Traditional Approach to the Cost of capital for domestic
The cost of capital or discount rate for a project can be reckoned as:
The minimum return required to induce an investor to invest in a certain
project (the return approach).
The cost paid by a corporation to obtain funds for investing in a certain
project (the cost approach).
The two approaches are conceptually the same, but in practice it might
sometimes be easier to use or the other.
According to the CAPM, the required rate of return on an asset is given
E(Ri) = Riskfree rate + bi(Market
where bi= beta of asset i, a measure
of its non-diversifiable risk -- this beta for domestic projects would,
normally be measured with respect to a domestic equity index, such as
the S&P 500 Index or the NYSE Index;
the market risk premium is the premium required by investors over and
above the risk-free rate, to hold the market portfolio.
In principle, the CAPM applies to all assets, but in practice, it is
used to estimate the cost of equity. It is rarely used to estimate the
cost of debt because it is very difficult to estimate a beta for debt
securities. In practice, the yield-to-maturity is used instead of the
required rate of return, for debt securities. Where the bond is not traded,
and hence no implied yield-to-maturity can be computed, firm-specific
variables, such as interest-coverage ratios are used to generate synthetic
bond ratings. Historical relationships between bond-ratings and bond spreads
over Treasuries are then used to come to an estimate of the bond's yield-to-maturity.
WACC: If the financial structure and risk of a project is the same as
that of the entire firm, then the appropriate discount rate or hurdle
rate for a project is the Weighted Average Cost of Capital (WACC):
WACC = (1-L)ke + (L)kd(1-t)
L = the firm’s target debt-to-assets ratio (debt ratio)
kd = before-tax cost of debt (in principle, the required rate
of return on the firm's debt)
ke = cost of equity (in principle, the required rate of return
on the firm's equity)
t = marginal tax rate of the firm
If the risk of a project is different, then it should be evaluated using
its own beta, and its own target debt-to-assets ratio, etc.
Traditional Approach to computing WACC for foreign projects:
There are several approaches that can be taken. If the project is a foreign
project, and the firm's equity investors are essentially holding a US
portfolio, then the beta should be computed for the new project with respect
to the US equity index (market portfolio) and the required rate of return
should be computed in the same way as above.
If the "US" firm's investors are really holding a globally
diversified portfolio, or if they are not restricted to the US (and hence,
once again, they hold globally diversified portfolios), then it makes
sense to compute an equity cost of capital for them by using the global
CAPM, i.e. computing the beta for the new project using the global "market"
portfolio (and a global risk premium).
Cost Differential between domestic projects and foreign projects:
Suppose a foreign subsidiary requires $I of new financing for a project
as follows: $P from the parent, $Ef from the subsidiary’s
retained earnings, $Df from foreign debt. Then, how do we compute
the WACC? Well, there should be no difference if there are no differences
in financing costs for the subsidiary versus the parent. However, suppose
the cost of retained earnings for the subsidiary is ks versus
the general cost of equity for the parent, ke, and that the
cost of debt financing after-tax for the subsidiary is if versus
the after-tax cost of debt for the parent of id(1-t), then
the total cost of financing the project in dollars is:
IkI = Iko - Ef (ke - ks)
- Df[id(1-t) - if]
Reworking this equation, we find that the WACC for the new project,
kI = ko - a (ke - ks) - b[id(1-t)
ko= cost of capital of the parent
ks = cost of retained earnings for the subsidiary
if = the after-tax cost of foreign debt
a = Ef/I
b = Df/I
Note: The question of how much of the projects funding should be raised
domestically and how much locally (i.e. abroad) itself requires to be
determined in conjunction with relative costs of financing here and abroad
-- this issue is not considered in this section.
Approximations to the Traditional Approach:
If we assume that the multinational in question is a US multinational
with investors who are globally diversified, then, in principle, the beta
of the foreign subsidiary should be estimated with respect to a global
market portfolio, and a global market risk premium should be used.
Furthermore, if cashflows are measured in dollars, the right risk-free
rate to be used is also the US Treasury rate.
However, in practice, US investors may not be globally diversified; still
it may be easier to obtain US data than global data. Consequently, US
MNEs often evaluate projects from the viewpoint of a US investor, who
is not diversified internationally. The following issues are relevant.
First of all, if the project is not similar to the existing firm,
it should be evaluted on its own terms. Computing betas, etc. for a project
without any history can be very difficult; hence we first look for a proxy
company. Since we want a proxy as similar as possible to the project in
question, it makes sense that we use a local company.
If foreign proxies in the same industry are not available (say because
of data issues), then a proxy industry in the local market can be used,
whose beta can be expected to be similar to the beta of the project’s
Alternatively, we can compute the beta for a proxy US industry and multiply
it by the unlevered beta of the foreign country, relative to the US. This
will be valid, if:
- The US beta for the industry is the same as that of that industry
in the foreign market as well, and
- The only correlation, with the US market, of a foreign company in
the project’s industry is through its correlation with the local
market and the local market’s correlation with the US market.
The Relevant Base Portfolio
Although, in principle, it may be appropriate to use a global market
portfolio, in practice, we use the US market portfolio, for several reasons:
- the small amount of international diversification of US investor
- since US projects are evaluated using a US base portfolio, use of
a US base portfolio means that foreign projects can be easily compared
to a US project.
The Relevant Market Risk Premium
Again, in principle, one would want the global risk premium. However,
if the base portfolio used is a US one, then the market risk premium,
too, should be based on the US market.
As before, US markets have much more historical data available, and it
is a lot easier to estimate forward-looking risk premiums for the US market.
Furthermore, a recent study (Koedijk, Kees G. and Mathijs A. van Dijk,
“Global Risk Factors and the Cost of Capital,” FAJ, p. 32ff.,
v. 60, no. 2, March/April 2004) has shown that a cost of capital estimated
using a domestic CAPM model is insignificantly different from a cost of
capital computed using global risk factors.
Summary of the Traditional Approach:
- Find a proxy firm/portfolio in the country in which the project will
- Calculate its beta relative to the US market (assuming that we're
talking about investors who hold domestic diversified portfolios; if
the investors are internationally diversified, compute the beta relative
to the world portfolio, as discussed above).
- Multiply this beta by the market risk premium for the US market to
get a project risk premium. (Again, if the beta is computed relative
to the world portfolio, the beta should be multiplied by the market
risk premium for the global market).
- Add this risk premium to the long-term US nominal risk-free rate
to obtain a dollar cost of equity capital. (If we're talking about investors
holding internationally diversified portfolios, add the world nominal
Systematic Risk of Foreign Projects:
Foreign projects in non-synchronous economies (i.e. economies that are
synchronized with world markets) should be less correlated with domestic
markets. As a result of this, it can turn out that LDCs have greater political
risk but offer higher probability of diversification benefits, even though
this sounds paradoxical. Where there are barriers to international portfolio
diversification, corporate international diversification can be beneficial
to shareholders, contradicting the general Modigliani-Miller theorem that
argues that capital structure is irrelevant because investors can diversify
on their own. Hence this should be taken into account in the computation
of cost of capital for projects, and will be reflected in such a project's
However, Campbell Harvey argues that it is not enough to look at a country's
or a foreign project's beta, because this only deals with contribution
to volatility. Whereas skewness may be ignored if we're talking about
developed countries, when talking about emerging markets, it is not correct
to do so, because the impact of a project on the negative skewness of
the equityholder's portfolio could be significant! (View Campbell
Harvey's video exploring this issue.) For example, he says that India's
beta could be negative, but it would not be appropriate to discount Indian
projects at less than the US risk-free rate. As a result,
there are ad-hoc methods for adjusting the cost of capital for foreign
projects that often go beyond the CAPM in a conceptual or ad-hoc way.
Country Risk Premiums:
The traditional approach effectively ignores country risk premiums, assuming
that country risk is diversifiable. However, this may not be the case.
In fact, with globalization, cross-market correlations have increased,
leading to less diversifiability for country risk. Furthermore, as argued
above, vide Campbell Harvey, there may be skewness or catastrophic risk
to take into account. Strictly speaking then, considering that investors
do not like negative skewness (i.e. the likelihood of catastrophic negative
returns), we should augment the CAPM with a skewness term. Each project
should then have a co-skewness coefficient, i.e. the extent to which the
(negative) skewness of the portfolio would be increased by including that
project in the investor's (internationally diversified) portfolio. There
would also be a market skewness premium, and the co-skewness coefficient
for the project would be multiplied by the market skewness premium; the
result would then be added to the CAPM required cost of capital to get
a final cost of capital that takes the negative skewness risk of the project.
(Campbell, June 2000 JF.)
Campbell Harvey argues that this negative skewness risk could be quite
large for projects in emerging markets. Often, though, instead of taking
the (conceptually correct) approach described above -- viz. computing
a skewness premium, various ad hoc adjustments are used. In general, we
can use a larger country sovereign spread (explained below) to get a larger
cost of capital, or we can use a larger beta-like risk measure.
- Adding the sovereign yield spread for that country (the cost of debt
for that country's sovereign debt, denominated in US dollars -- or a
eurodollar rate for that country -- less the US riskfree rate) to the
global CAPM required rate of return. This is often called the Goldman
model, but other firms, such as Solomon, Smith Barney also use this.
This would give us
Reqd. Rate of return = US Riskfree rate + Sovereign yield spread
+ bi(Market Risk Premium), i.e.
Campbell Harvey doesn't like this approach because according to him,
this spread has to do with bond risk (and it doesn't even have to do
with corporate bond risk; hence it's not clear why we should be adding
this spread to a cost of equity.
Reqd. Rate of return = Risk free rate on sovereign debt of the country
in which the project is being undertaken + bi(Market
- Another approach (also attributed to Goldman Sachs) amplifies the
computed beta by using a volatility ratio, the ratio of std. devn. of
local equity returns to the std. devn. of world equity returns, instead
of using the computed beta.
- Another possibility is to use a weighted average of the historical
average return on equity in the foreign market and the CAPM rate.
- Yet another model uses a weighted average of the local CAPM and the
world CAPM. This model recognizes that the markets may not be entirely
integrated; hence it is appropriate to use a combination of the two.
The problem is to actually compute the weight to be applied to the two
CAPMs, especially since this would actually change over time.
- A final method is to compute an empirical relationship between an
S&P rating, or a Moody's rating or an ICRG rating or a Euromoney
rating -- something that is an ex-ante risk measure -- and the historical
average return for a security. Campbell (1995) found that the estimated
risk premium is similar whether the model is estimated for developed
countries or the developing countries (using the log of the risk rating
as an independent variable). This method can also be used even if the
country may not have a stock market, as long as we have a risk rating
for this company. This method can be used to compute a market risk premium
for all projects in a given country. We then compute a beta for the
project in question with respect to its local market. This is then used
to come up with the risk premium for the project as a whole.
What is interesting is that all these approaches seem to rely, in one
way or the other, on country risk premiums, which have to do with bond
risk. Even Campbell Harvey's approach using the empirical relationship
between an S&P or other rating and the equity return for the market
relies on bond ratings. The rationale underlying this is the comment made
earlier (attributed to Campbell Harvey's observation), viz. that the market
requires additional compensation for negative skewness risk. Bond returns
are clearly asymmetrically related to asset returns because they do not
share in upside risk. Hence, there must be a strong correlation between
measures of bond risk and skewness risk. This explains why Campbell Harvey
found stable relationships between local market returns and measures of
bond risk. This also justifies, to some extent, the seeming ad hoc approaches
of the investment banks that add the sovereign yield spread for the country
to the required rate return of return for projects in a given country
-- although the exact size of the adjustment, obviously, is incomplete.
Additional ways of estimating and using Country Premiums:
Country Premiums may be estimated by looking at the rating assigned to
a country’s sovereign debt.
One can then look at the spread over US Treasuries or a long-term eurodollar
rate for countries with such ratings. This spread would be a measure of
the country risk premium. One could also look at the spread for US firms’
debt with comparable ratings.
Optionally, one might then adjust this spread by the ratio of the standard
deviation of equity returns in that country to the standard deviation
of bond returns.
The country risk premium that is obtained can then be used in two ways:
- it could be added to the cost of equity of the project. This assumes
that the country risk premium applies fully to all projects in that
country (approach used by Goldman Sachs and some other investment banks).
This is equivalent to 1. above
- one could assume that the exposure of a project to the country risk
is proportional to its beta. In this case, one would add the country
risk premium to the US market risk premium to get an overall risk premium.
This would then be multiplied by the beta as before to obtain the project-specific
Finally, one could estimate a country risk premium based on the riskiness
of the country relative to a maturity market like the US, and to incorporate
this into the cost of equity of the project. This could be done by taking
the US market risk premium and multiplying it by the ratio of the volatility
of stock returns in the foreign country to the volatility of stock returns
in the US. This would be the country-risk adjusted market risk premium.
As before, then, this market risk premium would be multiplied by the beta
of the project to get the project-specific risk premium.