International Financial Management 15

⋄ A rating of BB or less is considered “junk” (also called “high-yield,” “speculative grade”). In the U.S., the usual spread of junk debt is between 400 to 600 bps over 1-yr T-bills. Range is very wide: Spreads can go over 2600 bps. ⋄ This Table is for short-maturities. As time to maturity increases, the spread (in bps) also increases. ⋄ Spreads are not constant over time, global and credit market conditions matter. We pointed out above that global factors matter. If developed markets are doing well, in general we tend to see that liquidity and appetite for risk in credit markets increases. These two factors will drive down spreads. ⋄ This Table gives spreads over T-bills, in USD. If we are interested in converting the YTM in USD into a YTM in the local currency, we use IFE combined with relative PPP to estimate E[ef]. That is, using the linearized version of both formulas, we get: YTMD (in local currency) YTMD (in USD) + (ID – IUS). Example: Suppose country DX wants to borrow short-term & medium-term in USD. Bertoni Bank evaluates the country risk of country DX. Short-term Horizon Factor Weight Grade Economic .3 80 Debt management .3 90 Political .3 67 Structural .1 75 Total Short-term ranking: A Medium-term ranking: BBB 24 27 12 15 78.6 Medium-term Horizon Weight Grade .3 70 .2 70 .2 50 .3 60 21 14 15 12 63 That is, the short-term debt of country DX will get a spread in the 60-100 bps range, say 78 bps over US Treasuries; while the medium-term debt will get a higher spread, say 138 bps. Suppose the short-term US Treasuries yield 3% (s.a.). Then, the short-term debt of country DX yields YTMDX (in USD) = 3% (s.a.) + 0.78% (s.a.) = 3.78% (s.a.). Based on the past 10 years, the expected inflation in country DX is 5% and in the U.S. is 2%, then YTMDX (in DX currency) = 3.78% + 3% = 6.78% .¶ Remark: The observed spread, the sovereign default spread, –i.e., the difference between the US Treasuries yield and another government debt yield (in USD)– is a good proxy for CR. The CDS (Credit Default Swap) market allows investors to buy insurance against CR. The insurance premium paid (say, 1.60% per year) is also a good indicator for CR! (Both indicators should be similar!) Example: Weights and Factors in Practice (Euromoney) – March 2014 The British magazine Euromoney produces semi-annual country risk analysis of 189 countries using a panel of more than 400 experts. Euromoney rates nine categories with a score (0 to 100). • Factors and weights: Economic performance: GDP growth - 25% weight IFM-LN.212 Political Risk Debt indicators: Debt/GDP Debt in default or rescheduled Credit rating: Moody’s or S&P’s or Fitch IBCA’s rating Short-term credit market access Access to bank finance: Commercial bank credit Access to Capital markets Discount default factor: Spread over US Treasury bills: - 25% weight - 10% weight - 10% weight - 10% weight - 5% weight - 5% weight - 5% weight - 5% weight Based on the weighted average for each country, each country is placed on a Tier (Tier 1=AAA, Tier 5=C). A world country risk weighted average is also calculated: 42.86 (B rating or Tier 4) • Measures to reduce CR ⋄ A cap on the total amount invested in a particular country ⋄ Diversification ⋄ Credit/Political Risk Derivatives Diversification and Country Risk Taken From “Profits in a Time of War,” The Economist, Sep 20, 2014. An excessive concentration on one country is a classic mistake. After China’s revolution in 1949 HSBC, then a purely Asian bank, lost half its business. Iran’s nationalisation in 1951 of the AngloIranian Oil Company’s assets devastated the firm, a precursor of BP. IFM-LN.213 There are modern echoes of these episodes. Repsol, a Spanish oil firm, fell in love with Argentina, leaving it vulnerable when YPF, the firm it bought there, was nationalised in 2012. First Quantum, of Canada, had made a third of its profits from a mine that the Democratic Republic of Congo nationalised in 2009. But as they have expanded over the past two decades, multinationals have spread themselves more. Only a dozen big, global, listed firms have over a tenth of their sales in Russia. BP is the country’s largest foreign investor but gets only about 10% of its value from its stake in Rosneft, an oil giant. McDonald’s Moscow outlets, once a symbol of détente, are temporarily shut, victims of a diplomatic tit-for-tat. Even so, the burger giant makes less than 5% of its profits in Russia. This picture is true in other hotspots. Telefonica, a Spanish firm, and Procter & Gamble (P&G), together have billions of dollars trapped in Venezuela, which has introduced capital controls. But it represents less than 5% of their sales. Ben van Beurden, the boss of Royal Dutch Shell, recently said diversification is “the only way to inoculate yourself”. • Review of CR ⋄ Pros - It is simple (many factors simplify to a letter) - It allows cross-country and across time comparison. ⋄ Cons - It is too simple. - In practice, ratings tend to converge (herding). - Not a lot of predictive power. The last point –i.e., the lack of predictive power– is a major criticism. For example, a month before the 1997 Asia crisis, South Korea was rated as Italy and Sweden. Then, Fitch went from rating Korea as AA- (investment grade) to B- (junk) in one month. Other rating agencies replicated the same dramatic sudden change in Korea’s CR rating. Similar sudden downgrades occurred during the 2009-2012 European debt crisis with Greece, Cyprus, Ireland, Italy, Portugal, and Spain. Given the lack of predictive power of CR, a single indicator may not be enough to capture the overall risk of a country. There are other indexes that may be help to signal the true riskiness of a country – i.e., indicators that can be correlated with the underlying true country risk. For example, FDI confidence index (produced by A.T. Kearny), Global competitiveness index (GCI) (produced by World Economic Forum), Index of economic freedom (produced by the Heritage Foundation and the Wall Street Journal), Opacity index (produced by PWC and The Milken Institute), etc. Examples of CR Ratings: 1) From A.M. Best, December 2018 (http://www.ambest.com/ratings/countryrisk.asp): A.M. Best uses country risk analysis to determine how the factors outside an insurer's control affect its ability to meet its obligations to its policyholders. These analyses include, amongst others, the assessment of local accounting rules, government policies and regulation, economic growth and social stability. A.M. IFM-LN.214 Best has a five-tier scale and assigns a Country Risk Tier I-V based on each country's level of risk (Ilowest risk, V-highest risk). Australia, Austria, Canada, Japan, Luxembourg, Singapore, Sweden, Switzerland, UK, USA Bermuda, Cayman Islands, Chile, HK, Italy, Ireland, New Zealand, Spain, South Korea, Taiwan China, Cyprus, Kuwait, Malaysia, Malta, México, Portugal, Poland, Qatar, UAE, Thailand Bahrain, Brazil, India, Indonesia, Jordan, Kazakhstan, Morocco, Panamá, Russia, Turkey Argentina, Ghana, Honduras, Kenya, Lebanon, Libya, Nigeria, Pakistan, Ukraine, Venezuela Tier I Tier II Tier III Tier IV Tier V 2) From Coface, Q3 2018 (http://www.coface.com): Coface is France's export credit underwriter, offering insurance against the risk that when you sell something to a foreign company, they won't pay their bills (for whatever reason, from bankruptcy to international war). Country Rating Business Defaulting Risk Austria, Germany, Luxembourg, Netherlands, Norway, Switzerland, A1 Very Low Australia, Belgium, HK, Japan, New Zealand, South Korea, Taiwan, USA A2 Low Canada, Chile, Hungary, Ireland, Lithuania, Malaysia, Poland, U.K. A3 Satisfactory Botswana, Bulgaria, Italy, Indonesia, Kenya, Perú, Thailand, Uruguay A4 Reasonable Brazil, China, Ghana, Kazakhstan, México, Russia, South Africa B Fairly High Argentina, Lebanon, Ethiopia, Ghana, Serbia, Togo, Turkey, Uganda C High Angola, Chad, Guyana, Haiti, Madagascar, Nepal, Nicaragua, Pakistan D Very High Cuba, Iraq, Libya, Mozambique, Syria, Sudan, Yemen, Zimbabwe E Extreme Example: Spread on government European bonds – Oct 31, 2018. Base Rate: German government bonds  Higher observed spreads, higher CR. IFM-LN.215 From MTS Indices: http://www.mtsindices.com/european-bond-spreads. ¶ IFM-LN.216 CHAPTER 16 – BRIEF ASSESMENT 1. Suppose the Brazilian government wants to borrow in USD for 7 years. You want to set the YTM in USD and in BRL. You have the following data: Brazil’s grade: BB (associated with a spread of 280 bps (2.80%) over US Treasuries). 7-yr US Treasuries yield = 2.5%. E[IUS] = 2% E[IBR] = 6% 2. Suppose Colombia wants to borrow for 3-yers (medium-term) in USD. Given the information below determine the YTM for Colombian debt. (Use Table 16.1 and a linear interpolation method to set the spread). Medium-term Horizon Factor Weight Grade Economic .30 90 Debt management .25 90 Political .25 70 Structural .20 60 3-year US Treasuries yield: 2.1%. 3. What is the effect on Colombia’s YTMs of the following events? (A) Commodity prices, say coffee prices, decrease. (B) The Colombian government runs an unexpectedly large government deficit. (C) Colombian economy grows more than expected. (D) The US Fed increases interest rates. IFM-LN.217 Chapter 17 – The Cost of Capital in an International Context Review from Chapter 16 - Country Risk (CR) affects discount rates - Different countries will have different risk free rates (kf). - High CR, high risk-free rate kf. Q: How do MNCs set discount rates for projects in foreign countries? In this chapter, we study the determination of the cost of capital for international projects. The cost of capital is the cost of a MNC’s funds for a project/investment. In equilibrium, it also represents the required return on a project/investment. We will use the WACC to calculate an MNC’s cost of capital of projects, which can be used as the discount rate for those projects. 17.1 Brief Review: Capital Structure A firm can raise new capital by: ⋄ Issuing new equity (E) –a firm gives away ownership and has to pay dividends ⋄ Issuing debt (D) –a firm borrows and has to pay interest payments. The firm can also use retained earnings for new investments, which we will consider E. (According to the pecking order theory, retained earnings are the first source of funds for a company.) Recall that the investment decision (NPV evaluation based on CFs and risk of project) is separate from the financing decision (selection of E and D). • Trade-off Theory of Capital Structure Firms will use the E and D mix that minimizes the cost of capital, kc. There is a U-shape relation between cost of capital and the amount of debt relative to the total value of the firm (V=E+D). Trade-off: Debt has its (tax) advantages, but also its disadvantages (bankruptcy). E and D need to be combined optimally. Before the optimal Debt Ratio, (D/V)*, the tax advantages dominate and decrease the cost of capital; after (D/V)*, the increased probability of bankruptcy dominates and increases the cost of capital. IFM-LN.218 Cost of Capital (kc) (D/V)* Debt Ratio (D/V) The capital structure that a firm desires is called their target structure. It should be close to (D/V)*. • Target Debt-Equity Ratio in Practice Suppose that GE’s target debt-equity ratio is 70%-30%. It is unlikely that GE will raise funds with a 70-30 debt-equity split for every project. For example, for a Brazilian project, GE may use a 6040 D/E split. The target (D/V)* reflects an average; it is not a hard target for each project. That is, for other projects GE will use D/E in order to compensate and be close to the target debt-equity ratio. It is expensive to issue shares for each project. It is common for companies to finance projects using retained earnings first (the easiest and cheapest form of E) and then use debt for the remaining part −following the Pecking order theory. 17.2 Measuring the Cost of Capital The cost of capital (discount rate) used should reflect both the riskiness and the type of cash flows under consideration. If the cash flows are cash flows due to E (D), then the appropriate cost of capital is the cost of equity, ke (cost of debt, kd). In general, firms use both E & D to finance projects. We will use weighted average cost of capital (WACC), kc, where t is the effective tax rate: 𝑘 𝑘 1 𝑡 𝑘 • Cost of debt (kd) The cost of debt of a project (kd): The interest a firm has to pay to borrow from a bank or the bond market to fund a project. Sometimes kd is called pre-tax cost of debt. It is easy to determine for a firm: A firm calls a bank/investment bank to find out the interest rate it has to pay to borrow capital. It is also easy to determine for companies that borrow from debt markets, which are rated. If the company is not rated or most of the debt is old bank debt, it is more difficult to calculate a current kd. In these cases, we benchmark kd with similar companies (similar size, similar industry, similar D/V, etc.) IFM-LN.219 Q: How does a bank set the interest rate for a given firm? A: Base rate (say, a risk free rate like T-bills, kf) + spread (reflecting the risk of the company/project, which includes CR). We will see this in Chapter 18. Note: Interest payments are tax deductible  After-tax cost of debt = kd*(1-t) • Cost of equity (ke) The cost of equity of a project (ke): The required (expected) return on equity a firm has to pay to investors. This is an equilibrium result. A model is needed to determine required rates of return on equity. We can use the CAPM or other risk-return models, for example a multifactor model, with the 3- or 5-Fama-French factors. (Recall that only undiversifiable risk is priced in expected returns.) We will use the CAPM, which produces a required rate of return on equity, to value the cost of equity: ke = kf +  (kM – kf) kf: Risk-free rate (ideally, the rate on a zero coupon government bond matching the time horizon of the investment). In practice, short-term government security rates, say 90-day T-bill rates. kM: Expected return on a market portfolio (in practice, the long-run return on a well-diversified market index). (kM – kf): Equity Risk premium (ERP), what investors demand for investing in an average risk investment, relative to the risk-free rate. In practice, the difference between the above calculated kM & kf . : Systematic risk of the project/firm = Cov(ke,kM)/Var(kM). In practice, a coefficient estimated by a regression against excess market returns or risk premium, (kM – kf)). : Systematic Risk of the project/firm = Cov(ke,kM)/Var(kM) (in practice, a coefficient estimated by a regression against excess market returns or risk premium, (kM – kf), using 5 years of data). Q: Which CAPM: World or Domestic? A: The (kM – kf) and  used depends on the view that a company has regarding capital markets. If capital markets are integrated (or if the shareholders are world-wide diversified) the appropriate equity risk premium should reflect a world benchmark (say, MSCI World Index), (kM – kf)W. But, if markets are segmented (or if the shareholders hold domestic portfolios), then the appropriate equity risk premium should be based on a domestic benchmark (say, the Bovespa Index for Brazilian companies), (kM – kf)D. The risk-free rate should also be adjusted accordingly. Then, - World CAPM: - Domestic CAPM: ke = ke,W = kf ,W + W (kM – kf)W ke = ke,D = kf,,D + D (kM – kf)D The difference between these two models can be significant. According to Bruner et al. (2008), on average, there is a 5.55% absolute difference for emerging markets and a 3.58% absolute difference for developed markets. The betas (W and D) tend to be different too: the average absolute difference is 0.44 for emerging markets and 0.21 for developed markets. IFM-LN.220 Given that the evidence for integrated capital markets is weak, especially for emerging markets; we tend to think of financial markets as partially integrated. Then, a weighted average can be used to calculate ke, where the weights can be ad-hoc or represent some measure of integration, say, based on international trade or international investments of a country as a proportion of GDP: - Partially Integrated CAPM: ke = wD ke,D + (1- wD) ke,W In general, we tend to find that World CAPM produces low expected returns. The Fama-French 3factor model tends to produce higher (and more realistic) expected returns. Many ad-hoc adjustments are used in the private sector. Notes: ⋄ Dividends are not tax deductible. There is an advantage to using debt! ⋄ Time-consistency with kf . The same maturity should be used for ke and kd. That is, if you use long-term bonds to calculate kd , you should also use long-term data to calculate ke. ⋄ In Chapter 16 we discussed country risk. For practical purposes, many emerging market government bonds may not be considered risk-free. Thus, the government bond rate includes a default spread, which, in theory, should be subtracted to get kf. ⋄ If the company is publicly traded, getting  is simple:  is estimated by the slope of a regression against a market index. If the company is not publicly traded, we need to benchmark . That is, we use the s of publicly traded similar companies. ⋄ There are many issues associated with the estimation of : choice of index, noisy data, adjustment by leverage, mean reversion, etc. We will not get into these issues. Issues: Q: Real or Nominal? If the CFs are nominal (the usual situation), then ke should be calculated in nominal terms. Q: Which kf to use? Local or Foreign? The kf that reflects the risk of the cash flows. If the CFs are in MXN, then kf should be a Mexican treasury rate (for example, CETES). Q: Which maturity for kf to use? The maturity that reflects the duration of the cash flows. In practice, the duration of the project is matched to the maturity of kf (potentially a problem for many emerging markets where there is no long-term debt market). Q: Which  to use? The  of the company or the  of the project?  should reflect the systematic risk of the project. Example: GE wants to do an investment in Brazil. Equity investment: BRL 100M Debt issue: BRL 150 Value of Brazil investment = D + E = BRL 250 ( 60-40 D/E split) Brazilian Tax Rate = t = 34% (25% corporate rate + 9% social contribution on net profits) Cost of capital of project = kc = ? • Cost of debt (kd) GE decides to use a domestic CAPM, with the following data. GE can borrow in Brazil at 60 bps over Brazilian Treasuries (kf) kf = 11.90% (3-year Brazil government bond yield) IFM-LN.221 kd (for GE) = .1190 + .0060 = .1250 (12.50%) • Cost of equity (ke) Similar projects in Brazil have a beta of 1.1 (GE-Brazil = 1.1) Return of the Brazilian market (BOVESPA) in the past 20 years: 14% (kM = 14%) ke = kf +  (kM – kf) = .1190 + 1.1 * (.14 - .1190) = 0.1421 (14.21%) • Cost of Capital –WACC- (ke) kc = D/(E+D) kd (1-t) + E/(E+D) ke kc = (.60) x .1250 x (.66) + (.40) x .1421 = .10634 (10.634%) This is the discount rate that GE should use to discount the cash flows of the Brazilian project. That is, GE will require a 10.634% rate of return on the investment in Brazil. ¶ Remark: Every time the cost of capital increases, the NPV of projects goes down. Anything that affects kc, it will also affect the profitability (NPV) of a project. Application: Argentina defaults in some of its debt. Argentine country risk increases, kf,Arg goes up and kc,Arg also goes up. Then, NPV projects in Argentina can become negative NPV projects:  MNCs may suddenly abandon Argentine projects. Estimating the Equity Risk Premium: (kM – kf) To compute the ERP, we need to determine a market portfolio (S&P? MSCI World?), and a method (and sample period) to compute the expectation. There are three different methods to compute kM: 1) Surveys. Usually an average of ERPs provided by individual investors, institutional investors, managers and, even, academics. 2) Historical data. Expectations are computed using past data. This is the most popular approach. For example, compute kM with the historical sample mean equity market return, 𝑋. If we use this approach, it pays to use as much data as possible –more data, lower S.E. We think of kM as a longrun average of market returns. 3) Forward-looking data. An (implied) ERP is derived from market prices, for example, market indexes, options & futures on market indexes, etc. Of course, we also need a model (a formula) that extracts the ERP from market prices. Once we compute kM and chose a corresponding kf, we are ready to determine the ERP. But, we make decisions along the way. For example, using Robert Shiller’s monthly data, with 150 years of data, we produce an estimate of the ERP = E[(rm,t - rf)] = (kM – kf). = 4.34%. This ERP estimate involved the following decisions: – Computation of returns (log returns) – Method of computing ERP (Historical data) – Sample period (1871-2021) – Market portfolio (S&P Composite Index) IFM-LN.222 – Risk-free rate (10-year U.S. bond rate). Then, Annualized Market return = 0.007378 * 12 = 0.088536 Annualized risk-free rate = 0.04511 ERP = 0.088536 - 0.04511 = 0.043426 (4.34%) Aside: Many economists consider this estimated ERP as “too high.” Why? The degree of risk aversion to justify it is unreasonable high. Estimating the Equity Risk Premium: Historical Method and Precision of Estimates Risk premiums are estimated with error. To deal with this issue, practitioners, using the historical data method, like to use as many years as possible to build the long-run average. Remember, the sample average, 𝑋, comes with an associated standard error: S.E.(𝑋) = s √𝑇 where s is the standard deviation (SD) and T is the length of the data. Thus, more data means a lower standard error -i.e., more precision. This may be a problem for emerging markets, where there is limited reliable return data. Example: Suppose we have 2 markets: a Developed Market (DM) with T=100 annual observation and an annualized standard deviation (SD) equal to 15%; & an Emerging Market (EM) with T=50 and SD=30%. We can calculate the S.E. for both markets. S.E.DM = .15/sqrt(100) = .015 (or 1.5%) S.E.EM = .30/sqrt(50) = .0424 (or 4.24%). Note: A 95% C.I. for an EM around 0% goes from [-8.5% to 8.5%]. Not very precise! ¶ But, note that even with more than 100 years of data for developed markets there is no consensus on an ERP. As a matter of fact, in a recent review paper, by two Federal Reserve economists, Duarte and Rosa (2015) list over 20 different approaches to estimate the ERP in the U.S. Using data from 1960 to 2013, Duarte and Rosa (2015) report estimates from -0.4% to 13.1%, with a 5.7% average for all model. A wide range! Table 17.1 presents ERP estimates in international markets, translated to USD, using monthly data from 1970 to 2021. The estimates range from 0.88% (Italy) to 11.56% (Hong Kong), with a 3.17% world average. Again, a wide range. Table 17.1: MSCI Index USD Equity Returns and ERP – Developed Markets: (1970-2021) Market Equity Return IFM-LN.223 Standard Deviation ERP U.S. Canada France Germany Italy Switzerland U.K. Japan Hong Kong Singapore Australia 8.31 7.95 8.80 8.80 5.37 10.34 7.37 9.56 16.06 11.71 7.35 15.01 19.21 21.95 21.48 25.25 17.64 21.20 20.46 33.23 27.48 23.42 0.0382 0.0346 0.0431 0.0431 0.0088 0.0585 0.0288 0.0506 0.1156 0.0722 0.0273 World EAFE 7.66 7.69 14.54 16.64 0.0317 0.0306 Table 17.2 reports equity returns and ERP estimates for EM, with, as expected, higher numbers. Table 17.2: MSCI Index USD Equity Returns and ERP – Emerging Markets: (1987*-2021) Market Argentina (404) Brazil (404) Mexico (404) Poland (344) Russia (320) India (344) China (344) Korea (404) Thailand (404) Egypt (320) South Africa (344) World (620) EM Asia Equity Return 24.21 22.23 17.67 15.88 21.09 12.10 4.90 11.75 11.58 11.61 9.47 Standard Deviation 51.49 47.67 29.26 43.24 47.54 28.35 31.94 34.08 32.24 31.69 26.31 ERP 0.1972 0.1774 0.1318 0.1139 0.1660 0.0760 0.0041 0.0726 0.0606 0.0862 0.0498 7.66 8.85 14.54 23.13 0.0317 0.0436 Estimating the Equity Risk Premium: Ad-hoc adjustments Given the imprecision of ERP estimates, for a market with limited reliable return history, say Brazil, Hungary or a generic Country J, it is sometimes easier to adjust a (kM – kf) from a well-established market, say, the U.S., to get a more precise estimate of that market’s ERPJ. IFM-LN.224 There are several ways to do this adjustment. These approaches are mainly intuitive, with simplicity in mind (taken from Damodaran (2012)): ⋄ Country Risk Approach: The U.S. market risk premium is increased by country risk (CRJ, the sovereign default spread of the bond issued by Country J): (kM – kf)J = (kM – kf)US + CRJ ( no distinction between bond and equity risk!) ⋄ Relative Equity Market Approach: The U.S. market risk premium is modified by the volatility of the Country J’s equity market, σJ, relative to the volatility of the U.S equity market, σUS: (kM – kf)J = (kM – kf)US * σJ/ σUS ( problem: σJ is also an indicator of liquidity!) ⋄ Mixed Approach: The U.S. market risk premium is increased by combining Country J’s CR, equity market volatility and bond market volatility. We expect equity spreads to be higher than debt spread. Then, we need to adjust the CR upward. One way to do this is to use the relative volatility of Country J’s equity market to the volatility of Country J’s bond market, σJ,bond: (kM – kf)J = (kM – kf)US + CRJ * σJ/ σJ,bond. Notes: ⋄ We may have very different numbers from these three approaches. Judgement calls/adjustments may be needed. ⋄ Following the idea of CR from bond markets, a country equity risk premium (CER) can be easily derived for Country J: CERJ = (kM – kf)J - (kM – kf)US. ⋄ We construct a market risk premium for Country J based on USD rates. To convert this premium into a local currency premium, we can use IFE combined with relative PPP to estimate E[ef]. That is, using the linearized version of both formulas, we get: (kM – kf)J (in local currency) (kM – kf)J + (IJ – IUS). Example: Suppose the limited returns history of Brazil’s equity markets makes GE’s risk manager uncomfortable. She wants to adjust (kM – kf)Brazil using different methods, using the U.S. market as a benchmark: the relative equity market approach and the mixed approach. GE uses the following data: (kM – kf)US = 0.0382 (from Table 17.1) kf,US = 4.50% σUS = 15.01% σBrazil = 37.3% (based on past 15 years) σBrazil,bond = 23.1% (based on past 15 years) CRBrazil = 2.80% IBrazil = 8% IUS = 3% ⋄ Relative Equity Market Approach: (kM – kf)Brazil = 0.0382 + .028 *.373/.231 = 0.093741  ke,Brazil = rf +  (kM – kf)Brazil = .0450 + 1.1 * 0.093741 = 0.1481. If we want the ERP in local currency (BRL), then: IFM-LN.225 (kM – kf)Brazil (in BRL) 0.093741 + (0.08 - 0.03) = 0.093741 + 0.05 = 0.1437 ⋄ Mixed Approach: (kM – kf)Brazil = 0.0382 + .028 *.373/.231 = 0.08341  ke,Brazil = rf +  (kM – kf)Brazil = .0450 + 1.1 * 0.08341 = 0.1368. Note: We can calculate CERBrazil from any of these approaches. For example, using the Mixed Approach: CERBrazil = 0.08341 - 0.0382 = 0.04521 (in USD!) ¶ CER as a factor in the estimation of ke: Q: How sensitive are companies to CER? There are different ways to incorporate CER into ke. (They are all CAPM extensions, delivering two-factor models.) ⋄ Beta as a Measure of Exposure: We assume that CER exposure is proportional to the  of the company/project. That is, the sensitivity to CER is treated in the same way as the sensitivity to market risk. (This is the implicit assumption of the CAPM used above). Then, ke,J = kf,US +  (kM – kf)J = kf,US +  [(kM – kf)US + CERJ]. ⋄ Using different weights for CER Exposure (“lambda approach”): We can allow each project/company to have its own sensitivity to CER. This sensitivity is called lambda, λ. Similar to , λ is scaled around 1 (λ=1, average exposure). ke,J = kf,US +  (kM – kf)US + λ CERJ. There is no consensus on how to estimate λ. The easier way to do this: Estimate λ using the proportion of revenue generated by the company/project in the country relative to the rest of the companies in the country. (It is possible to adjust this estimate by where the production facilities are located, by a company’s risk-management, etc.). A regression (say, returns against a CR indicator) can also be used to estimate λ. ⋄ Equal CER Exposure: A popular alternative method to estimate ke is to estimate ke as a U.S. company/project and, then, add CER. Very simple method that treats all companies/projects as equally exposed to CER: ke,J = kf,US +  (kM – kf)US + CERJ. Example: Suppose that GE’s risk manager wants to re-estimate ke using the lambda approach. She uses the following additional data: kf,US = 4.50% CERBrazil = 0.04521 (using the Mixed Approach) Revenue from Brazil: 50% Exports contribution to Brazil’s GDP: 13% ⟹ average revenue for a typical Brazilian firm: 87% λGE-Brazil = .50/.87 = 0.5747 ke,Brazil = kf,US +  (kM – kf)US + λGE-Brazil CERBrazil = .0450 + 1.1 * (0.0382) + .5747 * (0.04521) = 0.1130 IFM-LN.226