See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/228302611
The WACC User's Guide
Article in SSRN Electronic Journal · April 2005
DOI: 10.2139/ssrn.683313
CITATIONS
READS
0
4,308
1 author:
Justin Pettit
IHS Markit
48 PUBLICATIONS 311 CITATIONS
SEE PROFILE
Some of the authors of this publication are also working on these related projects:
Ten reasons to update your E&P operating model View project
The Final Frontier: E&P's Low-Cost Operating Model View project
All content following this page was uploaded by Justin Pettit on 15 December 2018.
The user has requested enhancement of the downloaded file.
March 2005
Investment
Banking
The WACC
User's Guide
The estimation of corporate capital costs is complicated
by many practical issues that create numerous degrees
of freedom and lead to wide-ranging results. We provide
pragmatic solutions including:
A global market risk premium (MRP) of about 5%, based on historical
data, market expectations, and a review of the literature
Several methods to derive reliable beta estimates including direct
regressions, portfolio regressions, and constructed betas
A "normalized" nominal riskless rate of about 5%, based on forward
looking market data
A value of tax shield framework that implies lower value and higher
WACCs for more leveraged or volatile situations
Justin Pettit
Executive Director
Head of Strategic Advisory
1-212-821-6315
Justin.Pettit@ubs.com
Azad Badakhsh
Analyst
Strategic Advisory Group
1-212-821-2135
Azad.Badakhsh@ubs.com
Marc Klein
Analyst
Strategic Advisory Group
1-212-821-5189
Marc.Klein@ubs.com
The WACC of a convertible bond, based on its economic decomposition
of debt and equity
A framework for global capital costs to supplement the risk analysis and
qualitative considerations involved in global investing where risks are
subject to rapid change … other international risks and costs should be
incorporated into the cash flows and sensitivity analysis
Based in part on previously published research of one of the authors, Justin Pettit, "Corporate Capital
Costs: A Practitioners Guide," Journal of Applied Corporate Finance. Vol 12 Number 1 (Spring 1999) and
Justin Pettit, Mack Ferguson and Robert Gluck, "A Method for Estimating Global Corporate Capital Costs:
The Case of Bestfoods" The Journal of Applied Corporate Finance. Vol 12 Number 3 (Fall 1999)
THE WACC USER'S GUIDE
Contents
OVERVIEW
1
WHAT DO INVESTORS REALLY EXPECT?
2
TOWARD A BETTER BETA
6
THE "RISKLESS" RATE
8
COST OF DEBT
9
CAPITAL COSTS & THE GLOBAL PORTFOLIO
11
APPENDIX A – COST OF CAPITAL BY INDUSTRY AND SUB-INDUSTRY
18
APPENDIX B – COST OF CAPITAL BY COUNTRY
19
BIBLIOGRAPHY
20
LIST OF TABLES
21
LIST OF FIGURES
21
STRATEGIC ADVISORY GROUP PUBLICATIONS
21
THE WACC USER'S GUIDE
OVERVIEW
A critical input for
evaluating both
investments and
operating
performance
Perceived CAPM
limitations arise
from application
challenges
The weighted average cost of capital (WACC) is a critical input for evaluating
investment decisions - it is typically the discount rate for net present value (NPV)
calculations.1 And it serves as the benchmark for operating performance, relative
to the opportunity cost of capital employed, to create value.2
We focus on issues that arise when calculating the cost of capital. While there have
been challenges to the Capital Asset Pricing Model (CAPM), it remains the most
practical approach to determine a cost of equity. In fact, many perceived limitations
arise from challenges in applying the model. We draw on our research and experience
to provide suggestions to deal with two of the primary difficulties in applying CAPM:
(1) estimating the market risk premium (MRP) for equities; and (2) measuring the
systematic risk, or “beta,” of a company.
We estimate the MRP at about 5%, based on both historical data and forward
looking market data. We provide tools for deriving more reliable estimates of beta,
especially helpful for business units and unlisted companies, but also illiquid stocks
with unreliable betas. Direct regression is the most commonly used approach but
we also employ alternative methodologies such as constructed betas, portfolio betas,
segment regression betas and multi-variable regression betas. We also "normalize"
the riskless rate with a forward view of the capital markets. Table 1 illustrates our
WACC estimates for several sectors.
Table 1 – Cost of Capital By Industry
Power
BBB+ BBB-
A-
A-
BBB+
AA-
BBB+
A-
Credit Spread
1.0
1.2
0.8
0.8
1.0
1.0
1.0
0.6
1.0
0.8
Cost of Debt
5.2
5.4
5.0
5.0
5.2
5.2
5.2
4.8
5.2
5.0
Tax Rate
36
36
36
36
36
36
36
36
36
36
Expected Value
81
81
91
90
86
88
95
97
97
97
A/T Cost of Debt (%)
3.7
3.8
3.4
3.4
3.6
3.6
3.4
3.1
3.4
3.3
% of Enterprise Value
44
43
23
27
34
29
15
10
10
8
5
5
5
5
5
5
5
5
5
5
0.33 0.40
0.64
0.69
0.81
0.79
0.86
0.85
1.01
1.44
0.49 0.60
5
5
7.5 8.0
57
56
0.76
5
8.8
77
0.86
5
9.3
73
1.08
5
10.4
66
1.00
5
10.0
71
0.96
5
9.8
85
0.91
5
9.6
90
1.08
5
10.4
90
1.53
5
12.6
92
WACC (%)
5.8 6.2
7.6
7.7
8.1
8.1
8.8
SOURCE: UBS Investment Bank, Public Filings, Compustat Bloomberg (March ’05)
8.9
9.7
11.9
Industry Rating
Riskless Rate
Asset Beta
Levered Beta
Market Risk Premium
Cost of Equity (%)
% of Enterprise Value
Global corporate
capital costs
capture both
sovereign and
inflation risk
Real Consumer Energy Telecom Industrials Media
Financials Healthcare Technology
Estate
Institutions3
BBB+ BBB+
Our approach to global corporate capital costs quantifies and captures both
sovereign risk and inflation risk. However, we do recommend that cash flows be
adjusted for the costs and unsystematic risks of global investing, coupled with a
more rigorous risk analysis. Given the many opportunities for profitable growth
abroad, more reliable estimates of global capital costs can help ensure that
companies will choose to undertake investments that show promise to add value.
1
2
3
WACC is a market weighted average, at target leverage, of the cost of after tax debt and equity. Financing
events per se may not reflect changes in financial policy and may not be permanent changes to the capital
structure. Temporary fluctuations in the mix should not affect WACC. We estimate the cost of equity = Rf +
beta x MRP, Rf is the riskless return, Market Risk Premium (MRP) is the expected return premium for bearing
equity market risk over the riskless rate, and beta is the systematic risk of the business relative to the market.
Pettit, Justin, and Alisdairi, M.K., “How to Find Your Economic Profits,” UBS Investment Bank, January 2004.
The WACC for financial institutions is (generally) simply the cost of equity, as most debt is “funding debt” (not
financing debt) and should be expensed (not capitalized) where the cost of funds is a “cost of goods sold.”
1
THE WACC USER'S GUIDE
WHAT DO INVESTORS REALLY EXPECT?
The return
premium of stocks
over bonds ranges
from 3% to 8%
The return premium afforded by stocks over long government bonds (i.e. market
risk premium) is generally believed to be anywhere from 3% to 8%. The widely
cited Ibbotson and Sinquefeld study (generally 7-8%), is based on the U.S.
arithmetic mean from 1926. It's not that 1926 was an important year in
econometric history - this is just when the market tapes started to be archived.
If the study started either one year earlier, or one year later, the risk premium would
change by a full percentage point. Other U.S. studies (employing manual data
retrieval) do go back much further (to when the market was largely railroad stocks)
and provide estimates closer to the low end of the range.4 Some studies rely on
more recent history and this again leads to the lower end of the range.
Structural
economic change
over the century
makes the early
data less relevant
Provided the data represent a “random walk” and there are no discernible trends
up or down, more observations will lead to greater predictive accuracy. However,
structural economic changes over the past century make the early data much less
relevant for estimating expected returns today. Macroeconomic factors have
conspired such that, in our opinion, a shorter history is more appropriate.
Based on both the arithmetic average of annualized monthly return premiums, and
forward looking multiples, stock market investors now expect about a 5% premium
for bearing the market risk of equities. The risk of holding equities has generally
declined while at the same time the risk of investing in government bonds has
increased - reducing the premium between these two security classes.5
Converging Volatilities and Returns
The volatility of stock returns versus bond returns has decreased. As shown in
Figure 1, the trailing average standard deviation of annualized monthly stock
returns fell from 25% in the 1950s to about 16% in 2004. During that period,
the standard deviation of bond returns increased from 4% to almost 12%.6
Figure 1 – Converging Volatilities – Stocks and the Long Bond
30-Yr. Trailing Standard
Deviation of Returns (%)
Volatility of stock
returns has been
falling and the
volatility of bond
returns rising
Stock Volatility
30
25
20
15
10
5
0
1959
1964
1969
1974
1979
Long Bond Volatility
1984
1989
1994
1999
2004
SOURCE: SBBI Handbook, Compustat, Bloomberg (March ’05)
Consistent with changes in relative volatility over the past century, the premium
investors received for stocks relative to bonds fell from over 10% to about 5%.
This drop in the risk premium was attributable not only to a reduction in the level
of stock market risk, but also to an increase in real required returns on bonds.
4
5
6
In “The Shrinking Equity Premium,” Jeremy Siegel estimates the equity premium over U.S. government bonds
for the period 1802-1998 to be between 3.5% and 4.7% (using geometric and arithmetic means, respectively).
The study is based on monthly returns on the S&P 500 index (which included only 90 stocks before 1957) and on
US Treasury long bonds, from 1926 through 2004. We reran the study using a value-weighted index that included
all NYSE, AMEX and NASDAQ stocks as a market proxy. Because the results were not materially different from
the ones using S&P 500 data, and since S&P 500 returns are easier for practitioners to access, we recommend
using the S&P 500 index as a market proxy.
In our study, we used all available historical returns from 1926 through 2004. Because we used 30 years of data
to calculate the trailing averages, the graphs begin in 1958. The same trends emerge when using 10- and 20year averaging periods instead of 30 years.
2
THE WACC USER'S GUIDE
What Has Changed?
Several factors contribute to support the notion that earlier history may be less
relevant to the ex post derivation of expected equity returns. We have documented
the impact in our charts and speak to the possible causes below:
Prudent monetary
policies have
reduced business
cycle volatility
More liquidity, less
net volatility
Regulation & Public Policy. Prudent monetary policies of the Federal Reserve
and its foreign counterparts, as well as the general liberalization of regulatory
policies, appear to have reduced the volatility of business cycles. 7 Liberalization
of developing economies, establishment of trading blocks, and the increase of
international trade have all contributed to global economic growth and stability,
despite tremendous political change and upheaval.
Growth & Globalization. Growth in worldwide market capitalization affords more
liquidity, less net volatility, and less net risk. The growth of emerging markets helps
to buffer the down cycles of developed economies. Emerging markets also help
drive developed economies to invest further in human and technical capital. Emerging
market volatility is often, in turn, buttressed by the developed markets. Although
claims of a borderless global economy are overstated, there is a reduced sensitivity
to the economics of any single nation, which reduces systematic risk.
Risk is isolated,
traded, syndicated
and managed
Market Sophistication. Despite claims to the contrary, the proliferation of risk
management products (interest rate, f/x, commodity, and equity) has increased the
liquidity of risk, allowing it to be isolated, traded, syndicated and managed. Most
individuals invest in the market through funds and institutions leading to an
increased sophistication and change in the nature of our equity markets.
More immediate
and comprehensive
disclosure
Information & Technology. Despite recent accounting scandals, disclosure is
more immediate and comprehensive, reducing uncertainty and required returns.
Notwithstanding Regulation FD, segment data, reporting requirements, and analyst
coverage are all more extensive and of higher quality today than 50 years ago. And
technology has reduced the price and raised the quality of information processing.
Mobile, marketable
knowledge
workers lower
fixed costs
Labor Mobility. The nature of employment has changed. Tremendous growth
in the service sector allows service and manufacturing cycles to be somewhat
offsetting. Service economies also have less fixed costs and are thus less susceptible
to pricing pressures in times of over-capacity. The trend toward mobile, marketable
knowledge workers helps reduce fixed costs and improve resource allocation.
Institutional
investors are more
active
Agency Costs. Large institutional investors today are much more active in
influencing companies to maximize shareholder value, which reduces the risk of
common stock. This force is supported by the success of LBOs and the widespread
adoption of value-based management. The importance of agency costs and
ownership concentration in improving corporate performance are well documented.
7
In “The End of the Business Cycle” (Foreign Affairs, Volume 76 Number 4 (July/August 1997), Steven Weber of
University of California at Berkeley makes a strong case for fundamental structural economic and capital market
changes making observations of events in US history less representative of responses in the future.
3
THE WACC USER'S GUIDE
How Much History?
Consistent with changes over the past century, the premium investors received for
stocks relative to bonds (Figure 2) fell from over 10% to about 5%. With such a
clear trend in the data toward lower equity premiums it would be a mistake to go
too far back in time when estimating the market risk premium.
Figure 2– Declining Market Risk Premium
Trailing MRP Over
Long Bonds (%)
The premium
investors received
for stocks relative
to bonds fell from
over 10% to 5%
25
20
15
10
5
0
-5
1958
10 Year Rolling Average
1964
1970
20 Year Rolling Average
1975
1981
1987
30 Year Rolling Average
1993
1998
2004
SOURCE: SBBI Handbook, Compustat, Bloomberg (March ’05)
The estimate of the market risk premium (Figure 3) depends on how much history is
used. Indeed, one could almost justify any premium. The far left observation on the
graph uses only returns for 2004 (-5%). Moving right adds more history. The
estimate at the extreme right uses all 78 years of available history (+7%).
Stock Returns Less
Bond Returns (%)
Figure 3 – Market Risk Premium Depends on How Much History
10
5
0
-5
-10
0
10
20
30
40
50
60
70
Years of History
SOURCE: SBBI Handbook, Compustat, Bloomberg (March ’05)
Structural changes in the economy and markets may suggest that more recent data
provide a better basis for predicting the future. Provided you choose a period that
goes back at least as far as the early 1980s, it is clear that the market risk premium
has drifted down. The question that one must answer is: How far down, and can we
expect it to cycle back up? We have chosen to use the second part of the past
century (instead of ¾), a sufficiently long period to achieve statistical reliability, while
avoiding the potentially less relevant early market returns. Consequently, we
estimate the market risk premium over the long bond to be about 5%.
International
studies provide
similar results
A Global Risk Premium?
Several recent international studies have provided similar results - yielding estimates
of the market risk premium in the vicinity of 5%.8 Most market studies from other
countries also tend to draw on shorter histories - their earlier data is often
unavailable, unreliable, or irrelevant due to significant changes in exchange controls
and monetary policy. Foreign market derivations of market risk premiums are often
undermined by unreliable historical information, irrelevant history and liquidity
issues, making the analysis and its conclusions suspect both for many major and
8
The market risk premium was estimated to be proximate to 5% in various studies. Ibbotson, Roger G., and
Chen, Peng, “Long-Run Stock Returns: Participating in the Real Economy.” Financial Analysts Journal, 59,
88-98. Also see Mayfield, E. Scott, “Estimating the Market Risk Premium.” Journal of Financial Economics,
Volume 73, Issue 3, September 2004.
4
THE WACC USER'S GUIDE
emerging markets. And yet, current and future differences in taxes, treatment of
dividends, etc. may make a global market risk premium somewhat premature.
The US market
may serve as the
best proxy for a
global market
risk premium
Today's market
implies a cost of
equity of 10%
and MRP of 5%
Yet under the forces of globalism and capital market convergence, many experts
now suggest that increasingly the US market may serve as the best proxy for a
future global market risk premium.9 The U.S. has the largest economy and the most
liquid capital markets. Consequently, the 5% risk premium seems appropriate for
other markets, after adjusting for differences in tax rates, etc.
Market-Implied Risk Premium
In Figure 4, we benchmark our historically derived market risk premium against the
implied market risk premium of today's market capitalization and earnings, under
different assumptions for future earnings growth and reinvestment.10 While the
assumption of constant growth is problematic for an individual company, it is more
appropriate for an analysis of the broader market.
Based on today's market capitalization, depending on assumed future growth rates
and dividend yields, the dividend discount model implies a cost of equity of about
10% and a market risk premium of about 5%, using a riskless rate of 4-5%.
Estimates of long-term sustainable nominal growth rates now range from 5-7%,
consistent with expected inflation of 2-3% and real GDP growth of 3-4%.
Figure 4– Market-Implied Risk Premium Estimates
Dividend Yield
Growth Rate
0
2.1%
2.5%
2.9%
3.3%
3.7%
5%
2.2%
2.6%
3.0%
3.5%
3.9%
6%
3.2%
3.7%
4.1%
4.5%
4.9%
7%
4.2%
4.7%
5.1%
5.5%
6.0%
8%
5.3%
5.7%
6.1%
6.6%
7.0%
SOURCE: UBS Investment Bank
Sustainable growth rates may also be gauged with the retention growth model,
which derives growth rates from expected returns on equity (ROE) and plowback
ratios (1- payout ratio).11 From this approach, we estimated nominal growth rate
around 6-7% (Figure 5) and a cost of equity for the market of 9-10%. Again, this
approach supports a market risk premium on the order of 5%.
Figure 5 – Sustainable Growth Estimates
Return on Equity
Payout Ratio
We estimate
nominal
growth at 6-7%
and a cost of
equity of 9-10%
0
26%
28%
32%
34%
36%
8%
5.9%
5.8%
5.4%
5.3%
5.1%
9%
6.7%
6.5%
6.1%
5.9%
5.8%
10%
7.4%
7.2%
6.8%
6.6%
6.4%
11%
8.1%
7.9%
7.5%
7.3%
7.0%
12%
8.9%
8.6%
8.2%
7.9%
7.7%
SOURCE: UBS Investment Bank
9
10
11
An excellent discussion of globalism and its impact on integrated and integrating capital markets leading both to
falling risk premiums and risk premium convergence is presented by Rene Stulz, “Globalization, Corporate Finance,
and the Cost of Capital,” Journal of Applied Corporate Finance, Vol. 12 No. 3 (Fall 1999).
The dividend discount model (Gordon growth model) assumes growth rates remain constant over time. While
this may be problematic on a microeconomic basis, it is more useful on a broader market basis. Solving for cost
of equity, the Gordon growth model can be expressed as Ke=[(Div0/P0)*(1+g)]+g, where Div0 represents the
annual market dividend payments (approximately $185mm at 2/7/2005); P0 is equal to the total market
capitalization of the index ($11.1bn at 2/7/2005); and g is equal to the estimated dividend growth rate.
Retention growth assumes historical returns on book equity (i.e., net income/book equity) as a proxy for future
growth rates based on an earnings retention ratio (i.e., 1- dividend payout). This method is an ex-ante approach
to calculating expectations of future growth rates as follows: (Return on Equity) * (Retention Ratio). Damodaran,
Aswath, Investment Valuation, John Wiley & Sons, Inc., 1993.
5
THE WACC USER'S GUIDE
TOWARD A BETTER BETA
Estimating beta is
problematic for
unlisted or illiquid
stocks
1. Direct Regression
Most typically calculated using the most recent 60 monthly returns, other sampling
periods and frequencies can be more appropriate. For example, for sectors affected
by the "tech bubble" or "9/11" a three year sampling of weekly data may be more
appropriate. How much history is relevant to your company or industry? Beyond a
qualitative assessment for fundamental changes in risk, check the data.12
If no discernible trend is
evident and the data
10
represent a random
walk, longer periods can
5
be employed to provide
more data and improve
0
reliability. If a trend is
-5
evident or sufficient
history is not available,
-10
more data can be derived
-10
-5
0
5
10
from the shorter history
Market Returns (%)
with weekly or even
daily returns to provide
SOURCE: UBS Investment Bank Illustration
enough data for a
meaningful regression. Analyze the residuals of a regression by plotting or sorting–
what is not explained by the regression. Re-regressing the interquartile or interdecile
range of data should provide a similar slope (i.e. beta) but can give a much better
“fit” (i.e. a more statistically significant coefficient of determination). However, if
the slope changes, it raises questions around which slope is correct
Figure 6 – Beta Regression Illustration
Industry Returns (%)
Typically derived
from 60 months,
other sampling
periods and
frequencies can be
more appropriate
The determination of a robust proxy for systematic risk (beta) is often a problematic
area in the calculation of the cost of equity - not only for business units and private
companies but also for illiquid stocks or public companies with very little meaningful
historical data. Beta is typically the regression coefficient that describes the slope of
a line of “best fit” through a history of dividend-adjusted stock and market returns
(Figure 6). While reasonable and statistically meaningful betas can be difficult to
determine, let’s not throw out the baby with the bathwater—we provide some
alternative methods to apply CAPM with a reliable measure of systematic risk.
Sort the residuals
on size and plot by
time. Re-regress
the interquartile or
interdecile range
2. Industry Betas
Many stocks or markets are less liquid or have too little history, potentially leading
to spurious results if the beta is determined overly mechanically. A simple solution
in such cases, as well as for private companies and business units, is to determine a
proxy for systematic risk by calculating an industry beta. The underlying assumption
is that the systematic risk is similar for all businesses in that industry. However, these
approaches can be sensitive to the selection of peers.
a) Simple Mean or Median of Unlevered Beta: A simple mean or median of
pure-play comparable unlevered betas (i.e. asset betas) may serve as a representative
proxy for the company unlevered beta.13 The unlevered beta is then relevered
based on a target capital structure.
12
13
Potential questions might probe the interpretation and sensibility of the regression coefficients, summary statistics,
and residuals. Sorting the residuals will help you to flag and understand suspect data, as well as to guide your
choices regarding the amount of history and length of the return periods to be used.
The asset beta, or unlevered beta, is adjusted to exclude financial risk from the market beta: Unlevered Beta =
D/EV * Debt Beta (1-tax rate) + (1 - D/EV) * Levered Beta. Debt Beta may be estimated from credit spreads or
6
THE WACC USER'S GUIDE
A single regression
of cross-sectional
returns for all
company-market
return points
A secondary
regression for
estimating
segment, or lineof-business capital
costs in integrated
industries
b) Portfolio Beta: Where leverage ratios are similar across an entire industry, a
portfolio beta may serve as a proxy for a company beta. The portfolio beta is
derived from a single regression of cross-sectional returns for all company-market
return points. Include as much data as possible to minimize bias from any point.
3. Secondary Regression by Segment
In cases of highly vertically integrated industries (financial services, resource
industries), where there are often only a few pure-play peer companies, a secondary
regression by segment can be employed to determine a pure-play beta. This is
especially helpful for estimating segment, or line-of-business, costs of capital within
integrated industries. The dependent variable is each company’s unlevered beta
while the independent variables are the percentage exposures to different business
segment (e.g. by revenue, assets, or operating income). For example, Table 2
illustrates the development of an unlevered lumber beta of 0.50, versus the higher
0.66 for paper products, within the integrated forest products industry.14
Table 2 – Segment Beta Regression Illustration
Company
International Paper
:
Temple-Inland
Boise Cascade
Industry
Debt
(%)
40
:
51
54
Beta
0.99
:
1.26
1.99
Asset
Beta
0.70
:
0.77
0.69
Lumber
(%)
49
:
12
17
0.50
Paper
(%)
44
:
57
36
0.66
Other
(%)
7
:
31
47
nm
SOURCE: UBS Investment Bank Illustration
Beta = Correlation Coefficient Ind. x (Volatility Co. / Volatility Market)
Volatility of market returns may be measured directly from market data, as can a
correlation coefficient for the industry (Figure 7). If the business is not traded,
relative volatility may be estimated from the standard deviation of changes in
capitalized NOPAT, or EBIT, as a proxy for return volatility.
Figure 7 – Constructed Beta Illustration
10
Market Vol = 21%
Correlation = 69%
Industry Returns (%)
A construct for
where beta is
artificially
depressed by low
market correlation
due to low stock
liquidity
4. Constructed Beta
A constructed beta is especially helpful for illiquid stocks where the beta is artificially
depressed by a low correlation to the market due to extremely low stock liquidity.
Betas can be constructed as the product of an industry-portfolio correlation
coefficient and a company-specific relative volatility coefficient:
Company Vol = 40%
5
Constructed Beta =
69% x 0.40 / 0.21 = 1.31
0
-5
-10
-10
-5
0
Market Returns (%)
5
10
Returns Volatility
SOURCE: UBS Investment Bank Illustration
14
direct regression of market data. The beta for a conglomerate is a weighted average of division betas, based on
each division’s contribution to the firm’s intrinsic value (capitalized operating cash flow may serve as a proxy).
While the t-statistics were all highly significant, the “other” beta is clearly not meaningful due to the wide mix of
other segments within which diversified forest products companies operate.
7
THE WACC USER'S GUIDE
If operating results, which are generally available on monthly basis, exhibit seasonality
we recommend regressing the percentage change in capitalized NOPAT or EBIT over
the same period last year against respective annual market returns.
A novel
approach for
businesses that
share the
characteristics
of many sectors
5. Multi-Variable Regression Beta
We employ a novel approach for “hybrid” businesses that share the characteristics of
multiple sectors. For example, a privately owned industrial biotechnology company
shares specialty chemicals, pharmaceuticals and biotechnology characteristics. Our
multivariable regression incorporates valuable, company-specific data found to be
related to different degrees of systematic risk (Table 3).
Table 3 – Multivariate Regression Beta Illustration
Asset
Beta
1.33
0.90
:
1.16
1.49
Company
Alza
Dow
:
Eli Lilly
Hybrid Co.
Sales
ln(Capital) Growth (%)
14.3
25
16.9
(1)
:
:
16.4
9
10.0
25
R&D/
Sales (%)
7
4
:
16
15
NOPAT/
Sales/
Sales (%) Capital (x)
30
0.67
13
0.93
:
:
25
0.57
25
1.50
SOURCE: UBS Investment Bank Illustration
Our regression predicts an asset beta of 1.49 based on the company’s key drivers
(size, growth, R&D, margins, and capital turns) relative to those of publicly traded
pharmaceutical, biotechnology, and specialty chemicals companies.15
THE "RISKLESS" RATE
With the 10-year Treasury at "abnormally" low levels, we typically "normalize" the
riskless rate.16 At the time of writing, 10-year Treasuries were about 4% while the
10-year historical average was 5.4% and 30-year Treasuries were near 5%. Figure
8 shows the forward curve for 10-year Treasuries - a market-derived estimate for
the riskless rate - with an asymptote in the 5% range. As an alternative to historical
averaging, the forward curve is less sensitive to the choice of period, and provides a
stable and objective benchmark for a normalized riskless rate (Figure 8).
Figure 8 - Historical 10-Year Treasury Rates vs. Forward Rates
10-Yr. Treasury Yield
(%)
With the 10-year
Treasury at
"abnormally"
low levels, the
forward curve
provides a more
stable, objective
benchmark for a
"normalized"
riskless rate
10-Year Treasury
8
Forward Curve
6
FWD Rate = 5%
4
10-Yr. Average = 5.4%
2
0
'95
'96
'97
'98
'99
'00
'01
'02
'03
'04
'05
'06
'07
'08
'09
'10
SOURCE: Compustat, Bloomberg (March ’05)
15
16
We found significant and intuitively appealing coefficients with this model: 0.214 x sales growth + 0.687 x
R&D/sales–0.205 x sales/capital–0.081 x ln(capital) + 0.394 x net operating profit after tax (NOPAT) margin +
2.348 (intercept).
In practice, investors use as a proxy for the risk-free rate any number of government bond rates, each with its
own strengths and weaknesses. Those who use T-bill rates argue that the shorter duration and lower correlation
of the T-bill with the stock market make it truly riskless. However, because T-bill rates are more susceptible to
supply/demand swings, central bank intervention, and yield curve inversions, T-bills provide a less reliable
estimate of long-term inflation expectations and do not reflect the return required for holding a long-term asset.
For valuation, long-term forecasts, and capital budgeting decisions, the most appropriate risk-free rate is derived
from longer-term government bonds. They capture long-term inflation expectations, are less volatile and subject
to market movements, and are priced in a liquid market. See Bruner, Eades, Harris and Higgins, “Best Practices
in Estimating the Cost of Capital: Survey and Synthesis,” Financial Practice and Education, Spring/Summer 1998.
8
THE WACC USER'S GUIDE
COST OF DEBT
We also
"normalize"
credit spreads
for financial
policy purposes
WACC is calculated using the marginal cost of corporate debt – i.e. the yield the
company would incur for borrowing an additional dollar. Credit quality and
corporate bond ratings are the primary determinants of the cost of debt, and are
influenced by factors such as size, industry, leverage, cash flow and coverage,
profitability, and numerous qualitative factors (Figure 9).17
Interest expense is not an accurate reflection of a corporation’s true cost of debt.
The average coupon currently paid by a corporation is the result of yields and credit
rating at the times of issuance, and may not reflect the market environment or
corporate credit quality. Nor is it a marginal cost.
Figure 9 – The Costs of Debt
Average 10-Year Spread
10-Year Treasury Rate
8
4.8
0.6
4.9
0.7
5.0
5.1
5.3
5.4
5.5
5.7
0.8
0.9
1.1
1.2
1.3
1.5
2.4
2.9
3.3
3.7
4.3
5.3
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
A
A-
BBB
BBB-
BB+
BB
BB-
B+
B
2
7.5
9.5
8.5
A+
4
7.1
7.9
AA
6
6.6
Current Spreads
AAA
Cost of Debt (%)
10
B-
BBB+
SOURCE: Bloomberg (March ’05)
Table 4 – Expected Value Tax Shield Estimation
Annual Volatility of Stock Returns (%)
Target Leverage/
Enterprise Value (%)
Higher
financial
leverage and
cash flow
volatility
lowers the
expected value
of tax shield
Finally, the WACC calculation is based on an after tax cost of debt. However,
higher degrees of financial leverage and cash flow volatility will lead to lower
expected values for each dollar of tax shield. There will be less profits to shield, a
loss in time value from loss carry forwards, and an increased risk of financial distress.
10
20
30
40
50
60
70
20
100%
100%
100%
99%
97%
95%
92%
30
100%
98%
95%
91%
87%
83%
79%
35
99%
95%
90%
85%
81%
77%
73%
40
97%
91%
85%
79%
74%
70%
66%
45
93%
86%
79%
73%
68%
64%
60%
50
89%
80%
72%
66%
62%
57%
54%
60
79%
67%
60%
54%
50%
46%
43%
Source: UBS Investment Bank Estimates
We approximate this effect by analyzing the risk-laden corporate debt as risk-free
debt less a put option on the assets of the firm, with a strike price equal to the face
value of the debt.18 Based on option valuation framework, the probability of being
able to utilize the interest tax shield decays under increased leverage, volatility, and
duration.19 Table 4 estimates this impact over a range of leverage and volatilities.
17
18
19
Please refer to Pettit, Justin, Orlov, Serguei and Kalsekar, Ashwin, “The New World of Credit Ratings,” UBS
Investment Bank, September 2004.
At the debt's maturity equity-holders can "put" the firm assets to debt-holders in exchange for the face value of
debt (in bankruptcy the debt is effectively forgiven when debt-holders take possession of the assets). However,
if the Company's assets' value declines below the face value of its debt, the bondholders suffer a loss.
From the Put-Call parity we derive the probability that a firm will not be able to make a payment on its debt
obligations and thus will not realize a tax shield (G). S–Call (S) = PV (Strike Price @ Rf) – Put (S), where S is the
9
THE WACC USER'S GUIDE
Convertibles offer
significant tax
advantages while
minimizing cash
servicing costs via
amortization of
the warrant value
Hybrid Instruments
Convertibles can offer issuers significant tax advantages while minimizing cash
servicing costs via amortization of the warrant value. WACC estimations are
complicated by the introduction of hybrids into the capital structure. This is most
easily resolved through an effective bifurcation of the instrument's value into debt
and equity to reflect the true target debt-equity mix (Table 5). However, for ratings
agency purposes, cash-pay converts are typically treated as debt until conversion.
This is true regardless of how "in-the-money" they become. Some hybrids, such as
mandatory convertibles, do receive some equity credit for ratings purposes.20
Table 5 – Anatomy of a Convertible Illustration
NC First Put 5
Share Price
Equity Portion
Debt Portion
Exercise Price Premium (%)21
Option Term in Years 19
Risk-Free Rate (%) 22
Equity Volatility (%) 19
Warrant Value ($) 23
Number of Warrants/Bonds
Warrant Portion Value ($) 23
Book Value ($) 19
Coupon (%)
Discount Rate (%) 22
Straight Value ($) 23
30.00
33.3
5
3.9
35
5.0
25.0
124
1,000
1.50
4.3
876
Source: UBS Investment Bank Illustration
The effective
WACC of a
convertible is a
weighted average
cost of debt and
equity portions
In Table 6 we illustrate the effective WACC of a convertible security as a weighted
average of cost of the debt and equity portions. The cost of the debt is the grossed
up yield (coupon + accretion). The cost of the equity is the cost of warrant equity.19
Table 6 - Weighted Average Cost of a Convertible
NC First Put 5
Cost of
Equity
Cost of Debt
WACC
Warrant Beta23
Market Risk Premium (%)8
Cost of Warrant (%)
Warrant Portion of Total Value (%)
2.9
5
18.6
12
Convertible Yield (%)
1.50
Debt Portion of Total Value (%)
88
Grossed up Yield (%)24
Probability of Conversion
Tax Rate (%)
Expected Tax Benefit (%)
After Tax Cost of Debt (%)
1.7
59
30
0.5
1.2
Debt Portion of Total Value (%)
88
Weighted Average Cost of Convertible
3.4
SOURCE: UBS Investment Bank Illustration
20
21
22
23
24
assets of the firm, Call (S) is the value of Equity, PV (Strike Price @ Rf) is the value of riskless debt (Df), PV (Strike
Price @ Rf) – Put (S) is the value of risky Debt (Dr). Hence, Assets – Equity = Risky Debt. Dr/Df = (PV (Strike Price
@ Rf) – Put (S))/PV (Strike Price. @ Rf) = 1–Put (S)/PV (Strike Price @ Rf) = G. Key inputs in the option valuation
are time to maturity and volatility of returns of the underlying asset, in this case the Enterprise Value. We
calculate the later number as the volatility of a market value-weighted portfolio of equity and debt.
Refer to Moody’s Rating Methodology Handbook, April 2003; S&P’s Corporate Ratings Critera, 2003; Fitch’s
Corporate Ratings Methodology, June 2003.
Exercise Price Premium= (Strike Price/Share Price) – 1
Risk-Free Rate = Treasury rate with a tenor matching the option term in years; Discount Rate (%) = Average
“BBB-“ 10-year corporate bond yields
Warrant Value estimated using Black Scholes option pricing formula; Straight Debt Portion of Total Value = 1Warrant Value/ Value of the Convertible Bond; Warrant Beta = Equity Beta*Warrant Beta*Warrant Delta*Share
Price/Warrant Premium (Financial Theory and Corporate Policy, 3rd Ed, T.E. Copeland, FJ. Weston, pp 473-478).
Grossed up Yield = Convertible Yield/Debt Portion of Total Value
10
THE WACC USER'S GUIDE
CAPITAL COSTS & THE GLOBAL PORTFOLIO
Under the pressure of weak earnings and depressed valuations, companies now
face unprecedented demand for profitable, long-term growth. Corporate
expansion through foreign direct investment offers investors valuable growth
opportunities.
Financial
management
practices are at
odds with the
strategic benefits
of foreign direct
investment
Corporations pursuing global growth accomplish something their investors appear
unwilling or unable to do themselves.25, 26 Despite the development and integration
of world financial markets, investors continue to behave as if there are substantial
costs to foreign portfolio investment. Global growth remains an essential part of
the strategy of most large companies today.
However, today's corporate financial management practices are decidedly at odds
with the strategic benefits of foreign direct investment. Indeed, there may be no
other area where corporate practice diverges so far from finance theory. Many still
cling to standard practices and ad hoc rules of thumb where excessive hurdle rates
for overseas operations and investments often impede value-enhancing growth.
However, although the investment returns in emerging economies are often more
volatile than the returns on domestic operations, emerging market investments do
not contribute as significantly as one might expect to the risk of a multinational
corporation’s (MNC) portfolio.27 One of the key issues behind the wide range of
approaches, in practice, is the extent to which capital markets are now integrated.
A Segmented Markets Perspective
A local country perspective, assumes that country managers operate and invest
within the isolation of their own respective local markets. This perspective treats
each country operation as a stand-alone investment and uses a "local" version of
CAPM with local equity risk indices, local market risk premiums, debt costs and
country risk premiums. While this approach reflects managers' intuition that
international markets exhibit higher risk—it ignores the more global view of
shareholders and the beneficial effects of a diverse MNC portfolio, and often leads
to numerous practical challenges in obtaining reliable and intuitive results. From a
corporate financial policy perspective, this approach also introduces considerable
complexity, communications challenges, and administrative burden.
An Integrated Markets Perspective
An integrated markets perspective views investments as components of a global
portfolio. This approach calls for uniformly allocating the corporate portfolio's net
sovereign risk, inflation risk, and diversification effects to each and every countrybusiness unit or investment - one source of capital, and one cost of capital, for all.
Each element of the corporate portfolio fully bears the risks and benefits of the
portfolio, irrespective of its contribution to the systematic risk of the corporate
portfolio. While this works well for the consolidated cost of capital, for countryoperations and investments we propose a hybrid perspective that captures the
marginal impact to the systematic risk of the corporate portfolio.
25
26
27
Ian Cooper and Evi Kaplanis, "Home Bias in Equity Portfolios and the Cost of Capital for Multinational Firms,"
Journal of Applied Corporate Finance, Volume 8 Number 3 (Fall 1995).
Global diversification is a strategy to cope with economic exposures that market integration and risk
management were supposed to eliminate, but did not. Dennis E. Logue, "When Theory Fails: Globalization as a
Response to the (Hostile) Market for Foreign Exchange," Journal of Applied Corporate Finance, Volume 8
Number 3 (Fall 1995).
The global CAPM and application to Nestle is outlined by Rene M. Stulz, "Globalization of Capital Markets and
the Cost of Capital: The Case of Nestle," Journal of Applied Corporate Finance, Volume 8 Number 3 (Fall 1995).
11
THE WACC USER'S GUIDE
Our Case for a Hybrid Perspective
Although world financial markets are now much more integrated than they were
twenty years ago, several factors continue to contribute to a significant degree of
market segmentation. Perhaps most important, investors in all nations are still most
comfortable investing in companies in their home markets, leading to the welldocumented "home bias" in investor portfolios. But there are also legal, tax,
accounting and regulatory barriers at work.
As a result of these impediments to well-functioning markets, many of the world's
capital markets – particularly emerging markets—have continued to exhibit signs of
illiquidity – or, depending on your interpretation, market inefficiencies – that are
associated with market segmentation. But, far from discouraging foreign direct
investment by corporations, these barriers, in fact, make the benefits of foreign
direct investment even greater than if markets were completely integrated.
Foreign direct
investment
provides
shareholders
benefits they don't
obtain on their own
In a world that remains at least partly segmented, foreign direct investment is still
capable of providing the firm's shareholders with investment opportunities and
diversification benefits they cannot obtain on their own. Moreover, as global
economies and financial markets continue the process of integration, this
diversification benefit of foreign direct investment will gradually disappear; but
other benefits – notably the reduction in risks (sovereign and inflation) that come
with global integration – will take its place.
Figure 10 – MNC Portfolio Illustration
Cntry
Cntry
Home
Country
Cntry
Our hybrid perspective (Figure 10)
assumes that a company maintains a
dynamic portfolio of foreign and
domestic investments that is
continuously evaluated for possible
expansion, curtailment, or even sale;
and, as a result, the proportionate
weightings of each real portfolio
element are constantly changing.
But as a practical matter, the risk
profiles and volatilities of each market,
as well as their correlations between
Cntry
each other, are also changing.28
Therefore, we do not recommend that
SOURCE: UBS Investment Bank Illustration
a country beta relative to the home
country be used as a proxy for the
incremental risk to the portfolio for each operation or prospective investment.
We accommodate
both systematic and
unsystematic risks
To extend CAPM to the evaluation of operations and investments overseas, we
adjust the framework for both systematic and unsystematic risk as follows:
♦ Adjust operating cash flows for project-specific risks and costs. While simple
rules of thumb are easier to use, they obscure fundamental issues, undermine
strategic risk discussion, and become inapplicable as conditions change
♦ Perform comprehensive risk analysis, such as sensitivity analysis and Monte Carlo
simulations, of risk drivers to enhance active risk management for value
♦ Adjust the cost of capital for both sovereign risk and expected inflation - our
proposed methodology follows
28
The instability of sovereign ratings and sovereign risk makes any point estimate of WACC a gross
oversimplification in many markets. Historical distribution and standard deviation data can support the
development of a range estimate, to help quantify the risk of a value-dillutive investment via simulation.
12
THE WACC USER'S GUIDE
Risks & Returns of Global Investing
Beyond profitable growth, there are strategic benefits to global investing. Today’s
global companies are often more attractive than their domestic peers who missed
their chances to “go global,” in part, because of inflated international hurdle rates.
Consider the case of Japanese foreign direct investment in the US in the '80s. These
"transplants" enjoyed relief with low cost manufacturing resulting from an
unexpected strengthening of the yen against the dollar. Had production remained
in Japan, supply to the large US market would have been very uncompetitive.
But the returns of global investment cannot be realized without significant risk –
global investing entails risks and costs incremental to those domestic investing. We
distinguish clearly between unsystematic and systematic risks, and propose
approaches to the treatment of each (Figure 11).29
Figure 11 – Cost of Capital Reflects Systematic Risks
International Risk
is divided into Two
Categories
of Risk
Non-Systematic Risk which
includes:
♦ International Costs
♦ Project Risks
Typically these
costs or risks are
NOT
compounding
Therefore make a
NON-Compounding
Adjustment
for these risks through
NOPAT
Typically these
costs or risks
ARE
compounding
Systematic Risk
which includes:
♦ Sovereign Risks
♦ Currency Risks
♦ Diversification Benefit
Therefore make a
Compounding
Adjustment
for these risks through
COST OF CAPITAL
SOURCE: UBS Investment Bank Illustration
These costs and
uncertainties are
often ignored
Unsystematic Risks & Costs
Foreign direct investment brings new and significant incremental costs (foreign legal
and tax, currency repatriation and hedging, insurance and other transaction costs)
that reduce the intrinsic value of the investment or operation. There are also
numerous risks (heightened project uncertainty such as market success, labor strife
or other operational challenges) specific to the investment or operation. These are
best evaluated in cash flow scenario, sensitivity and simulation analysis. But despite
the heroic coaching of finance professors around the world, our experience has
shown that these costs and risks are still frequently omitted from the cash flow
projections of international investment decisions. Furthermore, they are often
“below the line” in the evaluation of any international operations.
Project uncertainty, and the recognition that many international costs are neglected,
is the oft-unspoken rationale to inflate the hurdle rates for these investments. But
managers typically have the best information about the potential impact of these
risks on the expected stream of operating cash flows. Managers do not have any
way to quantify the effect (if there is any) on shareholders' required rate of return and these risks are diversifiable by investors or companies with global portfolios.
29
Systematic risk, or market risk, stems from economy-wide perils that affect all businesses – by definition this would
include the currency and sovereign risks of the economy itself. What matters to the well-diversified corporation,
and ultimately the well-diversified investor, is any incremental contribution to risk, Modern Corporate Finance, Alan
C. Shapiro (1990) pp. 239-268.
13
THE WACC USER'S GUIDE
Hurdle Rates Destroy Value
A higher hurdle to
compensate for
poor sensitivity or
risk analysis, free
capital, and an
excessive reliance
on single-point IRR
or NPV estimates
Some companies use a higher required return for investments than their actual cost
of capital - often artificial decrees to compensate for poor sensitivity or risk analysis,
free capital and an excessive reliance on single-point estimates of IRR or NPV.30
To offset these two problems, higher rates are imposed on managers in an attempt
to subsume a proper risk analysis and compensate for the fact that overly optimistic
forecasts are the norm. And while some negative NPV projects invariably must be
undertaken for environmental, health and safety reasons (defensive capital), inflated
hurdle rates do not help and actually exacerbate this problem.31
Increasing a project's rate of return also does not allow for adequate consideration
of the time pattern and magnitude of risk being evaluated. Using a higher discount
rate to reflect additional risk indiscriminately penalizes future cash flows relative to
less distant ones and geometrically compounds the cost of any risk. The practical
corollary to the deceptively simple allure of inflated hurdle rates is a reduced
emphasis on even simple risk-analysis, and ever more optimistic forecasts.
Inflated hurdle
rates result in
foregone
opportunity, a
lower ROCE, and a
lower value
An inflated hurdle rate results in foregone opportunity, a lower ROCE, and a lower
value. We illustrate mathematically (Table 12) that lowering the hurdle rate down
from 18% (versus an 8% WACC and 10% ROCE) leads to increasingly higher
weighted average returns, more NPV, and larger enterprise values.
Table 12: Lower Hurdle Rates Lead To Higher Returns & Higher Values
WACC
Base
Business
8%
18% hurdle
15% hurdle
12% hurdle
8%
8%
8%
Profit
Capital
18
15
12
100
100
100
∑ Profit
∑ Capital
ROCE
NPV
EV
$120
$1,200
10%
$300
$1,500
138
153
165
1,300
1,400
1,500
10.6%
10.9%
11.0%
425
513
563
1,725
1,913
2,063
SOURCE: UBS Investment Bank Illustration
Instead of raising the cost of capital, project and business operating cash flows
should be adjusted downward to reflect the incremental risks, costs and
uncertainties. Where capital must be rationed, we recommend a ranking to
produce the largest incremental NPV available. The limitation to any “ranking” of
investments is that this must be done in a static environment with all investment
opportunities available for evaluation at the same time – this is rarely realistic.
Excessive hurdle
rates impede
growth and
ultimately require
large offsetting
acquisitions
And capital is very rarely in short supply – investors are clamoring for opportunity.
The greatest constraint, and one of the greatest strategic challenges facing publicly
traded corporations, is opportunity for growth. Stock prices routinely reflect
expectations of tremendous growth. At the time of writing, only 53% of the S&P
enterprise value could be justified by the present value of current cash flows
capitalized as perpetuity. A full 47% of the market capitalization was predicated on
profitable growth over and above today's level of cash flows.
Today's corporate financial policies and practices are at odds with this growth
imperative – excessive hurdle rates impede growth – especially organic growth and
smaller investments (the least amount of risk) and ultimately necessitate large
acquisitions (where risk is greatest) to supplement modest growth.32
30
Capital is "free" because once negotiated it is a sunk cost to operating managers. Thus, in most cases, capital
must be rationed precisely because it is free. If it carries a capital charge, it becomes plentiful, but expensive.
31
See Leaman, Rick, Neissa, Jimmy, Pettit, Justin, et al., “Renewing Growth: M&A Fact & Fallacy,” UBS Investment
Bank, June 2003
32
See Leaman, Rick, Neissa, Jimmy, Pettit, Justin, et al., “Where M&A Pays: Who Wins & How?” UBS Investment
Bank, December 2004
14
THE WACC USER'S GUIDE
Systematic Risks
We identify the systematic risks to discrete foreign direct investments that can be
quantified and treated within the cost of capital framework to manage better the
MNC portfolio. However, these risks do not need to be incorporated with arbitrary
and excessive risk premiums; rather, they can be addressed more rigorously in a
fairly straightforward manner.
1. Business & Financial Risks
The inherent business and financial risk need not change for foreign direct
investments because a company's core business and target capital structure does
not typically depend on any particular international operations – we would typically
expect these to be applicable worldwide. For example, in industries where operating
profit tends to be more volatile and correlated to the market (e.g. semiconductor
industry), business risk is high. These risks, measured by the company beta, are
already captured in the corporate cost of capital.
Future cash flows
and FX should
match inflation
expectations in the
discount rate
Sovereign risk is a
broad category of
risks unique to the
eco-political
environment
2. Expected Inflation
The rate at which prices are expected to increase, inflation risk, measures the
relative strength of a currency in relation to domestic expected inflation and are
typically reflected in forward foreign exchange rates. In effect, it represents the risk
arising from expected currency devaluation (longer term) due to differentials in long
run inflation expectations (assumes interest rate parity holds over the longer run).
These risks implied by the relative risk-free rates between countries or from
inflation-linked government bonds, are incorporated into both the cost of debt and
cost of capital calculations. This risk should be clearly distinguished from the short
run cases where parity breaks down – unexpected currency devaluation is a
possibility subsumed by sovereign risk.
3. Sovereign Risk
Sovereign risk is most commonly associated with the risk that a foreign government
will default on its loans or fail to honor other business commitments due to change
in government or policy. However, sovereign risk is a broad category of risks unique
to a country's political and economic environments that also include the impact of
currency controls, changes in tax or local content laws, quotas and tariffs, and the
sudden imposition of labor or environmental regulation:
♦ Unexpected Devaluation/Inflation: Sharp movements in the relative valuations of
currencies, as in Mexico in 1994, and in Russia and much of Asia in 1998, go
beyond the weakness implied by expected inflation differentials and are
frequently the result of unrealistic currency pegs. Sudden runaway inflation has
been "employed" to help satisfy debt obligations (e.g. Bolivia in the 1980s).
♦ Policy Risk: A host government, due to leadership or policy changes, may renege
on contracts, agreements or approvals, prevent currency conversion, or impede
repatriation. Other examples include sudden large changes in tax laws, local
content laws, quotas and tariffs, and environmental restrictions. For example,
witness the unexpected difficulties faced by both MNC loggers and miners in the
Pacific Northwest in the 1990s as a result of environmental lobbying.
♦ Expropriation: Host government policy may reduce or eliminate ownership of,
control over, or rights to, an investment by an overseas firm. This has happened
in Russia, Cuba, South America, Israel, and many other countries.
♦ War/Civil Disturbance: This includes acts of sabotage or terrorism, damage to
tangible assets, or interference with the ability of the enterprise to operate.
This has been particularly acute in sub-Saharan Africa and the Middle East.
15
THE WACC USER'S GUIDE
Multiple sources of
information to
"triangulate"
sovereign risk
Sovereign risks add a premium to the required rate of return for foreign direct
investment. One way of estimating the possible size of this premium is to look at
the "insurance premiums" charged by organizations such as the Overseas Private
Investment Corporation (OPIC) and the Multilateral Investment Guarantee Agency
(MIGA), which guarantee foreign investments against some of the risks cited above.
Other market-based methods may be more reliable. We generally employ multiple
sources of information to "triangulate" sovereign risk premiums: USD denominated
(Global Euro and stripped Brady) sovereign debt yields, and where bond yields are
unavailable or appear unreliable, we use the premiums implied by a basket of similarly
rated (S&P country ratings) countries.33 We begin by estimating a domestic cost of
capital and then add sovereign and expected inflation risk premiums.34
400
350
300
250
200
B
BB
BBB
A
150
100
50
0
AA
Sovereign
Risk (bps)
20
50
10
40
50
70
100
60
190
90
120
310
280
280
AAA
Canada
Belgium
Portugal
Italy
Hong Kong
Chile
Israel
Poland
South Africa
Bulgaria
India
Peru
Turkey
Indonesia
Country
USD Rating
AAA
AA+
AA
AAA+
A
ABBB+
BBB
BBBBB+
BB
BBB+
Sovereign Premium (bps)
Table 7 – Sovereign Risk
Sovereign Rating
SOURCE: S&P Global Ratings Handbook, Bloomberg; CreditDelta (March ’05)
Our sovereign risk premiums (Table 7) reflect the “country risk” relative to an AAA
credit such as the US. Developed countries possess very low risk premiums; Canada
and Italy have sovereign risk premiums of 20 and 40 bps respectively. Developing
sovereign risk premiums range from 70 bps for Chile to 3,190 bps for Argentina.35
Point estimates of
sovereign risk
represent false
precision - they
vary widely within
ratings and are
prone to sudden
change
For example, Chile USD sovereign debt yields 4.9%, and incorporates an incremental
required rate of return to compensate US (or globally diversified) investors for bearing
Chilean sovereign risk. To determine what portion of that 4.9% represents Chilean
sovereign risk, we effectively subtract the US sovereign yield from the local country
sovereign yield (excluding the effect of compounding) to determine the 70 bps
sovereign risk premium. And this appears consistent with the country USD rating.
But any point estimate of sovereign risk may represent false precision. Sovereign
risk premiums vary widely even within country ratings, and are subject to sudden
change. Figure 12 illustrates the uncertainty of a sovereign risk premium with a
Monte Carlo simulation based on historical sovereign yield data.
33
For the countries that make long-term borrowings predominantly in USD and not in the local currency, we may
use Eurobond yields or the stripped yield of their International/Brady bonds as a basis for USD-based risk free
rates. The stripped yield is the yield on the non-collateralized portion of the bond. For developed countries (and
those others who are able and tend to borrow long-term in the local currency) we may estimate USD based
sovereign yields based on S&P sovereign credit rating of such countries and corporate credit spread matrix.
34
This process is technically a somewhat iterative process, as the "domestic" cost of capital should not reflect the
net incremental risk of the global assets that are already reflected in the company beta. We skip this step where
the impact is not deemed to be material at the corporate level.
35
See Appendix B: Cost of Capital by Country
16
THE WACC USER'S GUIDE
Figure 12– Sovereign Risk Premium Simulation
2.5th Percentile
(4.5%)
Probability (%)
5
4
Average (5.2%)
3
97.5th Percentile
(6.4%)
2
1
0
3
4
5
6
7
Sovereign Premium (%)
8
9
10
SOURCE: Credit Delta, UBS Investment Bank Illustration. We assume a lognormal distribution for sovereign risk
with mean 5.2% and standard deviation 1.2% based on weekly yields of LC denominated sovereign debt.
Global Corporate Capital Costs
A helpful way of looking at the cost of capital for foreign countries is in terms of the
marginal impact of the two systematic risk components—sovereign and currency
risk. Calculating foreign WACC in USD involves adding a sovereign risk premium to
the domestic WACC. To calculate foreign WACC in local currency, we also add the
expected inflation premium.36
For example, in the case of Chile (sovereign risk premium 70 bps, inflation risk
premium 10 bps), a company with a domestic WACC of 8% will have a foreign
WACC in USD of roughly 8.7% and a WACC in local currency of about 8.8%.
Table 8 – Global Costs of Capital
Country
Canada
Belgium
Portugal
Italy
Hong Kong
Chile
Israel
Poland
South Africa
Bulgaria
India
Peru
Turkey
Indonesia
Sovereign
Risk (bps)
20
50
10
40
50
70
100
60
190
90
120
310
280
280
Inflation Risk
(bps)
20
-80
-40
-40
-120
10
-10
40
190
110
170
50
830
350
Local WACC
in LC (%)37
Local WACC
in USD (%)38
8.4
7.7
7.7
8.0
7.3
8.8
8.9
9.0
11.8
10.0
10.9
11.6
19.1
14.3
8.2
8.5
8.1
8.4
8.5
8.7
9.0
8.6
9.9
8.9
9.2
11.1
10.8
10.8
SOURCE: S&P Global Ratings Handbook, Bloomberg, UBS Investment Bank Estimates (March ’05)
Ultimately, the
business case,
quality of cash
flow forecasts,
sensitivity analysis,
and strategic risk
management will
have the greatest
impact on value
The local cost of capital in local currency provides local managers with a reference
frame when forecasts are based on local currency with local inflation expectations
embedded. But, for purposes of evaluating a contemplated investment in Brazil (or,
say, a major expansion of its current operations), a local cost of capital in USD (with
no significant revenue inflation) provides a better basis.
The cost of capital is an estimation that should be applied with care to avoid any
allusions of false precision. And despite its many degrees of freedom, financial
planning time and resources are better allocated to other areas. Ultimately, it is
the business case, quality of cash flow forecasts, sensitivity analysis, and strategic
risk management that will have the greatest impact on value creation.
36
37
38
We estimated currency risk from inflation-linked sovereign bonds, or from the difference between using
expected changes in CPI index, LC sovereign bond yields and the implied LC issuer yields based on S&P Country
Rating as well as yield differentials between local currency and USD denominated sovereign yields.
Local WACC in USD = Global WACC + Sovereign Risk Premium
Local WACC in LC = Local WACC in USD + Inflation Risk Premium
17
THE WACC USER'S GUIDE
Healthcare
Technology, Media,
Telecom
Power
Energy
Industrials
Real
Estate
Consumer &
Retailing
APPENDIX A – COST OF CAPITAL BY INDUSTRY AND SUB-INDUSTRY 39
Industry/Sector
Asset Levered Cost of Credit
Name
Beta Beta Equity (%) Rating
0.64
0.76
8.8 AConsumer
Food & Beverages
0.48
0.57
7.9 AWine & Spirits
0.57
0.67
8.4 A
Tobacco
0.39
0.55
7.7 BBB+
Personal & Household 0.76
0.89
9.5 A
Consumer Durables
0.70
0.87
9.3 BBB
Restaurants
0.61
0.68
8.4 BBB+
Retail & Apparel
0.98
1.10
10.5 BBB+
0.40
0.60
8.0 BBBReal Estate
REIT's
0.34
0.51
7.6 BBBMgmt & Develop.
0.47
0.68
8.4 BB+
0.79
1.00
10.0 BBB+
Industrials
Forest Products
0.74
0.99
10.0 BBBMining & Materials
0.98
1.16
10.8 BBB
Chemicals
0.74
0.91
9.5 BBB+
Auto Parts
0.89
1.22
11.1 BBBAuto Assemblers
0.93
1.20
11.0 BBBCyclicals
0.77
0.88
9.4 BBB
Coal
0.48
0.69
8.5 BBB+
Industrial Goods
0.82
0.95
9.8 AA0.69
0.86
9.3 AEnergy
Drilling, Equip. & Svcs 0.98
1.08
10.4 BBB+
Oil and Gas
0.71
0.83
9.2 A+
Pipelines
0.39
0.59
8.0 BBB+
0.33
0.49
7.5 BBB+
Power
Electric Utilities
0.31
0.47
7.4 BBB+
Gas Utilities
0.30
0.45
7.3 BBB+
Multi-Utilities
0.48
0.75
8.8 BBBWater Utilities
0.24
0.32
6.6 BBB
1.44
1.53
12.6 ATechnology
Semiconductors
1.80
1.92
14.6 ASoftware
1.42
1.45
12.3 A
Hardware & Equip.
1.35
1.46
12.3 ATechnology Services
1.21
1.28
11.4 BBB+
0.81
1.08
10.4 BBB+
Telecom
Wireless
0.85
1.10
10.5 BBB
Diversified
0.78
1.06
10.3 A0.86
0.96
9.8 BBB+
Media
1.01
1.08
10.4 BBB+
Healthcare
Specialty Pharma
1.24
1.32
11.6 BBBMedical Tech
0.96
0.99
10.0 BBB+
Managed Healthcare
0.82
0.87
9.3 BBB+
Large Cap Pharma
0.83
0.89
9.5 AA+
Healthcare Services
0.77
0.87
9.4 BB+
Biotechnology
1.43
1.52
12.6 BBB
Cost of
Debt D/Cap D/EV G WACC
(%)
(%) (%) (%) (%)
5.0
50
23 91
7.6
5.0
48
22 91
6.9
4.9
53
21 93
7.3
5.2
57
39 84
6.1
4.9
46
22 92
8.1
5.2
42
27 90
7.8
5.2
52
14 95
7.7
5.2
51
17 94
9.3
5.4
66
43 81
6.2
5.4
69
46 80
5.9
5.8
63
40 82
6.7
5.2
57
29 88
8.1
5.4
56
34 85
7.8
5.2
34
23 92
9.1
5.2
49
25 91
8.0
5.4
57
37 84
8.4
5.4
91
31 87
8.7
5.2
52
19 93
8.3
5.2
54
41 82
6.5
4.8
65
19 93
8.5
5.0
45
27 90
7.7
5.2
36
14 96
9.4
4.8
32
22 93
7.9
5.2
67
45 80
6.1
5.2
61
44 81
5.8
5.2
61
45 80
5.7
5.2
59
46 79
5.6
5.4
66
47 79
6.4
5.2
58
36 85
5.5
5.0
21
8 97
11.9
5.0
11
9 96
13.6
4.9
12
4 98
11.9
5.0
29
11 96
11.3
5.2
30
8 98
10.7
5.2
44
34 86
8.1
5.2
39
32 87
8.3
5.0
49
36 85
7.8
5.2
32
15 95
8.8
5.2
30
10 97
9.7
5.4
30
10 96
10.8
5.2
27
5 98
9.6
5.2
24
8 98
8.9
4.7
28
10 98
8.8
5.8
41
17 93
8.4
5.2
28
9 97
11.8
SOURCE: FactSet, Compustat, Bloomberg (March ’05)
39
Tax Rate = 36%, Market Risk Premium = 5%, Riskless Rate = 5%, 10 Yr. T-Bond Yield = 4.2%
18
THE WACC USER'S GUIDE
APPENDIX B – COST OF CAPITAL BY COUNTRY
Asia & Africa &
Australia
Latin
America
Europe &
Middle
East
European Union
G7
USD Rating LC Rating
United States
Canada
France
Germany
Italy
Japan
United Kingdom
Austria
Belgium
Czech Republic
Denmark
Finland
Greece
Hungary
Ireland
Netherlands
Poland
Portugal
Spain
Sweden
Bulgaria
Israel
Norway
Russia
Switzerland
Turkey
Argentina
Brazil
Chile
Colombia
Mexico
Peru
Venezuela
Australia
China
Hong Kong
India
Indonesia
Malaysia
New Zealand
Philippines
Singapore
South Africa
South Korea
Taiwan
Thailand
AAA
AAA
AAA
AAA
AAAAAAA
AAA
AA+
AAAA
AAA
A
AAAA
AAA
BBB+
AA
AAA
AAA
BBBAAAA
BBBAAA
BBSD
BBA
BB
BBB
BB
SD
AAA
BBB+
A+
BB+
B+
AAA+
BBAAA
BBB
AAABBB+
AAA
AAA
AAA
AAA
AAAAAAA
AAA
AA+
A
AAA
AAA
A
A
AAA
AAA
AAA
AAA
AAA
BBB
A+
AAA
BBB
AAA
BB
SD
BB
AA
BBB
A
BB+
B
AAA
BBB+
AABB+
BB
A+
AAA
BB+
AAA
A
A+
AAA
Sovereign
Risk (%)
0.0
0.2
0.0
0.3
0.4
0.0
0.2
0.3
0.5
1.5
0.4
0.2
1.3
1.4
0.1
0.2
0.6
0.1
0.3
0.3
0.9
1.0
0.0
2.5
0.0
2.8
31.9
4.3
0.7
3.8
1.4
3.1
3.6
0.0
0.6
0.5
1.2
2.8
1.0
0.4
4.5
0.0
1.9
0.7
0.8
1.7
B
B
B
A
B
A
A
B
B
B
A
B
B
B
A
B
A
B
B
A
B
A
A
B
A
A
A
A
A
A
A
A
A
A
A
B
B
B
B
A
B
A
A
B
B
Inflation
Risk (%)
0.0
0.2
-0.4
-0.6
-0.4
-2.5
1.4
-0.6
-0.8
0.0
-0.6
-0.6
0.5
1.9
-0.4
-0.5
0.4
-0.4
0.4
-0.4
1.1
-0.1
-0.2
6.5
-1.7
8.3
4.7
3.2
0.1
2.6
4.5
0.5
23.9
-0.2
0.8
-1.2
1.7
3.5
-0.4
0.0
4.2
-1.0
1.9
-0.3
-0.8
0.5
D
D
D
C
D
C
E
D
D
D
D
D
D
D
C
D
D
D
D
D
D
D
D
D
D
D
D
D
D
E
D
D
C
C
D
D
C
D
D
E
D
E
E
D
C
Total Risk
(%)
0.0
0.4
-0.4
-0.3
0.0
-2.5
1.6
-0.3
-0.3
1.5
-0.2
-0.4
1.8
3.3
-0.3
-0.3
1.0
-0.3
0.7
-0.1
2.0
0.9
-0.2
9.2
-1.7
11.3
38.1
7.6
0.8
6.5
6.0
3.6
28.4
-0.2
1.4
-0.7
2.9
6.4
0.6
0.4
8.9
-1.0
3.8
0.4
0.0
2.2
F
F
F
G
F
G
F
F
F
F
G
F
F
F
G
F
G
F
F
G
F
G
G
F
G
G
G
G
G
F
G
G
G
G
G
F
F
F
F
F
F
F
F
F
F
ABCDEFG
Source: S&P Global Ratings Handbook, The Economist, Bloomberg, CreditDelta (March ’05)
A
Sovereign Risk = (1+Sovereign Yield in USD)/(US Treasury Yield)-1
Sovereign Risk = (1+Total Risk Premium)/(1+Relative Currency Risk)-1
C
Relative Currency Risk = (1+Sovereign Yield in LC)/(1+ Sovereign Yield in USD) -1
D
Relative Currency Risk = [1+[(Expected Inflation in Sovereign Country)/(1+ Excpected Inflation in US)-1)]. Expectations
of inflation were obtained from either differentials between sovereign inflation linked bond yields and nominal
sovereign bond yields or UBS Investment Bank estimates of future inflation dated 2/12/05
E
Relative Currency Risk = (1+ Total Risk Premium)/(1+ Sovereign Risk)-1
F
Total Risk Premium = (1+ Sovereign Yield in LC)/(1+ US Treasury Yield)-1
G
Total Risk Premium = (1+ Sovereign Risk)*(1+ Relative Currency Risk) - 1
B
19
THE WACC USER'S GUIDE
BIBLIOGRAPHY
Bruner, Eades, Harris and Higgins. “Best Practices in Estimating the Cost of Capital:
Survey and Synthesis.” Financial Practice and Education. Spring/Summer 1998
Copeland, T.E. and J. Weston. Financial Theory and Corporate Policy. 3rd Edition
Cooper, Ian and Evi Kaplanis. "Home Bias in Equity Portfolios and the Cost of Capital
for Multinational Firms.” Journal of Applied Corporate Finance, Volume 8 Number 3.
Fall 1995
Damodaran, Aswath, Investment Valuation. John Wiley & Sons, Inc., 1996.
Ibbotson, Roger G., and Peng Chen. “Long-Run Stock Returns: Participating in the
Real Economy.” Financial Analysts Journal, 59, 88-98.
Logue, Dennis E. "When Theory Fails: Globalization as a Response to the (Hostile)
Market for Foreign Exchange." Journal of Applied Corporate Finance, Volume 8
Number 3. Fall 1995
Mayfield, E. Scott. “Estimating the Market Risk Premium.” Journal of Financial
Economics. Volume 73, Issue 3, September 2004
Pettit, Justin. “Corporate Capital Costs: A Practitioners Guide.” Journal of Applied
Corporate Finance, Volume 12 Number 1. Spring 1999
Pettit, Justin, Mack Ferguson and Robert Gluck. “A Method for Estimating Global
Corporate Capital Costs: The Case of Bestfoods.” The Journal of Applied Corporate
Finance, Volume 12 Number 3. Fall 1999
Shapiro, Alan C. Modern Corporate Finance. 1990
Siegel, Jeremy J. “The Shrinking Equity Premium.” Journal of Portfolio Management,
Fall 1999, 26, 1.
Stulz, Rene. "Globalization, Corporate Finance, and the Cost of Capital.” Journal of
Applied Corporate Finance, Vol. 12 No. 3. Fall 1999
Stulz, Rene M. "Globalization of Capital Markets and the Cost of Capital: The Case
of Nestle." Journal of Applied Corporate Finance, Volume 8 Number 3. Fall 1995
Weber, Steven. “The End of the Business Cycle.” Foreign Affairs, Volume 76 Number 4.
July/August 1997
20
THE WACC USER'S GUIDE
LIST OF TABLES
TABLE 1 – COST OF CAPITAL BY INDUSTRY
TABLE 2 – SEGMENT BETA REGRESSION ILLUSTRATION
TABLE 3 – MULTIVARIATE REGRESSION BETA ILLUSTRATION
TABLE 4 – EXPECTED VALUE TAX SHIELD ESTIMATION
TABLE 5 – ANATOMY OF A CONVERTIBLE ILLUSTRATION
TABLE 6 - WEIGHTED AVERAGE COST OF A CONVERTIBLE
TABLE 7 – SOVEREIGN RISK
TABLE 8 – GLOBAL COSTS OF CAPITAL
1
7
8
9
10
10
16
17
LIST OF FIGURES
FIGURE 1 – CONVERGING VOLATILITIES – STOCKS AND THE LONG BOND
FIGURE 2– DECLINING MARKET RISK PREMIUM
FIGURE 3 – MARKET RISK PREMIUM DEPENDS ON HOW MUCH HISTORY
FIGURE 4– MARKET-IMPLIED RISK PREMIUM ESTIMATES
FIGURE 5 – SUSTAINABLE GROWTH ESTIMATES
FIGURE 6 – BETA REGRESSION ILLUSTRATION
FIGURE 7 – CONSTRUCTED BETA ILLUSTRATION
FIGURE 8 - HISTORICAL 10-YEAR TREASURY RATES VS. FORWARD RATES
FIGURE 9 – THE COSTS OF DEBT
FIGURE 10 – MNC PORTFOLIO ILLUSTRATION
FIGURE 11 – COST OF CAPITAL REFLECTS SYSTEMATIC RISKS
FIGURE 12– SOVEREIGN RISK PREMIUM SIMULATION
2
4
4
5
5
6
7
8
9
12
13
17
STRATEGIC ADVISORY GROUP PUBLICATIONS
The WACC User's Guide, March 2005
Rethinking Capital Strategy, February 2005
Strategic Decapitalisation: Does Excess Cash Matter? February 2005
Where M&A Pays: Who Wins & How? December 2004
The New World of Credit Ratings, September 2004
Positioning for Growth: Carve-Outs & Spin-Offs, April 2004
How to Find Your Economic Profits, January 2004
FX Strategy Revisited, October 2003
Renewing Growth: M&A Fact & Fallacy, June 2003
The Shareholder Distributions Handbook, May 2003
Financial Strategy for a Deflationary Era, March 2003
21
THE WACC USER'S GUIDE
UBS AG
299 Park Avenue
New York, NY 10171-0026
Tel: +1-212-821-3000
www.ubs.com
UBS Securities LLC is a subsidiary of UBS AG
UBS Investment Bank is a business group of UBS AG
This material has been prepared by UBS AG, or an affiliate thereof ("UBS"). In certain countries UBS AG is referred to as UBS SA. This material is
an investment banking communication and should not be viewed as research.
This material is for distribution only under such circumstances as may be permitted by applicable law. It has no regard to the specific investment
objectives, financial situation or particular needs of any recipient. It is published solely for informational purposes and is not to be construed as a
solicitation or an offer to buy or sell any securities or related financial instruments. No representation or warranty, either express or implied, is
provided in relation to the accuracy, completeness or reliability of the information contained herein, nor is it intended to be a complete statement
or summary of the securities, markets or developments referred to in the materials. It should not be regarded by recipients as a substitute for the
exercise of their own judgment. Any opinions expressed in this material are subject to change without notice and may differ or be contrary to
opinions expressed by other business areas or groups of UBS as a result of using different assumptions and criteria. UBS is under no obligation to
update or keep current the information contained herein. UBS, its directors, officers and employees' or clients may have or have had interests or
long or short positions in the securities or other financial instruments referred to herein and may at any time make purchases and/or sales in them
as principal or agent. UBS may act or have acted as market maker in the securities or other financial instruments discussed in this material.
Furthermore, UBS may have or have had a relationship with or may provide or has provided investment banking, capital markets and/or other
financial services to the relevant companies. Neither UBS nor any of its affiliates, nor any of UBS' or any of its affiliates, directors, employees or
agents accepts any liability for any loss or damage arising out of the use of all or any part of this material.
Options, derivative products and futures are not suitable for all investors, and trading in these instruments is considered risky. Past performance is
not necessarily indicative of future results. Foreign currency rates of exchange may adversely affect the value, price or income of any security or
related instrument mentioned in this presentation. Prior to entering into a transaction you should consult with your own legal, regulatory, tax,
financial and accounting advisers to the extent you deem necessary to make your own investment, hedging and trading decisions. Any transaction
between you and UBS will be subject to the detailed provisions of the term sheet, confirmation or electronic matching systems relating to that
transaction. Clients wishing to effect transactions should contact their local sales representative. Additional information will be made available
upon request.
United Kingdom and rest of Europe: Except as otherwise specified herein, this material is communicated by UBS Limited, a subsidiary of UBS
AG, to persons who are market counterparties or intermediate customers (as detailed in the FSA Rules) and is only available to such persons. The
information contained herein does not apply to, and should not be relied upon by, private customers. Switzerland: These materials are distributed
in Switzerland by UBS AG to persons who are institutional investors only. Italy: Should persons receiving this materials in Italy require additional
information or wish to effect transactions in the relevant securities, they should contact Giubergia UBS SIM SpA, an associate of UBS SA, in Milan.
United States: These materials are distributed by UBS Securities LLC or UBS Financial Services Inc., subsidiaries of UBS AG, or solely to US
institutional investors by UBS AG or a subsidiary or affiliate thereof that is not registered as a US broker-dealer (a "non-US affiliate"). Transactions
resulting from materials distributed by a non-US affiliate must be effected through UBS Securities LLC or UBS Financial Services Inc. Canada: These
materials are being distributed in Canada by UBS Securities Canada Inc., a subsidiary of UBS AG and a member of the principal Canadian stock
exchanges & CIPF. Hong Kong: The materials relating to equities, corporate finance and other securities business, and related research, are being
distributed in Hong Kong by UBS Securities Asia Limited. The material relating to foreign exchange, fixed income products and other banking
business, and related research, are being distributed in Hong Kong by UBS AG, Hong Kong Branch. Singapore: These materials are distributed in
Singapore by UBS Securities Singapore Pte. Ltd or UBS AG, Singapore Branch. Japan: The materials relating to equities, fixed income products,
corporate finance and other securities business, and related research, are distributed in Japan by UBS Securities Japan Ltd. The materials relating to
foreign exchange and other banking business, and related research, are distributed in Japan by UBS AG, Tokyo Branch. Australia: These materials
are distributed in Australia by UBS Capital Markets Australia Ltd and UBS Securities Australia Ltd, licensed securities dealers. New Zealand: These
materials are distributed in New Zealand by UBS New Zealand Ltd.
 2005 UBS. All rights reserved. UBS specifically prohibits the redistribution of this material and accepts no liability whatsoever for the actions of
third parties in this respect.
View publication stats