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Problem 11.1 Houston Oil Company Houston Oil Company‟s cost of debt is 7%. The risk-free rate of interest is 3%. The expected return on the market portfolio is 8%. After depletion allowances Houston Oil‟s effective tax rate is 25%. Its optimal capital structure is 60% debt and 40% equity. a. If Houston‟s beta is estimated at 1.1, what is Houston‟s weighted average cost of capital? b. If Houston‟s beta is estimated at 0.8, significantly lower because of the continuing profit prospects in the global energy sector, what is Houston‟s weighted average cost of capital? Assumptions a) Values b) Values Houston's beta 1.10 0.80 Cost of debt, before tax 7.000% 7.000% Risk-free rate of interest 3.000% 3.000% Corporate income tax rate 25.000% 25.000% General return on market portfolio 8.000% 8.000% Optimal capital structure: Proportion of debt, D/V 60% 60% Proportion of equity, E/V 40% 40% Calculation of the WACC Cost of debt, after-tax 5.250% 5.250% kd x ( 1 - t ) Cost of equity, after-tax 8.500% 7.000% ke = krf + ( km - krf ) β WACC 6.550% 5.950% WACC = [ ke x E/V ] + [ ( kd x ( 1 - t ) ) x D/V ] Problem 11.2 Carlton's cost of capital Exhibit 11.2 showed the calculation of Carlton‟s weighted average cost of capital. Assuming that financial conditions have worsened, and using the following current data, recalculate: a. Carton's cost of equity b. Carlton's cost of debt c. Carlton's weighted average cost of capital Values used Original assumptions in Chapter in Chapter New Values Carlton's beta, β 1.20 1.30 Cost of debt, before tax, kd 8.00% 7.000% Risk-free rate of interest, krf 5.00% 4.000% Corporate income tax rate, t 35.00% 30.000% General return on market portfolio, km 15.00% 9.000% Optimal capital structure: Proportion of debt, D/V 40% 50% Proportion of equity, E/V 60% 50% a) Carlton's cost of equity 17.000% 10.500% ke = krf + ( km - krf ) β b) Carlton's cost of debt, after tax 5.200% 4.900% kd x ( 1 - t ) c) Carlton's weighted average cost of capital 12.2800% 7.7000% WACC = [ ke x E/V ] + [ ( kd x ( 1 - t ) ) x D/V ] One of the most interesting aspects of capital costs is how they have been trending downward in recent years as a result of lower interest rates, lower equity market returns, and in some countries, lower tax rates. As a result of the general decline in business and economic performance, many firms have been reducing their debt levels -- if possible -- in roder to reduce their debt service requirements. But, one factor which has not necessarily fallen in value is the beta of the individaul firm. Here Carlton's cost of capital has fallen dramatically, but its beta is actually higher than before due to more market volatility. Problem 11.3 Sunshine Pipelines Inc. Sunshine Pipelines, Inc., is a large U.S. natural gas pipeline company that wants to raise $120 million to finance expansion. Sunshine wants a capital structure that is 50% debt and 50% equity. Its corporate combined federal and state income tax rate is 40%. Sunshine finds that it can finance in the domestic U.S. capital market at the rates listed below. Both debt and equity would have to be sold in multiples of $20 million, and these cost figures show the component costs, each, of debt and equtiy if raised half by equity and half by debt. A London bank advises Sunshine that U.S. dollars could be raised in Europe at the following costs, also in multiples of $20 million, while maintaining the 50/50 capital structure. Each increment of cost would be influenced by the total amount of capital raised. That is, if Sunshine first borrowed $20 million in the European market at 6% and matched this with an additional $20 million of equity, additional debt beyond this amount would cost 12% in the United States and 10% in Europe. The same relationship holds for equity financing. a. Calculate the lowest average cost of capital for each increment of $40 million of new capital, where Sunshine raises $20 million in the equity market and an additional $20 in the debt market at the same time. b. If Sunshine plans an expansion of only $60 million, how should that expansion be financed? What will be the weighted average cost of capital for the expansion? Assumptions Values Combined federal and state tax rate 40% Desired capital structure: Proportion debt 50% Proportion equity 50% Capital to be raised $ 120,000,000 Cost of Cost of Cost of Cost of Domestic Domestic European European Costs of Raising Capital in the Market Equity Debt Equity Debt Up to $40 million of new capital 12% 8% 14% 6% $41 million to $80 million of new capital 18% 12% 16% 10% Above $80 million 22% 16% 24% 18% Incremental a. To raise $120,000,000 Debt Market Debt Cost Equity Market Equity Cost WACC First $40,000,000 European 6.00% Domestic 12.00% 7.80% Second $40,000,000 European 10.00% European 16.00% 11.00% Third $40,000,000 Domestic 16.00% Domestic 22.00% 15.80% Weighted average cost 10.67% 16.67% 11.53% (equal weights) (equal weights) Incremental b. To raise $60,000,000 Debt Market Debt Cost Equity Market Equity Cost WACC First $40,000,000 European 6.00% Domestic 12.00% 7.80% Additional $20,000,000 European 10.00% European 16.00% 11.00% Weighted average cost 7.33% 13.33% 8.87% (2/3 & 1/3 weights) (2/3 & 1/3 weights) Problem 11.4 Tata's cost of capital Tata is the largest and most successful specialty goods company based in India. It has not entered the North American marketplace yet, but is considering establishing both manufacturing and distribution facilities in the United States through a wholly owned subsidiary. It has approached two different investment banking advisors, Goldman Sachs and Bank of New York, for estimates of what its costs of capital would be several years into the future when it planned to list its American subsidiary on a U.S. stock exchange. Using the following assumptions by the two different advisors, calculate the prospective costs of debt, equity, and the WACC for Tata U.S. Assumptions Symbol Goldman Sachs Bank of New York Components of beta: β Estimate of correlation between security and market ρjm 0.90 0.85 Estimate of standard deviation of Tata's returns σj 24.0% 30.0% Estimate of standard deviation of market's return σm 18.0% 22.0% Risk-free rate of interest krf 3.0% 3.0% Estimate of Tata's cost of debt in US market kd 7.5% 7.8% Estimate of market return, forward-looking km 9.0% 12.0% Corporate tax rate t 35.0% 35.0% Proportion of debt D/V 35% 40% Proportion of equity E/V 65% 60% Estimating Costs of Capital Estimated beta β = ( ρjm x σj ) / ( σm ) β 1.20 1.16 Estimated cost of equity ke = krf + (km - krf) β ke 10.200% 13.432% Estimated cost of debt kd ( 1 - t ) kd (1-t) 4.875% 5.070% Estimated weighted average cost of capital WACC = (ke x E/V) + ( (kd x (1-t)) x D/V) WACC 8.336% 10.087% Problem 11.5 Country Equity Risk Premiums Using the century of equity market data presented in Exhibit 11.3, answer the following questions: a. Which country had the largest differential between the arithmetic mean and geometric mean? b. If a Swiss firm were attempting to calculate its cost of equity using this data, assuming a risk- free rate of 2.0% and a security beta of 1.4, what would be its estimated cost of equity using both the arithmetic mean and geometric means for the equity risk premium? Arithmetic Mean Geometric Mean Country Risk Premium Risk Premium Differential Australia 8.0% 6.3% 1.7% Belgium 4.8% 2.9% 1.9% Canada 6.0% 4.5% 1.5% Denmark 3.3% 2.0% 1.3% France 7.0% 4.9% 2.1% Germany 9.9% 6.7% 3.2% Ireland 4.5% 3.2% 1.3% Italy 8.4% 5.0% 3.4% Japan 10.3% 6.2% 4.1% Netherlands 6.7% 4.7% 2.0% South Africa 7.1% 5.4% 1.7% Spain 4.2% 2.3% 1.9% Sweden 7.4% 5.2% 2.2% Switzerland 4.2% 2.7% 1.5% United Kingdom 5.6% 4.4% 1.2% United States 7.0% 5.0% 2.0% World 5.6% 4.9% 0.7% a) Japan demonstrates the largest differential between the arithmethic mean and geometric mean; a full 4.1%. b) A Swiss firm estimating its cost of equity using the capital asset pricing model, would find the cost of equity as: ke = krf + ( km - krf ) β where ( km - krf ) is the risk premium Arithmetic Geometric Risk-free rate 2.00% 2.00% Risk premium 4.20% 2.70% beta 1.40 1.40 Cost of equity 7.88% 5.78% Problem 11.6 Cargill's cost of capital Cargill is generally considered to be the largest privately held company in the world. Headquartered in Minneapolis, Minnesota, the company has been averaging sales of over $50 billion per year over the past 5 year period. Although the company does not have publicly traded shares, it is still extremely important for it to calculate its weighted average cost of capital properly in order to make rational decisions on new investment proposals. Assuming a risk-free rate of 2.50%, an effective tax rate of 40%, and a market risk premium of 5.50%, estimate the weighted average cost of capital first for companies A and B, and then make a „guestimate‟ of what you believe a comparable WACC would be for Cargill. Comparables Assumptions Symbol Company A Company B Cargill Total sales Sales $4.5 billion $26 billion $50 billion Company's beta β 0.86 0.78 0.90 Company credit rating S&P AA A AA Risk-free rate of interest krf 2.5% 2.5% 2.5% Market risk premium km-krf 5.5% 5.5% 5.5% Weighted average cost of debt kd 6.885% 7.125% 6.820% Corporate tax rate t 40.0% 40.0% 40.0% Debt to total capital ratio D/V 34% 41% 28% Equity to total capital ratio E/V 66% 59% 72% International sales as % of total sales 12% 26% 45% Estimating Costs of Capital Symbol Company A Company B Cargill Cost of equity ke = krf + (km - krf) β ke 7.230% 6.790% 7.450% Cost of debt, after-tax kd ( 1 - t ) 4.131% 4.275% 4.092% Weighted average cost of capital WACC 6.176% 5.759% 6.510% WACC = (ke x E/V) + ( (kd x (1-t)) x D/V) Once the data is organized, the absence of a beta for Cargill is the obvious data deficiency. A series of observations is then helpful: 1. Note that beta and credit ratings do not necessarily parallel one another 2. Credit rating and cost of debt do follow expected norms; lower the rating, the higher the cost 3. Both comparable companies, in the same industry as Cargill (commodities), possess relatively low betas 4. Cargill's sales are twice that of the next largest firm 5. Cargill's sales are significantly more internationally diversified than either of the other two companies; the question is whether this is a positive or negative factor for the estimation of Cargill's cost of equity? If we take the approach that the beta for Cargill has to pick up all the incremental information, the beta would then fall between say 0.80 and 1.00. If the higher degree of international sales was interpreted as increasing risk, beta would be on the higher end; yet being a commodity firm in the current market, its beta would rarely surpass 1.0. A value of 0.90 is shown here giving a WACC of 6.510%. A series of sensitivities would find a WACC between 6.1% and 6.9%. Problem 11.7 The Tombs You have joined your friends at the local watering hole, The Tombs, for your weekly debate on international finance. The topic this week is whether the cost of equity can ever be cheaper than the cost of debt. The group has chosen Brazil in the mid-1990s as the subject of the debate. One of the group members has torn the following table of data out of Chapter 5 of this book, which is then the subject of the analysis. Larry argues that “its all about expected versus delivered. You can talk about what equity investors expect, but they often find that what is delivered for years at a time is so small – even sometimes negative – that in effect the cost of equity is cheaper than the cost of debt.” Mohammed – he goes by Mo – interrupts: “But you‟re missing the point. The cost of capital is what the investor requires in compensation for the risk taken going into the investment. If he doesn‟t end up getting it, and that was happening here, then he pulls his capital out and walks.” Curly is the theoretician. “Ladies, this is not about empirical results; it is about the fundamental concept of risk-adjusted returns. An investor in equities knows he will reap returns only after all compensation has been made to debt-providers. He is therefore always subject to a higher level of risk to his return than debt instruments, and as the capital asset pricing model states, equity investors set their expected returns as a risk-adjusted factor over and above the returns to risk-free instruments.” At this point both Larry and Mo simply stared at Curly, paused, and both ordered another beer. Using the Brazilian data presented, comment on this week‟s debate at the Tombs. Brazilian Economic Performance 1995 1996 1997 1998 1999 Mean Inflation rate (IPC) 23.20% 10.00% 4.80% -1.00% 10.50% 9.50% Bank lending rate 53.10% 27.10% 24.70% 29.20% 30.70% 32.96% Exchange rate (reais/$) 0.972 1.039 1.117 1.207 1.700 120.7% Equity returns (Sao Paulo Bovespa) 16.0% 28.0% 30.2% -33.5% 151.9% 38.52% All three are on the right track. It is mostly a matter of finding the linkages beween their individual arguments. 1. Theoretically, Curly is correct in that CAPM assumes that all equity returns are over and above risk-free rates. These are of course, expected returns, and are the investor's expectations or requirements going INTO the investment. 2. Mo is also correct in arguing that regardless of what investors may EXPECT, the results are often quite different, sometimes disappointing. Theoretically, when the investment does not yield at least the expected return, the investor should indeed liquidate their position. However, in reality, many investors for a variety of reasons (tax implications, investment horizon, etc.), may stay in the investment and just complain about the past and hope about the future. 3. Larry also is on the right track arguing that actual market returns will often result in less than various interest or debt instruments. One of the more helpful arguments here is that equity returns and interest returns arise from very different economic and financial processes. Most interest rate charges are stated and contracted for up-front, and represent lenders' perception of an adequate risk-adjusted return over the expected rate of inflation for the coming period. Equity returns, however, are that mystical process of equity markets in which the many different reasons of equity investors combine to move markets in sometimes mysterious ways, independent of interest rates, inflation rates, or any other fundamental money price. Problem 11.8 Sushmita-Chen's cost of equity Use the following information to answer questions 8 through 10. Sushmita-Chen is an American conglomerate which is actively debating the impacts of international diversification of its operations on its capital structure and cost of capital. The firm is planning on reducing consolidated debt after diversification. Senior management at Sushmita-Chen is actively debating the implications of diversification on its cost of equity. Although both parties agree that the company‟s returns will be less correlated with the reference market return in the future, the financial advisors believe that the market will assess an additional 3.0% risk premium for „going international‟ to the basic CAPM cost of equity. Calculate Sushmita-Chen‟s cost of equity before and after international diversification of its operations, with and without the hypothetical additional risk premium, and comment on the discussion. Before After Assumptions Symbol Diversification Diversification Correlation between S-C and the market ρjm 0.88 0.76 Standard deviation of S-C's returns σj 28.0% 26.0% Standard deviation of market's returns σm 18.0% 18.0% Risk-free rate of interest krf 3.0% 3.0% Additional equity risk premium for internationalization RPM 0.0% 3.0% Estimate of Tata's cost of debt in US market kd 7.2% 7.0% Market risk premium km-krf 5.5% 5.5% Corporate tax rate t 35.0% 35.0% Proportion of debt D/V 38% 32% Proportion of equity E/V 62% 68% Estimating Costs of Capital Estimated beta β = ( ρjm x σj ) / ( σm ) β 1.37 1.10 Estimated cost of equity ke = krf + (km - krf) β ke 10.529% 9.038% Estimated cost of equity with additional risk premium ke* = krf + (km - krf) β + RPM ke + RPM 10.529% 12.038% This may be a case where everyone is correct. When Sushmita-Chen's beta is recalculated, it falls in value as a result of the reduced correlation of its returns with the home market (diversification benefit). This then creates a standard cost of equity which is cheaper at 9.038% (previous cost of equity was 10.529%). If, however, the market was to add an additional risk premium to the firm's cost of equity as a result of internationally diversifying operations, and if that risk premium were on the order of 3.0%, the final risk-adjusted cost of equity is indeed higher, 12.038% to the before value of 10.529%. Problem 11.9 Sushmita-Chen's WACC Calculate the weighted average cost of capital for Sushmita-Chen for before and after international diversification. a. Did the reduction in debt costs reduce the firm‟s weighted average cost of capital? How would you describe the impact of international diversification on its costs of capital? b. Adding the hypothetical risk premium to the cost of equity introduced in question 8 (an added 3.0% to the cost of equity because of international diversification), what is the firm‟s WACC? Before After Assumptions Symbol Diversification Diversification Correlation between S-C and the market ρjm 0.88 0.76 Standard deviation of S-C's returns σj 28.0% 26.0% Standard deviation of market's returns σm 18.0% 18.0% Risk-free rate of interest krf 3.0% 3.0% Additional equity risk premium for internationalization RPM 0.0% 3.0% Estimate of Tata's cost of debt in US market kd 7.2% 7.0% Market risk premium km-krf 5.5% 5.5% Corporate tax rate t 35.0% 35.0% Proportion of debt D/V 38% 32% Proportion of equity E/V 62% 68% Before After Estimating Costs of Capital Diversification Diversification Estimated beta β = ( ρjm x σj ) / ( σm ) β 1.37 1.10 Estimated cost of equity ke = krf + (km - krf) β ke 10.529% 9.038% Estimated cost of equity with additional risk premium ke* = krf + (km - krf) β + RPM ke + RPM 10.529% 12.038% Cost of debt, after-tax kd (1-t) kd ( 1 - t ) 4.680% 4.550% Weighted average cost of capital WACC WACC = (ke x E/V) + ( (kd x (1-t)) x D/V) 8.306% 7.602% Weighted average cost of capital with RPM WACC* WACC = (ke* x E/V) + ( (kd x (1-t)) x D/V) 8.306% 9.642% There are a number of different factors at work here. First, as a result of international diversification, their access to debt has improved, resulting in a lower cost of debt capital. This is not fully appreciated, however, as the firm has chosen to reduce its overall use of debt post-diversification (common among MNEs). The firm's WACC does indeed drop for the standardized case. If, however, the market assesses an additional equity risk premium of 3.0%, the benefits are swamped by the higher required return on equity by the market. Problem 11.10 Sushmita-Chen's WACC and effective tax rate Many MNEs have greater ability to control and reduce their effective tax rates when expanding international operations. If Sushmita- Chen was able to reduce its consolidated effective tax rate from 35% to 32%, what would be the impact on its WACC? Before After Assumptions Symbol Diversification Diversification Correlation between S-C and the market ρjm 0.88 0.76 Standard deviation of S-C's returns σj 28.0% 26.0% Standard deviation of market's returns σm 18.0% 18.0% Risk-free rate of interest krf 3.0% 3.0% Additional equity risk premium for internationalization RPM 0.0% 3.0% Estimate of Tata's cost of debt in US market kd 7.2% 7.0% Market risk premium km-krf 5.5% 5.5% Corporate tax rate t 35.0% 32.0% Proportion of debt D/V 38% 32% Proportion of equity E/V 62% 68% Before After Estimating Costs of Capital Diversification Diversification Estimated beta β = ( ρjm x σj ) / ( σm ) β 1.37 1.10 Estimated cost of equity ke = krf + (km - krf) β ke 10.529% 9.038% Estimated cost of equity with additional risk premium ke* = krf + (km - krf) β + RPM ke + RPM 10.529% 12.038% Cost of debt, after-tax kd (1-t) kd ( 1 - t ) 4.680% 4.760% Weighted average cost of capital WACC WACC = (ke x E/V) + ( (kd x (1-t)) x D/V) 8.306% 7.669% Weighted average cost of capital with RPM WACC* WACC = (ke* x E/V) + ( (kd x (1-t)) x D/V) 8.306% 9.709% The reduction in the effective tax rate obviously impacts WACC through the cost of debt. This does have substantial benefits in the company's WACC -- as long as additional equity risk premiums are not assessed. Then, even the lower effective tax rate does not offset the higher equity costs associated with the international risk premium. Problem 11.11. JPMorgan: Petrobras's WACC JPMorgan‟s Latin American Equity Research department produced the following WACC calculation for Petrobras of Brazil versus Lukoil of Russia in their June 18, 2004 report. Evalue the methodology and assumptions used in the calculation. Assume a 28% tax rate for both companies. Petrobras Lukoil Capital Cost Components (Brazil) (Russia) Risk Free Rate 4.800% 4.800% Sovereign Risk 7.000% 3.000% Equity Risk Premium 4.500% 5.700% Market Cost of Equity 16.300% 13.500% Beta (relevered) 0.87 1.04 Cost of equity 18.981% 18.840% Cost of Debt 8.400% 6.800% Tax rate 28.000% 28.000% Cost of debt, after-tax 6.048% 4.896% Debt/Capital ratio 33.300% 47.000% Equity/Capital ratio 66.700% 53.000% WACC (calculated) 14.674% 12.286% WACC (I-Bank report) 14.700% 12.300% This approach applies the sovereign risk premium to the cost of equity for both companies, but not to their cost of debt. Since the comparison is for two oil companies from two different countries, and the same risk free rate is used for both, it is implied, though not stated, that the WACC calculation is based in US dollars. Source: "Petrobras: A Diamond in the Rough," JP Morgan, Latin American Equity Research, June 18, 2004, p. 24. Problem 11-12. UNIBANCO: Petrobras's WACC UNIBANCO estimated the weighted average cost of capital for Petrobrás to be 13.2% in Brazilian reais in August of 2004. Evaluate the methodology and assumptions used in the calculation. Capital Cost Components 2004 Risk Free Rate 4.500% Levered Beta 0.99 Risk Premium 6.000% Country Risk Premium 5.500% Cost of equity (US$) 15.940% Exchange Rate 2.000% Cost of equity (R$) 18.259% Cost of Debt 8.600% Tax rate 34.000% Cost of debt, after-tax (R$) 5.676% Debt/Capital ratio 40.000% Equity/Capital ratio 60.000% WACC (R$) calculated 13.2% WACC (R$) (I-bank report) 13.2% This calculation adds the country risk premium to the risk free rate in the cost of equity, but not the cost of debt (as was the case in the previous problem). This cost of equity in US$, however, is then compounded by a percentage change in the expected exchange rate of the reais against the dollar to arrive at a cost of equity in reais. The cost of debt, which indicates reais-denomination, is not adjusted for the country risk premium or the expected currency movement. Source: "Petrobras: Reinitiation of Coverage," UNIBANCO, August 12, 2004, p.4. Problem 11-13. Citigroup SmithBarney (dollar): Petrobras's WACC Citigroup regularly performs a U.S. dollar-based discount cash flow (DCF) valuation of Petrobrás in its coverage. That DCF analysis requires the use of a discount rate which they base on the company's weighted average cost of capital. Evaluate the methodology and assumptions used in the 2003 Actual and 2004 Estimates of Petrobras's WACC below. July 28, 2005 March 8, 2005 Capital Cost Components 2003A 2004E 2003A 2004E Risk free rate 9.400% 9.400% 9.000% 9.000% Levered Beta 1.07 1.09 1.08 1.10 Risk Premium 5.500% 5.500% 5.500% 5.500% Cost of equity 15.285% 15.395% 14.940% 15.050% Cost of debt 8.400% 8.400% 9.000% 9.000% Tax rate 28.500% 27.100% 28.500% 27.100% Cost of debt, after-tax 6.006% 6.124% 6.435% 6.561% Debt/capital ratio 32.700% 32.400% 32.700% 32.400% Equity/capital ratio 67.300% 67.600% 67.300% 67.600% WACC (calculated) 12.25% 12.39% 12.16% 12.30% WACC (I-bank report) 12.2% 12.3% 12.1% 12.3% This approach uses a relatively high assumed value for the risk free rate of interest in the cost of equity calculation, without expressly charging the company a country risk premium. Since the U.S. dollar risk-free rate at this time was somewhere around 4%, this risk-free rate must implicitly include a country risk premium. The cost of debt, before-tax, is actually below the risk- free rate, which is difficult to understand or rationalize. Source: "Petrobras," Citigroup SmithBarney, March 8, 2005, and July 28, 2005. Problem 11-14. Citigroup SmithBarney (reais) In a report dated June 17, 2003, Citigroup SmithBarney calculated a WACC for Petrobrás denominated in Brazilian reais (R$). Evaluate the methodology and assumptions used in this cost of capital calculation. Petrobras Cost of Equity June 2003 Risk-free rate (Brazilian C-Bond) 9.90% Petrobras levered beta (β) 1.40 Market risk premium 5.50% Cost of equity 17.60% Petrobras Cost of Debt Petrobras cost of debt 10.00% Brazilian corporate tax rate 34.00% Cost of debt, after-tax 6.60% WACC Calculation (in R$) Petrobras cost of debt, after-tax 6.60% Long-term debt ratio (% of capital) 50.60% Petrobras cost of equity 17.60% Long-term equity ratio (% of capital) 49.40% WACC (calculated) 12.03% WACC (I-bank report) 12.00% Identifying the risk-free rate as the Braizilian C-Bond rate, and using a relatively high value of beta compared to other analyst estimates, the cost of equity is relatively high. The cost of debt, also high compared to the other estimates, results in a final WACC calculation, in Brazilian reais, which is similar in value to other estimates. Source: "Petroleo Brasileiro S.A.,Citigroup Smith Barney, June 17, 2003, p.17. Problem 11.15. BBVA Investment Bank: Petrobras's WACC BBVA utilized a rather innovative approach to dealing with both country and currency risk in their December 20, 2004 report on Petrobras. Evaluate the methodology and assumptions used in this cost of capital calculation. Cost of Capital Component 2003 Estimate 2004 Estimate US 10-year risk-free rate (in US$) 4.10% 4.40% Country risk premium (in US$) 6.00% 4.00% Petrobras premium "adjustment" 1 -1.00% -1.00% Petrobras risk-free rate (in US$) 9.10% 7.40% Petrobras Cost of Equity Petrobras risk-free rate (in US$) 9.10% 7.40% Petrobras beta (β) 0.80 0.80 Market risk premium (in US$) 6.00% 6.00% Cost of equity (in US$) 2 13.90% 12.20% Projected 10-year currency devaluation 2.50% 2.00% Cost of equity (in R$) 3 16.75% 14.44% Petrobras Cost of Debt Petrobras cost of debt (in R$) 8.50% 8.50% Brazilian corporate tax rate 35.00% 35.00% Cost of debt, after-tax (in US$) 5.53% 5.53% WACC Calculation (in R$) Petrobras cost of debt, after-tax 5.53% 5.53% Long-term debt ratio (% of capital) 31.00% 28.00% Petrobras cost of equity 16.75% 14.44% Long-term equity ratio (% of capital) 69.00% 72.00% WACC (calculated) 13.27% 11.95% WACC (I-Bank report) 13.30% 12.00% This analysis clearly begins with a U.S. dollar-based risk-free rate, 4.1% and 4.4%, adds a country risk premium to it, and then adjusts the sum downward for a Petrobras premium. The Petrobras premium is the analyst's opinion that Petrobras is an oil and gas company, and therefore operates in a global dollar market which is in many ways less risky than a pure-play on a Brazilian firm. The resulting cost of equity is then converted from reais to dollars with the application of a currency devaluation multiplier, a stated average expectation for the coming decade.The cost of debt assumed is very low -- 5.53% -- which is clearly a dollar cost and not a reais cost as stated. The final WACC in reais terms is roughly equivalent to the various estimates from the previous problems. Notes: 1 Petrobras premium adjustment is the reduction in country risk given an oil and gas company operating in a global industry which operates in a market of US dollar denominated returns. 2 Cost of equity in US$ = risk free rate + ( beta x market risk premium ) 3 Cost of equity in R$ = [ (1 + cost of equity in US$) x (1 + projected devaluation) ] - 1 Source: "Petrobras," BBVA Securities, Latin American Research, December 20, 2004, p. 7. Problem 11.16. Petrobras's WACC Comparison The various estimates of the cost of capital for Petrobras of Brazil appear to be very different, but are they? Reorganize your answers to the previous five prolbems into those costs of capital which are in U.S. dollars versus Brazilian reais. Use the estimates for 2004 as the basis of comparison. U.S. dollar WACCs Brazilian reais WACCs JPMorgan Citigroup ($) UNIBANCO Citigroup (R$) BBVA Capital Cost Components (June 18, 2004) (March 8, 2005) (Aug 12, 2004) (June 17, 2003) (Dec 20, 2004) Risk Free Rate 4.800% 9.400% 4.500% 9.900% 4.400% Sovereign/Country Risk Premium 7.000% 0.000% 5.500% 0.000% 4.000% Petrobras Company Premium 0.000% 0.000% 0.000% 0.000% -1.000% "Adjusted" Risk Free Rate 11.800% 9.400% 10.000% 9.900% 7.400% Levered Beta 0.87 1.09 0.99 1.40 0.80 Market/Equity Risk Premium 4.500% 5.500% 6.000% 5.500% 6.000% Cost of equity (US$) 18.981% 15.395% 15.940% 17.600% 12.200% Exchange Rate 2.000% 0.000% 2.000% Cost of equity (R$) 18.259% 17.600% 14.444% Cost of Debt 8.400% 8.400% 8.600% 10.000% 8.500% Tax rate 28.000% 27.100% 34.000% 34.000% 35.000% Cost of debt, after-tax 6.048% 6.124% 5.676% 6.600% 5.525% Debt/Capital ratio 33.300% 32.400% 40.000% 50.600% 28.000% Equity/Capital ratio 66.700% 67.600% 60.000% 49.400% 72.000% WACC (calculated) 14.7% 12.4% 13.2% 12.0% 11.9% WACC (I-bank report) 14.7% 12.3% 13.2% 12.0% 12.0%