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Cross-border DCF valuation in a nutshell
Andreas Schueler*
The papers deals with cross-border DCF valuation. It focusses on key choices the valuator has to make:
should the foreign currency (FC) or the home currency (HC) approach be used? How should a valuator deal
with the covariance between cash flows and exchange rates? In doing so, the paper addresses inter alia
the prerequisites and consequences of using forward exchange rates, reveals a tax effect on repayments,
and questions the use of constant discount rates.
1. Introduction
It is common knowledge that flexible exchange rates
vary over time. It is also clear that conducting business
abroad is relevant for many firms. As shown in Table
1, there are a large number of household names in the
corporate world which engage in significant business.
Table 1. Relevance of business abroad; Transnationality Index (TNI): average of foreign assets/tot. assets, foreign sales/tot.
sales and foreign employment/tot. employment; 2019; Source: UNCTAD: United Nations Conference on Trade and Develop-
ment, https://unctad.org/node/29280
Corporation Home
economy
Assets ($MM) Sales ($MM) Employment TNI
in %
Foreign Total Foreign Total Foreign Total
Royal Dutch
Shell plc
UK 376 417 402 681 276 518 331 684 59 000 83 000 82.6
Toyota Motor
Corporation
Japan 307 538 485 422 187 768 275 390 227 787 359 542 65.0
BP plc UK 259 860 295 194 215 203 278 397 58 900 72 500 82.2
Softbank Group
Corp
Japan 253 163 343 306 29 286 56 910 55 272 74 953 66.3
Total SA France 249 678 273 865 137 438 175 985 71 456 107 776 78.5
Volkswagen
Group
Germany 243 469 548 271 227 940 282 776 374 000 671 000 60.3
Anheuser-Busch
InBev NV
Belgium 192 138 237 142 44 352 52 251 148 111 171 915 84.0
British American
Tobacco PLC
UK 184 959 186 194 25 232 32 998 31 196 53 185 78.2
Daimler AG Germany 179 506 339 742 163 875 193 357 124 842 298 655 59.8
Chevron
Corporation
USA 172 830 237 428 75 591 140 156 22 800 48 200 58.0
Exxon Mobil
Corporation
USA 169 719 362 597 123 801 255 583 35 058 74 900 47.4
Vodafone Group
Plc
UK 168 394 184 253 42 530 49 971 58 429 68 724 87.2
EDF SA France 155 021 340 692 30 625 79 827 34 381 165 790 34.9
CK Hutchison
Holdings Ltd
Hong Kong,
China
143 367 155 523 32 556 38 163 279 000 300 000 90.2
Honda Motor
Co Ltd
Japan 143 180 188 541 116 150 137 382 153 215 219 722 76.7
* Professor of Finance, Universitaet der Bundeswehr Muenchen,
Germany.
Business Valuation OIV Journal Spring 2021 3
Cross-border DCF valuation in a nutshell
n
Volume 3 - Issue 1
Companies with business abroad, or more generally,
cash flows denominated in foreign currency (FC) must
be valued occasionally or on a regular basis due to - for
example - M&A-activities, taxation, transfer pricing,
impairment tests, or restructuring.
Cross-border valuation of companies has been ana-
lyzed extensively - for example - regarding the ex-
pected rate of returns for shareholders (cost of equity),
and a number of textbooks address cross-border valua-
tion: Bekaert and Hodrick (2018), Chapters 15 & 16,
Berk and DeMarzo (2020), Chapter 31, Brealey et al.
(2019), Chapter 27, Holthausen and Zmijewski
(2020), Chapter 17, and Koller et al. (2020), Chapter
27. However, when it comes to be specific and com-
prehensive on how to link the literature on company
valuation with that on macroeconomics in order to
come up a with a DCF framework that works for
cross-border valuation, the literature thins out consid-
erably (see Schueler 2021 for a more extensive litera-
ture review).
This paper will provide an overview of the key con-
siderations or inputs in cross-border valuation.
1
I
would like to point out some conceptual choices faced
by the valuator (Section 2), and present some recom-
mendations regarding the DCF framework using two
numerical examples (Section 3). Section 4 concludes.
2. Conceptual choices
I am assuming a two-country-setting, relevant cur-
rencies are the home (domestic) currency (HC) and
the foreign currency (FC). Direct quotation is used, i.e.
the price for one unit of FC is quoted in HC. The
valuation is done from the perspective of a domestic
investor, and company value is to be denominated in
HC. Risk is priced according to the global CAPM.
This requires the relative purchase price parity to hold
(see Koller et al. 2020, p. 514, Bekaert and Hodrick
2018, p. 569, Stulz 1995, p. 12). Covered interest
parity and the international Fisher hypothesis are as-
sumed to hold as well. Domestic and foreign corporate
income is subject to a constant and identical corporate
tax rate. Neither personal income taxes nor barriers to
repatriation of cash flows are considered here.
First, the valuator must choose between the FC ap-
proach and the HC approach. Applying the former
require cash flows in FC to be discounted by the
risk-adjusted discount rate (RADR) in FC. The result-
ing company value in FC (V
FC
) is then to be con-
verted into HC by the spot exchange rate at the va-
luation date (S
0
) to get to the company value in HC
(V
HC
). The latter requires the cash flows in FC to be
converted into HC by the expected spot exchange
rates before they are discounted by the RADR in
HC, leading to the company value in HC at the va-
luation date.
The second and the third choice apply only to the
HC approach:
Secondly, the valuator must decide how to address
the covariance between the cash flows in FC and the
exchange rates. The amount and timing of cash flows
in FC depend on the foreign exchange rate on a reg-
ular basis. Just consider the case of an exporter in a
foreign country. If the valuator derives the RADR HC
from the RADR FC, the covariance of the RADR FC
and the exchange rates has to be taken into account as
well. These covariances do not occur if the FC ap-
proach is used and cash flows in FC are discounted
by RADR in FC. There are (at least) three options
for the HC approach: (a) neglect the covariance of the
cash flow with the exchange rates, justified by a delib-
erate estimate of its (negligible) relevance, and use the
RADR in HC; (b) neglect the covariances in both the
cash flows and the RADR which can be shown algeb-
raically, or (c) consider the covariance in the cash
flows while converting them into HC and use the
RADR in HC. The proof that (b) is indeed possible,
can be found in Schueler (2021). Please note that
option (b) requires the use of the RADR FC multi-
plied by the expected change in the exchange rate.
There is a fourth option (d): use forward exchange
rates as the certainty equivalent of the expected spot
exchange rates. Covariances are not relevant for (d),
too. Since (d) needs to be elaborated in greater detail,
I am covering it within the following discussion of the
third conceptual choice.
Third, the valuator must decide how to determine
future exchange rates for converting the cash flows in
FC into HC. Theory has taught us that for valuing
risky cash flows for risk averse investors we could use
either expected values or certainty equivalents. This
applies to exchange rates, too. We can use either ex-
pected exchange rates or forward exchange rates, be-
cause forward exchange rates are the certainty equiva-
lents of expected exchange rates. The choice affects
the RADR to be used. How can we determine ex-
pected exchange rates? As exchanging major curren-
cies is a multi-billion business, we should refrain from
guessing these rates nor accepting the guesses of others,
like managers, bankers, or analysts. The international
parity conditions provide a solution: the relative pur-
chasing power parity (rPPP) establishes the link be-
tween the expected inflation rates in both countries
1
It is based on a presentation by the author at the EACVA con-
ference on business valuation in March 2021, and another paper of the
author (Schueler 2021) that contains a more fundamental and tech-
nical discussion of the topic. The author wishes to thank the partici-
pants of the conference and especially the reviewers of Schueler
(2021).
4Business Valuation OIV Journal Spring 2021
Volume 3 - Issue 1
n
Cross-border DCF valuation in a nutshell
and the expected exchange rate. Therefore, if we could
obtain reliable estimates of the expected inflation rates
over the forecast horizon, we could derive the ex-
pected exchange rates. However, the expected infla-
tion rates might be difficult to find, particularly for a
long-term forecast horizon. The uncovered interest
parity (UIP) together with the unbiasedness hypoth-
esis (UH) establish a link between the risk-free interest
rates in both countries and the forward exchange rates
that are set equal to the expected forward exchange
rates. There exists intense discussion about whether we
can assume the UIP to be valid. We cannot answer
that question here. I would rather point out that we
could either use the forward exchange rate as a starting
point to estimate the expected exchange rate by add-
ing a risk premium, because the certainty equivalent
plus the risk premium equals the expected value in
general. Then, one needs to come up with an estimate
of the risk premium, if it is not negligible. Or, one
could treat the forward exchange rates as certainty
equivalents. Then, the appropriate discount rate is
the RADR in FC multiplied by the ratio of the risk-
free interest rates in both countries (1 added to each of
both).
To summarize, the use of forward exchange rates can
be justified in several ways. The valuator must make
clear which reasoning applies to the valuation at hand
because this affects the definition of the RADR to be
used. In this context, a table shown in Ruiz de Vargas
(2018) is helpful, since it illustrates that data on for-
ward exchange rates is readily available (Table 2).
3. DCF framework
There are some requirements for implementing
cross-border DCF valuation by one of the three major
variants of DCF (Adjusted Present Value APV, Flow-
to-equity FtE, WACC). Due to the necessity to ex-
change cash flows in FC into HC and to define the
RADR accordingly, especially the HC approach is af-
fected by them.
For both FC and HC approach it should be noted
that tax effects due to debt financing not only consist
of the well-known tax shield on interest expenses gener-
ated by subtracting interest expenses from taxable in-
come, but also, a tax effect related to the repayment
(RP) of debt that must be considered as well if a do-
mestic company is using debt denominated in FC.
Depending upon the development of the exchange
rate between the point of time the debt was received
(period s) and it has to be repaid (period t), taxable
income might be reduced if the repayment of FC-debt
Table 2. Data on forward exchange rates; CCY - currency; ECB - European Central Bank; B - Bloomberg, spot rate; C -
Bloomberg, contributed or cross-calculation; IN - Bloomberg, interpolated; CIP - Bloomberg, calc. through covered interest
parity ; D - Datastream; CIP stands for covered interest parity, i. e. forward exchange rates calculated by multiplying the
current spot exchange rate by the ratio of the risk-free interest rates in both countries (1 added to each of both); Ruiz de
Vargas (2018)
CCY Spot
rate
Forward exchange rates
6M 1Y 2Y 3Y 4Y 5Y 6Y 7Y 8Y 9Y 10Y 15Y 20Y 25Y 30Y
AUD ECB/B/D C,D C,D C,D C C C,D CIP CIP CIP CIP CIP CIP CIP CIP CIP
DKK ECB/B/D C,D C,D C,D C C C,D CIP CIP CIP CIP CIP CIP CIP CIP CIP
HKD ECB/B/D C,D CIP, D CIP, D CIP CIP CIP, D CIP CIP CIP CIP CIP CIP CIP CIP CIP
ILS ECB/B/D C,D C,D C,D CIP CIP CIP CIP CIP CIP CIP CIP CIP CIP CIP CIP
JPY ECB/B/D C,D C,D C,D C C C,D CIP CIP CIP CIP CIP CIP CIP CIP CIP
CAD ECB/B/D C,D C,D C,D C C C,D CIP CIP CIP CIP CIP CIP CIP CIP CIP
NZD ECB/B/D C,D C,D C,D C C C,D CIP CIP CIP CIP CIP CIP CIP CIP CIP
NOK ECB/B/D C,D C,D C,D C C C,D CIP CIP CIP CIP CIP CIP CIP CIP CIP
SEK ECB/B/D C,D C,D C,D C C C,D CIP CIP CIP CIP CIP CIP CIP CIP CIP
CHF ECB/B/D C,D C,D C,D C C C,D IN IN IN IN C CIP CIP CIP CIP
SGD ECB/B/D C,D C,D C,D CIP CIP CIP CIP CIP CIP CIP CIP CIP CIP CIP CIP
GBP ECB/B/D C,D C,D C,D C C C,D CIP CIP CIP CIP CIP CIP CIP CIP CIP
USD ECB/B/D C,D C,D C,D C,D C,D C,D CCCCCCIPCIPCIPCIP
CNY ECB/B/D C,D C,D C,D IN IN C,D CIP CIP CIP CIP CIP CIP CIP CIP CIP
INR ECB/B/D C,D C,D C,D CIP CIP CIP CIP CIP CIP CIP CIP CIP CIP CIP CIP
RUB ECB/B/D C,D C,D CIP,D CIP CIP CIP,D CIP CIP CIP CIP CIP CIP CIP CIP CIP
Business Valuation OIV Journal Spring 2021 5
Cross-border DCF valuation in a nutshell
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Volume 3 - Issue 1
converted into HC exceeds the amount of initial debt
financing in HC, or taxable income might be in-
creased if the repayment in HC is lower than the in-
itial amount of debt in HC. Calculating this tax shield
on repayments starts with the HC approach, but also
needs to be considered for the FC approach. It might
look a bit awkward to first compute the effect by con-
verting debt-related cash flows originally denominated
in FC into HC and then back to FC. But it is neces-
sary, because the cash impact of that tax shield would
be overlooked in the FC approach otherwise. Table 3
shows an example for a domestic company that uses
debt denominated in foreign currency. We assume that
the domestic tax regime requires the currency effects of
repayments to be considered in the taxable income.
For this example, we assume a decreasing expected
HC/FC-exchange rate. This leads to negative tax
shields on repayments that results in negative total
tax shields. The sum of the repayments in HC (72)
is smaller than the debt in t=0 denominated in HC
(85.5), representing the cumulated (13.5) effects on
taxable income.
If the HC approach is to be applied, the RADR must
fit to the decision of the valuator about how to convert
the cash flows in FC into HC, as we discussed in sec-
tion 2. For the sake of simplification, I am only focus-
ing on the case that cash flows are converted by for-
ward exchange rates here, treating them as certainty
equivalents. Thus, we neither assume exchange risk
premia to be negligible nor the UIP to hold. In this
case, the RADR to be used, labelled RADR*, is the
RADR in FC adjusted by the risk-free interest rates i
(plus 1) of both countries:
Table 4 illustrates this for a simple valuation of an
unlevered company, i. e. a company that is financed by
equity only.
Table 3. Tax shields on debt denominated in FC employed by a domestic company; corporate tax rate 30%
Year (t) 0123Sum
Exchange rate (HC/FC) HC/FC 0.95 0.90 0.80 0.70
Exchange rate in t vs. 0.95 HC/FC 0.05 0.15 0.25
Debt FC 90.00 60.00 30.00 0.00
HC 85.50 54.00 24.00 0.00
Interest (4 %) FC 3.60 2.40 1.20 7.20
HC 3.24 1.92 0.84 6.00
Tax shield on interest expenses HC 0.97 0.58 0.25 1.80
Repayments FC 30.00 30.00 30.00 90.00
HC 27.00 24.00 21.00 72.00
Applied to repayment = increase in taxable income HC 1.50 4.50 7.50 13.50
Tax shields on repayments HC -0.45 -1.35 -2.25 -4.05
Total tax shields HC 0.52 -0.77 -2.00 -2.25
Table 4. FC approach and HC approach for valuing an unlevered company with a lifespan of 3 years using forward fx rates and
RADR*; constant yield curves in both countries (i
FC
= 1%; i
HC
= 2%)
Year (t) 0 1 2 3
FC approach
FCF FC 100.00 110.00 120.00
RADR FC 7.0%
Value FC 287.49
Spot fx rate HC/FC 0.95
Value HC 273.1
6Business Valuation OIV Journal Spring 2021
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Cross-border DCF valuation in a nutshell
This simple example illustrates that even if the HC
approach is used, the RADR has to be adjusted starting
from the RADR in FC. One could argue that the
valuator should simply stick with the FC approach. If
a RADR in HC is derived first (or top-down), one has
to keep in mind that it implies a premium for ex-
change rate risk and might not be applied to cash flows
converted by forward exchange rates in every case.
Rather, it requires the exchange rate risk premium to
be negligible or the UIP to hold.
The example is also simple in that regard that we
assume the risk-free rates in both countries to be con-
stant over time. If they were not, the risk-free rates
used for deriving the RADR in both countries would
need to be based upon forward interest rates. Other-
wise, the reconciliation between FC and HC approach
would be impossible. The reason for that being that
the forward exchange rate Ffor periods t > 0 depend
upon the forward interest rates (S
0
being the current
spot exchange rate):
Finally, the example is simplified, because the com-
pany is assumed to have a life-span of only 3 years. In
practice, companies are assumed to exist forever, unless
we know that their lifespan is limited. Therefore, I
would like to point out that the growth rate to be used
for deriving the terminal value needs to be derived
while keeping the change of the exchange rate in
mind. If forward exchange rates are used to convert
the cash flows in FC into HC, for example, we could
split up the growth rate gto be applied to the con-
verted cash flows (HC approach) as follows:
If a levered company is to be valued the relation
shown in (1) can be applied to the RADR needed
for the DCF variant chosen. For the WACC (FCF)
approach, the WACC in FC has to be adjusted ac-
cordingly. For the FTE approach, the levered cost of
equity has to be adjusted. The principle remains the
same. Unfortunately, things can quickly become com-
plicated, because the financial risk, the risk of default
and the risk of the tax effects induced by debt finan-
cing. All three would need to be addressed properly.
These issues are discussed in Schueler (2021), but are
beyond the scope of this paper.
4. Conclusions
We categorize our conclusions into those related to
the valuation method, those related to the cash flow to
be discounted, and those related to the RADR:
Valuation method
FC or HC approach: in general, the FC approach
avoids most of the challenges imposed by exchange
rates, since the exchange rate is only relevant for
converting the present value in FC into HC by
using the observable current spot exchange rate.
Covariances need not be addressed, and future ex-
change rates need not be estimated. However, there
might be valuation cases for which the discount rate
(RADR) in FC is not easily derived. Otherwise, it
might be easier in practice to convert a stream of
cash flows in FC or sporadic FC-cash flows into HC,
thereby following the HC approach, and integrate it
in the overall cash flow forecast for the cash gener-
ating unit, business unit or company. Another prac-
tical example for which the HC approach might be
easier, is a domestic company that uses debt finan-
cing in FC. As previously mentioned, this also en-
ables the valuator to address the tax shields on re-
payments caused by changes in the exchange rate in
a more straightforward manner.
Choice between different DCF variants: the popu-
larity of the WACC approach, also referred to as
FCF approach, stems from the possibility to use
constant cost of capital (WACC) if the leverage
ratio (capital structure) can be assumed to be con-
stant. For a cross-border valuation, the need to use
forward interest rates to establish consistency be-
tween FC and HC approach, and the tax shields
on repayments question the robustness of this as-
HC approach
Forward fx rate HC/FC 0.9407 0.9315 0.9223
FCF HC 94.07 102.46 110.68
RADR =
RADR
FC
x (1+i
HC
)/(1+i
FC
) 5.95%
Value HC 273.1
Business Valuation OIV Journal Spring 2021 7
Cross-border DCF valuation in a nutshell
n
Volume 3 - Issue 1
sumption even for the FC approach. The valuator
should consider to follow the APV approach.
Cash flow forecast
Additional tax effect: the repayment of debt in
foreign currency used by a domestic firm can lead
to a tax effect in addition to the well-known tax
shields on interest expenses. This tax shield on
repayments occurs, if the exchange rate has chan-
ged between the period the debt financing has
been received and the period a repayment occurs.
Covariances: if cash flows in FC are correlated
with exchange rates, the covariance between these
variables needs to be considered. If it can be as-
sumed to be small, it might not be of relevance for
the valuation result and could be neglected. Other
than that, there is the possibility to skip it and to
use a RADR also without considering the covar-
iance, or to use forward exchange rates.
Future exchange rates: this problem arises for the
HC approach. Forward exchange rates are an im-
portant point of reference for estimating future ex-
change rates. They can be interpreted in general as
the certainty equivalent of the unknown future ex-
change rates. Therefore, they could be treated as
certainty equivalents directly, or an exchange risk
premium could be added to them resulting in the
expected exchange rates. If one assumes the UIP to
hold or the exchange risk premium to be neglect-
able, forward exchange rates serve as a direct proxy
for the expected exchange rate. Another possibility
to estimate the expected exchange rate is com-
pound the current spot exchange rate by the ratio
of the expected inflation rates (1 added to each of
them). Although that sounds tempting and is in
line with the relative purchase power parity, practi-
tioners might encounter difficulties in coming up
with mid and long-term estimates of the yearly ex-
pected inflation rates in both countries.
Growth rate for the terminal value: for the HC
approach, the rate of change in exchange rates
has to be considered besides the growth in FC-cash
flows. If forward exchange rates are used, the latter
rate of change is determined by the ratio of one
plus the risk-free rates. The valuator should first
estimate the growth in FC-cash flows and then
consider how to address the change in exchange
rates for the terminal value.
RADR
Risk-free rate: the use of yearly forward interest rates
is necessary to ensure the equivalence between the
HC and the FC approach. Valuators should not use
a ‘‘one size fits all’’ constant risk-free rate.
RADR depend upon the way to estimate future
exchange rates within the HC approach: if the
valuator is able to determine expected spot rates,
the RADR in HC has to contain a premium for
exchange rate risk. If forward exchange rates are
used, the ‘‘regular’’ RADR in HC can be used only,
if the exchange rate risk premium is assumed to be
negligible or the UIP is assumed to hold. If forward
exchange rates serve as certainty equivalents, the
RADR in FC adjusted by the ratio of interest rates
(1 added to each of them) is to be used.
Interpretation of RADR empirically derived for
the company or the peer group: if the RADR in
HC is estimated empirically without any risk ad-
justments, it contains inter alia a premium for the
exchange rate risk implicitly. The same is true
analogously, if the RADR for the firm to be valued
is derived by referring to the beta values for com-
parable companies (peer group). These beta values
contain premia for the exchange rate risk from the
perspective of each peer company. The valuator
should keep this in mind while implicitly applying
these risk premia to the company to be valued.
Although the paper provides only an overview about
cross-border valuation, it might be helpful in increas-
ing the awareness regarding the choices, challenges
and pitfalls for valuation practitioners.
5. References
Bekaert G, Hodrick R (2018): International finan-
cial management, 3rd edn. Cambridge University
Press, Cambridge.
Berk J, DeMarzo P (2020): Corporate Finance, 5th
edn. Pearson Education Limited, Harlow.
Brealey RA, Myers SC, Allen F (2019): Principles of
Corporate Finance, 13th edn. McGraw-Hill, New York.
Drukarczyk J, Schu¨ler A (2021): Unternehmensbe-
wertung, 8th edn. Vahlen, Mu¨nchen.
Holthausen RW, Zmijewski ME (2020): Corporate
Valuation: Theory, Evidence & Practice, 2nd edn.
Cambridge Business Publishers, Cambridge.
Koller T, Goedhart M, Wessels D (2020): Valuation:
Measuring and Managing the Value of Companies, 7th
edn. Wiley, New Jersey.
Ruiz de Vargas S (2018): Prognosemethoden fu¨r
marktdeterminierte Wechselkurse bei rechtlich gepra
¨g-
ten Unternehmensbewertungen. BWP 2/2018: 34-49.
Schueler A (2021): Cross-border DCF valuation:
discounting cash flows in foreign currency. Journal of
Business Economics 91:617-654.
Sercu P (2009): International Finance: Theory into
Practice. Princeton University Press, Princeton.
Stulz RM (1995): The cost of capital in internation-
ally integrated markets: The case of Nestle
´. Europ Fi-
nanc Manag 1:11-22.
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