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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

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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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Cross-border DCF valuation in a nutshell