domestic and export oriented. The second approach is only slightly less bludgeon-like since it assumes that betas measure exposure not only to all other macroeconomic risk but also to country risk. The third approach provides for the maximum flexibility. You can consider it a two factor model, with one factor being country risk. The lambda looks a lot like beta - it is standardized around one, with one being average risk exposure.
  • This approach, based only on revenues, is simplistic, but may be the only realistic choice given information constraints. In fact, it would be useful to know where a company’s factories are located, what currency its contracts are denominated and how much it uses derivatives. An alternative approach worth exploring is to regress the returns on a company’s stock against the country bond and using the slope on this regression as the lambda. Note, though, that a company could potentially then have multiple country risk exposures and that this exposure is independent of where the company is incorporated and traded. Thus, Nestle and Coca Cola should have emerging market risk premiums reflected in their costs of equity - you could look at the proportion of the revenues that each company derives from emerging markets and adjust the cost of equity accordingly.
  • The three approaches yield three very different estimates of cost of equity for Embraer. The last approach is probably the most realistic because it allows for the fact that Embraer, which derives 90% of its revenues outside Brazil (primarily from the United States and Western Europe), should be less exposed to country risk than the typical Brazilian firm.
  • The simplest analogy is to a bond. If you know the price of a bond, you can compute the yield to maturity as the discount rate that makes the present value of the expected cashflows on the bond equal to the price of the bond. Similarly, if you know the current market value of equities in the aggregate (or of an equity index), you can compute the discount rate that makes the present value of the expected cashflows on the index equal to the price of the index today. There are two practical problems: Unlike a bond, the cashflows on stocks are not promised but expected - you need an expected growth rate. Unlike a bond, stocks have infinite lives. You have to consider cashflows forever.
  • Example of equity risk premium calculation as of January 1, 2001. I am assuming that the growth rate after 5 years will converge on the growth rate of the economy. (I used a growth rate of 5.5% for the economy, but it might be safer to set it equal to the treasury bond rate of 5.1%. For the inputs, I used: The 10- year bond rate for the T.Bond rate The consensus estimate of growth in earnings for the S&P 500 from Zacks I used only net stock buybacks (stock buybacks - new stock issues) in addition to dividends as a percent of the index. Excel spreadsheet: implprem.xls
  • Traces the ebb and flow of implied premiums over time. Note that as the implied premium rises, stock prices are falling. The implied premium reached a historical high of 6.5% in 1978 and a historical low of 2% in December 1999. Would you buy equities if you were told that you could expect to make a premium of 2% over the riskless rate? If the answer is no, you think equities are over priced.
  • The advantage of implied premiums is that they can be estimated for emerging markets with limited historical data. The only input that is problematic is the expected growth rate - I used the average of analyst estimates for Brazilian companies that had ADRs listed in the United States.
  • Risk premiums matter. If I used the historical premium plus (5.51% + 10.24%) and lower it through time, I would value Embraer at 11.22. If I use the implied premium of 6.66% all the way through the valuation, I would arrive at an estimate of value of 20.02 BR. Which one I would choose to do would depend upon what I was asked to do. If I was asked to be market neutral (I.e. assume the market is correctly priced), I would use the latter. If I have the freedom to pass judgment on the market and believed in mean reversion, I would use the former.
  • The standard approach for estimating betas- regressions - leads to flawed and backward looking estimates of risk.
  • Note the standard error problem. Amazon has a beta estimate of 2.23, but the standard error of 0.50 results in a considerable range around this estimate.
  • This beta looks much better (in terms of standard error) but it is misleading. Nokia dominates the Helisinki index (it was 70% of the index at the time of this regression). The reason it is misleading is because Nokia’s largest single investor was Barclays, which manages one of the worlds’ largest global index funds. Barclays would not view the beta of this regression as a good measure of risk. (They would probably prefer a beta estimate against a global equity index like the Morgan Stanley Capital Index).
  • These are the three fundamentals that drive betas. Firms that produce luxury goods (such as Gucci and Tiffanys) should have higher betas than firms that cater to more basic needs (Walmart). These firms tend to have revenues that are much more sensitive to changes in economic conditions. Firms in businesses with high fixed cost structures (like airlines) should have higher betas than firms with more flexible cost structures. Firms that borrow more money will have higher equity betas than otherwise similar firms that do not borrow money.
  • In some books, the unlevered beta is referred to as the asset beta. To derive this equation, set up a balance sheet with the tax benefit from debt shown as an additional asset: Assets Value Liabilities Value Operating Assets A (  =  u) Debt D (  =0) Tax Asset tD (  =0) Equity E (  =  lev) You can set the weighted averages of the two sides equal:  u (A/(A+tD) =  lev (E/(D+E)) Substituting in A = D+E -tD, you get the first equation. If you set the beta of debt be  d instead of zero, you will get the second equation. The first equation assumes that debt carries no market risk and works reasonably well for investment grade firms. For firms with junk bonds (which tend to behave like equity and carry market risk), the second approach works better. You will need to estimate a beta for debt - I use betas that are a function of the rating of the firm, with debt betas increasing as the rating falls.
  • Changing the regression parameters, which is what we do in the first approach, will yield such a large range of betas (with large standard errors) that it will leave you more confused about the true beta of a firm rather than less confused. While you can use standard deviations to compute a relative standard deviation, you are assuming that market risk and total risk are perfectly correlated. With accounting earnings, the biggest limitation is that you will have relatively few observations in your regression. We prefer bottom-up betas….
  • While we still use regression betas to compute bottom-up betas, the law of large numbers works in your favor. The average of a large number of imprecise betas is more precise than any one regression beta. The reason we unlever and relever is because different firms may have different debt ratios. Three measurement issues come up: How broadly or narrowly do we define comparable firms? We would argue for a broader rather than a narrow definition, because the savings in standard error increase with the number of firms. How do we deal with differences in operating leverage and business mix that may persist across these firms? Assume that there are no differences in operating leverage and business mix or that the differences average out. Adjust for the differences quantitatively. For instance, you could decompose the unlevered beta further into a business beta and the operating leverage effect: Unlevered beta = Business beta (1 + (Fixed Cost/Variable costs)) How do we compute an average - simple or weighted? I prefer simple averages. Otherwise, your betas reflect those of the largest and most stable firms in the business.
  • The information on business breakdown is usually available in the 10K… However, you can usually get only revenues and operating income by division. To estimate the value, I used the average enterprise value/sales multiple in each business: Business Revenues EV/Sales Enterprise Value Aircraft $26.9 billion 1.12 $30.16 billion Defense $18.1 billion 0.7 $12.69 billion You can use other multiples such as value to book and value to EBIT as well.
  • We used the average unlevered beta for steel companies globally, because there are not enough steel companies in Argentina or even in Latin America to comprise a large enough sample.
  • I would say yes, as long as there are no significant regulatory differences between steel companies in Argentina and steel companies in the United States Steel is not a discretionary product in one market and a non-discretionary product in another Note, though, that using the same unlevered beta does not translate into using the same cost of equity for U.S. and Argentine steel companies because the country risk premium (estimated earlier) would increase the cost of equity for the latter.
  • Big Picture of Cost of Equity
  • The cost of debt is not the rate at which you borrowed money historically. That is why you cannot use the book cost of debt in the cost of capital calculation. While many companies have bonds outstanding, corporate bonds often have special features attached to them and are not liquid, making it difficult to use the yield to maturity as the cost of debt. While ratings are often useful tools for coming up with the cost of debt, there can be problems: A firm can have multiple ratings. You need a rating across all of a firm’s debt, not just its safest… A firm’s bonds can be structured in such a way that they can be safer than the rest of the firm’s debt - they can be more senior or secured than the other debt of the firm.
  • This is a simplistic approach but it uses the ratio that explains the largest proportion of the differences between ratings at non-financial service U.S. companies - I tried the 8 ratios that S&P said it depends upon the most to rate companies (which are available on its web site) and correlated them with bond ratings in 1999. You could expand this approach to incorporate other ratios and create a score - similar to the Altman Z score - but you have to decide on whether the trade off is worth it - more complexity for less transparency.
  • This table was last updated in 1999 (for interest coverage ratios and ratings). The default spreads get updated more frequently. Note how much the spreads increased from 2000 to 2001, reflecting the slowing of the economy.
  • When estimating the cost of debt for an emerging market company, you have to decide whether to add the country default spread to the company default spread when estimating the cost of debt. For smaller, less well known firms, it is safer to assume that firms cannot borrow at a rate lower than the countries in which they are incorporated. For larger firms, you could make the argument that firms can borrow at lower rates. In practical terms, you could ignore the country default spread or add only a fraction of that spread.
  • To develop an interest coverage ratio/ratings table, you need lots of rated firms and objective ratings agencies. This is most feasible in the United States. As long as interest rates in another country are similar to those in the United States, the ratings yielded by the table are fairly reasonable. When interest rates are high, interest coverage ratios will come under downward pressure and the table may need to be adjusted to reflect this.
  • The rationale for using market values is simple. You are considering how much someone who would buy the company today should be willing to pay for the company. Since he or she can buy equity and debt at today’s market value, you use those as weights. However, you could very well push the market values towards your estimated values in the process of buying the company. If this is a concern, you can iterate the weights in the cost of capital calculation to make the values used in the weights converge on the values estimated in the analysis.
  • End product of the analysis for Titan Cement. Note that the costs of equity and debt incorporate country risk (though the magnitudes are different) and that the weights used are market value weights.
  • If you use book value weights, your cost of capital will be much lower. This puts to rest the notion that you are being conservative when you use book value weights. In fact, you will over estimate values for most firms (those with market equities that exceed book equities) by using book value weights.
  • Same process. Much bigger impact of country risk.
  • The two approaches will give you different answers because they make different assumptions about the equity risk premium. In the first approach, the risk premium remains a constant as you switch from one currency to another. In the second, you scale up the risk premium for higher interest rate currncies. The second approach will give you more consistent valuations as you switch from currency to currency.
  • Big picture of the cost of capital.
  • Sahil Eco

    1. 1. Discounted Cash Flow Valuation: Estimating Discount Rates Read Chapter 2, Damodaran on Valuation Chapters 7 & 8 Investment Valuation
    2. 2. OutlineEquity versus Firm ValuationEstimating cost of equityEstimating Cost of DebtEstimating the cost of capital for the firmUsing different risk and return models
    3. 3. Discounted Cashflow Valuation: Basis for Approach t = n CF Value = ∑ t t t = 1 (1 + r)where CFt is the cash flow in period t, r is the discount rate appropriate given the riskiness of the cash flow and t is the life of the asset.Proposition 1: For an asset to have value, the expected cash flows have to be positive some time over the life of the asset.Proposition 2: Assets that generate cash flows early in their life will be worth more than assets that generate cash flows later; the latter may however have greater growth and higher cash flows to compensate.
    4. 4. Equity Valuation versus Firm ValuationValue just the equity stake in the businessValue the entire business, which includes, besides equity, theother claimholders in the firm
    5. 5. I.Equity ValuationThe value of equity is obtained by discounting expected cashflows toequity, i.e., the residual cashflows after meeting all expenses, taxobligations and interest and principal payments, at the cost of equity,i.e., the rate of return required by equity investors in the firm. t=n CF to Equity t Value of Equity = ∑ (1+ k e )t t=1 where, CF to Equityt = Expected Cashflow to Equity in period t ke = Cost of EquityThe dividend discount model is a specialized case of equity valuation,and the value of a stock is the present value of expected futuredividends.
    6. 6. II. Firm ValuationThe value of the firm is obtained by discounting expectedcashflows to the firm, i.e., the residual cashflows after meetingall operating expenses and taxes, but prior to debt payments, atthe weighted average cost of capital, which is the cost of thedifferent components of financing used by the firm, weighted bytheir market value proportions. t= n CF to Firm t Value of Firm = ∑ (1+ WACC) t =1 t where, CF to Firmt = Expected Cashflow to Firm in period t WACC = Weighted Average Cost of Capital
    7. 7. 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 Firm1 $ 50 $ 40 $ 902 $ 60 $ 40 $ 1003 $ 68 $ 40 $ 1084 $ 76.2 $ 40 $ 116.25 $ 83.49 $ 40 $ 123.49Terminal Value $ 1603.0 $ 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.
    8. 8. Equity versus Firm ValuationMethod 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 = $1073Method 2: Discount CF to Firm at Cost of Capital to get value of firmCost 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
    9. 9. First Principle of ValuationNever mix and match cash flows and discount rates.The key error to avoid is mismatching cashflows and discountrates, since discounting cashflows to equity at the weightedaverage cost of capital will lead to an upwardly biased estimateof the value of equity, while discounting cashflows to the firm atthe cost of equity will yield a downward biased estimate of thevalue of the firm.
    10. 10. The Effects of Mismatching Cash Flows and Discount RatesError 1: Discount CF to Equity at Cost of Capital to get equity value PV of Equity = 50/1.0994 + 60/1.09942 + 68/1.09943 + 76.2/1.09944 + (83.49+1603)/1.09945 = $1248 Value of equity is overstated by $175.Error 2: Discount CF to Firm at Cost of Equity to get firm value PV of Firm = 90/1.13625 + 100/1.136252 + 108/1.136253 + 116.2/1.136254 + (123.49+2363)/1.136255 = $1613 PV of Equity = $1612.86 - $800 = $813 Value of Equity is understated by $ 260.Error 3: Discount CF to Firm at Cost of Equity, forget to subtract out debt, and get too high a value for equity Value of Equity = $ 1613 Value of Equity is overstated by $ 540 1
    11. 11. 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 cash flows 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 firm 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. 1
    12. 12. Generic DCF Valuation Model DISCOUNTED CA SHFLOW V A LUA TION Ex p e cte d G rowth C ash flows Firm: Growth in Firm: Pre-deb t cash Op erating Earnings flow Equity: Growth in Equity: After deb t Net Income/EPS Firm is in stab le growth: cash flows Grows at constant rate forever Terminal Value C F1 C F2 C F3 CF4 C F5 CFnValue .........Firm: Value of Firm ForeverEquity: Value of Equity Le ngth of Pe riod of H igh G rowth D iscount R ate Firm:C ost of Cap ital Equity: C ost of Equity 1
    13. 13. Estimating Discount Rates 1
    14. 14. Estimating Inputs: Discount RatesCritical ingredient in discounted cashflow valuation. Errors inestimating the discount rate or mismatching cashflows anddiscount rates can lead to serious errors in valuation.At an intuitive level, the discount rate used should be consistentwith both the riskiness and the type of cashflow beingdiscounted. • 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 1
    15. 15. Cost of EquityThe cost of equity should be higher for riskier investments andlower for safer investmentsWhile risk is usually defined in terms of the variance of actualreturns around an expected return, risk and return models infinance assume that the risk that should be rewarded (and thusbuilt into the discount rate) in valuation should be the riskperceived by the marginal investor in the investmentMost risk and return models in finance also assume that themarginal investor is well diversified, and that the only risk thathe or she perceives in an investment is risk that cannot bediversified away (I.e, market or non-diversifiable risk) 1
    16. 16. The Cost of Equity: Competing ModelsModel Expected Return Inputs NeededCAPM E(R) = Rf + β (Rm- Rf) Riskfree Rate Beta relative to market portfolio Market Risk PremiumAPM E(R) = Rf + Σj=1 βj (Rj- Rf) Riskfree Rate; # of Factors; Betas relative to each factor Factor risk premiumsMulti E(R) = Rf + Σj=1,,N βj (Rj- Rf) Riskfree Rate; Macro factorsfactor Betas relative to macro factors Macro economic risk premiumsProxy E(R) = a + Σj=1..N bj Yj Proxies Regression coefficients 1
    17. 17. 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 are estimated by regressing stock returns against market returns 1
    18. 18. Short term Governments are not riskfreeOn a riskfree asset, the actual return is equal to the expectedreturn. Therefore, there is no variance around the expectedreturn.For an investment to be riskfree, then, it has to have • No default risk • No reinvestment riskThus, the riskfree rates in valuation will depend upon when thecash flow is expected to occur and will vary across timeA simpler approach is to match the duration of the analysis(generally long term) to the duration of the riskfree rate (alsolong 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) 1
    19. 19. Estimating a Riskfree RateEstimate a range for the riskfree rate in local terms: • Approach 1: Subtract default spread from local government bond rate: Government bond rate in local currency terms - Default spread for Government in local currency • Approach 2: Use forward rates and the riskless rate in an index currency (say Euros or dollars) to estimate the riskless rate in the local currency.Do the analysis in real terms (rather than nominal terms) usinga 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.Do the analysis in another more stable currency, say USdollars. 1
    20. 20. A Simple TestYou are valuing Ambev, a Brazilian company, in U.S. dollarsand are attempting to estimate a riskfree rate to use in theanalysis.What is the riskfree rate that you should use? 2
    21. 21. 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 AverageHistorical Period T.Bills T.Bonds T.Bills T.Bonds1928-2001 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% 2
    22. 22. 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. 2
    23. 23. Country Risk PremiumsHistorical risk premiums are almost impossible to estimate with anyprecision in markets with limited history - this is true not just ofemerging markets but also of many Western European markets.For such markets, we can estimate a modified historical premiumbeginning with the U.S. premium as the base: • Relative Equity Market approach: The country risk premium is based upon the volatility of the market in question relative to U.S market. Country risk premium = Risk PremiumUS* σCountry Equity / σUS Equity • Country Bond approach: In this approach, the country risk premium is based upon the default spread of the bond issued by the country. Country risk premium = Risk PremiumUS+ Country bond default spread • Combined approach: In this approach, the country risk premium incorporates both the country bond spread and equity market volatility. 2
    24. 24. Step 1: Assessing Country Risk Using Country Ratings: Latin America - March 2001 Country Rating Typical Spread Market Spread Argentina B1 450 563 Bolivia B1 450 551 Brazil B1 450 537 Colombia Ba2 300 331 Ecuador Caa2 750 787 Guatemala Ba2 300 361 Honduras B2 550 581 Mexico Baa3 145 235 Paraguay B2 550 601 Peru Ba3 400 455 Uruguay Baa3 145 193 Venezuela B2 550 631 2
    25. 25. Step 2: From Bond Default Spreads to Equity Spreads Country ratings measure default risk. While default risk premiums and equity risk premiums are highly correlated, one would expect equity spreads to be higher than debt spreads. • One way to adjust the country spread upwards is to use information from the US market. In the US, the equity risk premium has been roughly twice the default spread on junk bonds. • Another is to multiply the bond spread by the relative volatility of stock and bond prices in that market. For example, – Standard Deviation in Bovespa (Equity) = 32.6% – Standard Deviation in Brazil C-Bond = 17.1% – Adjusted Equity Spread = 5.37% (32.6/17.1%) = 10.24% Ratings agencies make mistakes. They are often late in recognizing and building in risk. 2
    26. 26. Another Example: Assessing Country RiskUsing Currency Ratings: Western Europe• Country Rating Typical SpreadActual Spread• Austria Aaa 0• Belgium Aaa 0• Denmark Aaa 0• Finland Aaa 0• France Aaa 0• Germany Aaa 0• Greece A3 95 50• Ireland AA2 65 35• Italy Aa3 70 30• Netherlands Aaa 0• Norway Aaa 0• Portugal A3 95 55• Spain Aa1 60 30• Sweden Aa1 60 25• Switzerland Aaa 0 2
    27. 27. Greek Country Risk PremiumCountry ratings measure default risk. While default riskpremiums and equity risk premiums are highly correlated, onewould expect equity spreads to be higher than debt spreads.• One way to adjust the country spread upwards is to use information from the US market. In the US, the equity risk premium has been roughly twice the default spread on junk bonds.• Another is to multiply the bond spread by the relative volatility of stock and bond prices in that market. For example, – Standard Deviation in Greek ASE(Equity) = 40.5% – Standard Deviation in Greek GDr Bond = 26.1% – Adjusted Equity Spread = 0.95% (40.5%/26.1%) = 1.59%Ratings agencies make mistakes. They are often late inrecognizing and building in risk. 2
    28. 28. From Country Spreads to Corporate Risk premiums Approach 1: Assume that every company in the country is equally exposed to country risk. In this case,E(Return) = Riskfree Rate + Country Spread + Beta (US premium) Implicitly, this is what you are assuming when you use the local Government’s dollar borrowing rate as your riskfree rate. Approach 2: Assume that a company’s exposure to country risk is similar to its exposure to other market risk.E(Return) = Riskfree Rate + Beta (US premium + Country Spread) Approach 3: Treat country risk as a separate risk factor and allow firms to have different exposures to country risk (perhaps based upon the proportion of their revenues come from non- domestic sales) E(Return)=Riskfree Rate+ β (US premium) + λ (Country Spread) 2
    29. 29. Estimating Company Exposure to Country Risk Different companies should be exposed to different degrees to country risk. For instance, a Brazilian firm that generates the bulk of its revenues in the United States should be less exposed to country risk in Brazil than one that generates all its business within Brazil. The factor “λ” measures the relative exposure of a firm to country risk. One simplistic solution would be to do the following: λ = % of revenues domesticallyfirm/ % of revenues domesticallyavg firm For instance, if a firm gets 35% of its revenues domestically while the average firm in that market gets 70% of its revenues domestically λ = 35%/ 70 % = 0.5 There are two implications • A company’s risk exposure is determined by where it does business and not by where it is located • Firms might be able to actively manage their country risk exposures 2
    30. 30. Estimating E(Return) for Embraer Assume that the beta for Embraer is 0.88, and that the riskfree rate used is 4.5%. (Real Riskfree Rate) Approach 1: Assume that every company in the country is equally exposed to country risk. In this case,E(Return) =4.5% + 10.24% + 0.88 (5.51%) = 19.59% Approach 2: Assume that a company’s exposure to country risk is similar to its exposure to other market risk.E(Return) = 4.5% + 0.88 (5.51%+ 10.24%) = 18.36% Approach 3: Treat country risk as a separate risk factor and allow firms to have different exposures to country risk (perhaps based upon the proportion of their revenues come from non-domestic sales)E(Return)= 4.5% + 0.88(5.51%) + 0.50 (10.24%) = 14.47%Embraer is less exposed to country risk than the typical Brazilian firm since much of its business is overseas. 3
    31. 31. Implied Equity PremiumsIf we use a basic discounted cash flow model, we can estimatethe implied risk premium from the current level of stock prices.For instance, if stock prices are determined by a variation of thesimple 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 earningsgrowth greater than that of the economy, and then a stablegrowth period. 3
    32. 32. 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 5Expected Dividends =$34.72 $38.30 $42.24 $46.59 $51.39+ Stock BuybacksExpected dividends + buybacks in year 6 = 51.39 (1.0505) = $ 54.731148 = 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)5Solving for r, r = 8.67%. (Only way to do this is trial and error)Implied risk premium = 8.67% - 5.05% = 3.62% 3
    33. 33. 3 2000 1998 1996 1994 1992 1990 1988 1986Implied Premium for US Equity Market 1984 1982 Year 1980 1978 1976 1974 1972 1970 1968 1966 1964 1962 1960 7.00% 6.00% 5.00% 4.00% 3.00% 2.00% 1.00% 0.00% Implied Premium
    34. 34. Implied Premium for Brazilian Market: March 1, 2001 Level of the Index = 16417 Dividends on the Index = 4.40% of (Used weighted yield) Other parameters • Riskfree Rate = 4.5% (real riskfree rate) • Expected Growth – Next 5 years = 13.5% (Used expected real growth rate in Earnings) – After year 5 = 4.5% (real growth rate in long term) Solving for the expected return: • Expected return on Equity = 11.16% • Implied Equity premium = 11.16% -4. 5% = 6.66% 3
    35. 35. The Effect of Using Implied Equity Premiums on Value Embraer’s value per share (using historical premium + country risk adjustment) = 11.22 BR Embraer’s value per share (using implied equity premium of 6.66%) = 20.02 BR Embraer’s stock price (at the time of the valuation) = 15.25 BR 3
    36. 36. Estimating BetaThe standard procedure for estimating betas is to regress stockreturns (Rj) against market returns (Rm) - Rj = a + b R m • where a is the intercept and b is the slope of the regression.The slope of the regression corresponds to the beta of thestock, and measures the riskiness of the stock.This beta has three problems: • It has high standard error • 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. 3
    37. 37. Beta Estimation: The Noise Problem 3
    38. 38. Beta Estimation: The Index Effect 3
    39. 39. Determinants of BetasProduct or Service: The beta value for a firm depends uponthe sensitivity of the demand for its products and services andof its costs to macroeconomic factors that affect the overallmarket. • 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 productsOperating Leverage: The greater the proportion of fixed costsin the cost structure of a business, the higher the beta will be ofthat business. This is because higher fixed costs increase yourexposure to all risk, including market risk.Financial Leverage: The more debt a firm takes on, the higherthe beta will be of the equity in that business. Debt creates afixed cost, interest expenses, that increases exposure to marketrisk. 3
    40. 40. Equity Betas and Leverage The beta of equity alone can be written as a function of the unlevered beta and the debt-equity ratio βL = βu (1+ ((1-t)D/E))where βL = Levered or Equity Beta βu = 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: βL = βu (1+ ((1-t)D/E)) - βdebt (1-t) (D/E) 4
    41. 41. 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. 4
    42. 42. Bottom-up BetasThe 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. j =k  Operating Income j  ∑ βj    Operating Income Firm  j =1 (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 β levered = β unlevered[1+ (1− tax rate) (Current Debt/Equity Ratio)]The bottom up beta will give you a better estimate of the truebeta 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. 4
    43. 43. Bottom-up Beta: Firm in Multiple Businesses Boeing in 1998Segment Estimated Value Unlevered Beta Segment WeightCommercial Aircraft 30,160.48 0.91 70.39%Defense 12,687.50 0.80 29.61% Estimated Value = Revenues of division * Enterprise Value/SalesBusinessUnlevered Beta of firm = 0.91 (.7039) + 0.80 (.2961) = 0.88Levered Beta CalculationMarket Value of Equity = $ 33,401Market Value of Debt = $8,143Market Debt/Equity Ratio = 24.38%Tax Rate = 35%Levered Beta for Boeing = 0.88 (1 + (1 - .35) (.2438)) = 1.02 4
    44. 44. Siderar’s Bottom-up BetaSiderar is an Argentine steel company.Business Unlevered D/E Ratio Levered Beta BetaSteel 0.68 5.97% 0.71Proportion of operating income from steel = 100%Levered Beta for Siderar= 0.71 4
    45. 45. Comparable Firms?Can an unlevered beta estimated using U.S. steel companies be used to estimate the beta for an Argentine steel company? 4
    46. 46. The Cost of Equity: A Recap Preferab ly, a b ottom-up b eta, b ased up on other firms in the b usiness, and firm’s own financial leverageC ost of Equity = Riskfree Rate + Beta * (Risk Premium)Has to b e in the same Historical Premium Implied Premiumcurrency as cash flows, 1. Mature Equity Market Premium: Based on how equityand defined in same terms Average p remium earned b y or market is p riced today(real or nominal) as the stocks over T.Bonds in U.S. and a simp le valuationcash flows 2. C ountry risk p remium = model C ountry Default Sp read* ( σEquity/σCountry bond) 4
    47. 47. Estimating the Cost of DebtThe cost of debt is the rate at which you can borrow at currently,It will reflect not only your default risk but also the level ofinterest rates in the market.The two most widely used approaches to estimating cost of debtare: • Looking up the yield to maturity on a straight bond outstanding from the firm. The limitation of this approach is that very few firms have long term straight bonds that are liquid and widely traded • Looking up the rating for the firm and estimating a default spread based upon the rating. While this approach is more robust, different bonds from the same firm can have different ratings. You have to use a median rating for the firmWhen in trouble (either because you have no ratings or multipleratings for a firm), estimate a synthetic rating for your firm andthe cost of debt based upon that rating. 4
    48. 48. Estimating Synthetic RatingsThe rating for a firm can be estimated using the financialcharacteristics of the firm. In its simplest form, the rating can beestimated from the interest coverage ratio Interest Coverage Ratio = EBIT / Interest ExpensesFor Siderar, in 1999, for instance Interest Coverage Ratio = 161/48 = 3.33 • Based upon the relationship between interest coverage ratios and ratings, we would estimate a rating of A- for Siderar. With a default spread of 1.25% (given the rating of A-)For Titan’s interest coverage ratio, we used the interestexpenses and EBIT from 2000. Interest Coverage Ratio = 55,467/ 4028= 13.77 4
    49. 49. Interest Coverage Ratios, Ratings and Default Spreads If Coverage Ratio is Estimated Bond Rating Default Spread(1/99) Default Spread(1/01) > 8.50 AAA 0.20% 0.75% 6.50 - 8.50 AA 0.50% 1.00% 5.50 - 6.50 A+ 0.80% 1.50% 4.25 - 5.50 A 1.00% 1.80% 3.00 - 4.25 A– 1.25% 2.00% 2.50 - 3.00 BBB 1.50% 2.25% 2.00 - 2.50 BB 2.00% 3.50% 1.75 - 2.00 B+ 2.50% 4.75% 1.50 - 1.75 B 3.25% 6.50% 1.25 - 1.50 B– 4.25% 8.00% 0.80 - 1.25 CCC 5.00% 10.00% 0.65 - 0.80 CC 6.00% 11.50% 0.20 - 0.65 C 7.50% 12.70% < 0.20 D 10.00% 15.00% 4
    50. 50. Cost of Debt computationsCompanies in countries with low bond ratings and high defaultrisk might bear the burden of country default risk • For Siderar, the rating estimated of A- yields a cost of debt as follows: Pre-tax Cost of Debt in 1999 = US T.Bond rate + Country default spread + Company Default Spread = 6% + 5.25% + 1.25% = 12.50%The synthetic rating for Titan is AAA. The default spread in 2001is 0.75%. Pre-tax Cost of Debt = Riskfree Rate + Company Default Spread+ Country Spread = 5.10% + 0.75% + 0.95%= 6.80% 5
    51. 51. Synthetic Ratings: Some CaveatsThe relationship between interest coverage ratios and ratings,developed using US companies, tends to travel well, as long aswe are analyzing large manufacturing firms in markets withinterest rates close to the US interest rateThey are more problematic when looking at smaller companiesin markets with higher interest rates than the US. 5
    52. 52. Weights for the Cost of Capital Computation The weights used to compute the cost of capital should be the market value weights for debt and equity. There is an element of circularity that is introduced into every valuation by doing this, since the values that we attach to the firm and equity at the end of the analysis are different from the values we gave them at the beginning. As a general rule, the debt that you should subtract from firm value to arrive at the value of equity should be the same debt that you used to compute the cost of capital. 5
    53. 53. Estimating Cost of Capital: Titan Cements Mature Greek country premium market Equity premium • Cost of Equity = 5.10% + 0.96 (4%+1.59%) = 10.47% • Market Value of Equity = 739,217 million GDr (78.7%) Company default spread Country default spread Debt • Cost of debt = 5.10% + 0.75% +0.95%= 6.80% • Market Value of Debt = 199,766 million GDr (21.3 %) Cost of CapitalCost of Capital = 10.47 % (.787) + 6.80% (1- .2449) (0.213)) = 9.33 % 5
    54. 54. Titan Cement: Book Value WeightsTitan Cement has a book value of equity of 135,857 millionGDR and a book value of debt of 200,000 million GDR.Estimate the cost of capital using book value weights instead ofmarket value weights. 5
    55. 55. Estimating A U.S. Dollar Cost of Capital: Siderar - An Argentine Steel Company Mature Market Premium Country Risk Premium for Argentina Equity • Cost of Equity = 6.00% + 0.71 (4% +10.53%) = 16.32% • Market Value of Equity = 3.20* 310.89 = 995 million (94.37%) Debt • Cost of debt = 6.00% + 5.25% (Country default) +1.25% (Company default) = 12.5% • Market Value of Debt = 59 Mil (5.63%) Cost of CapitalCost of Capital = 16.32 % (.9437) + 12.50% (1-.3345) (.0563)) = 16.32 % (.9437) + 8.32% (.0563)) = 15.87 % 5
    56. 56. Converting a Dollar Cost of Capital into a Peso cost of capital Approach 1: Use a peso riskfree rate in all of the calculations above. For instance, if the peso riskfree rate was 10%, the cost of capital would be computed as follows: • Cost of Equity = 10.00% + 0.71 (4% +10.53%) = 20.32% • Cost of Debt = = 10.00% + 5.25% (Country default) +1.25% (Company default) = 16.5% (This assumes the peso riskfree rate has no country risk premium embedded in it.) Approach 2: Use the differential inflation rate to estimate the cost of capital. For instance, if the inflation rate in pesos is 7% and the inflation rate in the U.S. is 3%  1+ Inflation Peso  Cost of capital= (1 + Cost of Capital$ )   1+ Inflation$  = 1.1587 (1.07/1.03) = 1.2037--> 20.37% 5
    57. 57. Recapping the Cost of Capital C ost of b orrowing should b e b ased up on (1) synthetic or actual b ond rating Marginal tax rate, reflecting (2) default sp read tax b enefits of deb t C ost of Borrowing = Riskfree rate + Default sp readC ost of C ap ital = C ost of Equity (Equity/(Deb t + Equity)) + C ost of Borrowing (1-t) (Deb t/(Deb t + Equity)) C ost of equity b ased up on b ottom-up W eights should b e market value weights b eta 5
    58. 58. SummaryEquity value versus firm valueEstimating the cost of equity • CAPM, APT,.. • Real versus nominal • CurrencyEstimating the cost of debt • Estimating risk free rate • Estimating cost of raising debt for the firmEstimating the cost of capital • WACC 5