# Case Study Analysis & Examples Worksheet by SupremeLord

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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
Australia                                8.0%                     6.3%                       1.7%
Belgium                                  4.8%                     2.9%                       1.9%
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%
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

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

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%
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%

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%
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%

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%
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%

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%
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
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
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 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%

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